I’m moving!

Dear reader,

While I’m busy moving this site to a new place where I can give you a better overview of the content (and revisiting my reviews as I do) there’s no new update here.

If you’re daring, head over to the new place:

https://gammonrants.org/

Content there is growing fast, but so far it’s still only three reviews…

I’ll keep you updated once I’m more or less done.

How strong is that backgammon app? The big table

Update Sep 8,22: Backgammon KG added (PR 5.7 after 11 games)

Part of my app reviews is a solid test of the respective AI's playing strength. If the app supports it (and a good app should!) I play a couple of matches against it, export them to a file, and let Extreme Gammon 2 (PC) review our match on highest Roller++ level. This should give the reader a good understanding of the app's rating in "PR" (performance rating) points.

Apps that don't support export are harder to rate - I play something like a 3pt match on my iPad and transcribe it simultaneously into XG2, which is an exhausting process. Fortunately the apps that don't export are typically weak, so a rough rating is enough.

So, why not put them all together in a big table for you to compare? Here we go, (iOS) backgammon apps sorted from best to worst. 

 

 

 

Please note: this table is work in progress; I'll add new apps as time permits.

Please also note: it's difficult to rate the strongest apps; it might be unfair to rate a BGBlitz based app with XG2 only. I'm planning to compare the best 3 or so apps by analyzing a good number of matches with XG2, BGBlitz and GnuBG some day...

About the PR rating

PR ratings reflect how big an error on average you make per move, compared to the optimal move. The lower your PR, the better you're playing. XG uses the following names for the different PR ranges:

• 0,0 - 2,5 = World Champ 
  
• 2,5 - 5,0 = World Class  
  
• 5,0 - 7,5 = Expert 
• 7,5 - 12,5 = Advanced 
• 12,5 - 17,5 = Intermediate 
• 17,5 - 22,5 = Casual Player 
• 22,5 - 30,0 = Beginner 
• 30,0 and above = Distracted

The arguably strongest human backgammon player, Masayuki Mochizuki ("Mochy") has a PR of slightly above 2. Some sites call an average PR of less than 1.5 “superhuman”, which I’m also doing here.

The most embarassing extracts from the worst match I played in a long time

With the reasoning "if these positions were too difficult for me to find the right move they might also be interesting for you to see" I'm herewith showing you a couple of interesting positions from an embarassingly poor 5pt match I played against True Backgammon (iOS) on BGBlitz-2 (ie superhumanly strong) level.

Enjoy :-)

 

Blue to move 21

Things started out poorly in game 1, where I made my first 0.15 blunder in move 2 already. What should I have played here?

I wanted to play 13/11, staying out of direct hit range from his checker on the 4. So I entered on 24, playing BAR/24 13/11. 

Obviously, given that white has only a 1 point board, I should have played bold and hit on the 4, accepting the >50% risk (I counted 19/36 hitting numbers) of being hit for the chance of making the 4 point in the next roll. XG2 says the correct move is BAR/24 6/4*, followed by BAR/23, 6/5 (-0.074) and my AR/24 13/11 (-0.145)

Lesson to be learned: play very bold against a 1 point board.

The three difficulty levels of backgammon

Backgammon is not one game, but three games with increasing difficulty level.

LEVEL 1: matches to one point

You and your opponent roll the dice, move the checkers until one of you have won. It’s a tricky game already, with very different strategies to cover holding games, back games and such. If you master it well you’re ready for…

LEVEL 2: money games

Enters the doubling cube, maybe the most fiendish device created in any board game. Before every single move you must estimate whether you are more than 75% likely to win the game, and whether this assessment is likely to change next move.

I’m fairly good at level 1, regularly play on “advanced” level. But after years of backgammon my cube handling is still on “beginner” level. Sometimes I do well, sometimes I fail completely.

LEVEL 3: matches

Once you believe you have mastered the cube, proceed to level 3 and play matches. And all of a sudden, much changes. You play differently if you’re leading or if you’re far behind, and the cube’s value changes madly.

Yesterday (that’s why I’m writing this today :-) ) I reviewed a match I played on DailyGammon and came across this position:

 

 

Blue's move. Cube action? Redouble or play?

This is a match to 20 points (yeah, really), I'm leading 13:5. I hold the cube at 4, can redouble to 8. What should I do?

On level 2, this is an easy double. I need three rolls to bear off my checkers, he needs 3 rolls to bear off his checkers. 

So I doubled. And XG tells me "you were a really, really, REALLY dumb fool doubling." (okay it tells me I lost a full 0.83 points of equity, which (assuming a blunder costs you 0.08 points) is a tenfold blunder. 

At the same time XG confirms that I was correct with my "level 2" assessment: I'm 80% likely to win this game, so I should double, and white should pass.

 

Money game analysis - redouble/pass

But the thing is: I'm leading 13:5, and I'm 80% likely to end this match leading 17:5. XG says that in this situation I'm 90% likely to win the match before doubling. If I double to 8, white will redouble to 60. making this a "double match point". And as the figure above says: I'm 80% likely to win this match, so I reduced my match winning changes from 90% to 80% by doubling. Good move.

 

 

Match analysis (using match winning changes instead of equity)

 

Much left to learn to master level 3, the match play.

 

Which Back Game is how good?

tl;dr - avoid back games involving the ace point. Seek back games with two consecutive points (eg 34) - better if they are in the middle of your opponent's home board, maybe also with a single point owned by your opponent.

 

"Which Backgame is how good?" -  That's a question I was asking me for a long while? I know, some back games are actually fairly good for the defender. Some are not. But I didn't find good info on the internet.

So I'm trying them all out and log my results here.

I'm using three variations of the same position: one with maximum timing, one with minimum timing, one with a bit more than minimum. It's always white to move, with a roll that doesn't give blue an immediate hit. 

There's probably also an "optimal timing" which would be interesting, but which is too much to find out with my limited skills.

So here's the three positions, for an 21 backgame:

A backgame with little timing (35 pips behind)

In my "A" positions, blue has poor timing; his board will crumble in the next move.

 

A backgame with a lot of timing (80 pips behind)

 (In my "B" positions, blue has a lot of checkers to move before the board starts to crumble. Note that for some back games this is probably too much timing.

 

And finally, for the "C" position I moved the third checker on 20 in the "A" position to the 11 point for another 9 pips more timing.

A position in between the big alternatives (44 pips behind)

 

What I did then was feed the A and B and C positions for every single backgame of two points into XG2, analyze the move that it found best, initially, at Roller++, and looked at equity, winning chance for white, Gammon/Backgammon chance for white.

If I was analyzing a back game where the blot on 10 couldn't easily move to safety with the 32 roll (e.g. a 54 back game), I changed the roll to 31, and in the special case of a 65 backgame, to 42, so that white always has a roll that doesn't give blue a shot.

 For clarity here's position "B" - much timing for a 43 back game.

Findings

More timing, more gammon losses

Totally trivial Finding: much timing will lead to more gammon and backgammon losses. Only for an 12 back game this doesn't make a difference. A well timed 13 backgame already gives you 5% more gammons, and this percentage increases continuously until for a 65 backgamme the additional 5 checkers cause a 35% difference of gammon wins for white.

The reason is of course that 5 checkers on 12 and 11 need to be brought home, which adds a lot of gammons. In a 21 back game this is not critical, but e.g. in a 43 back game it is.

You don't want a back game with your ace point

The questions that made me embark on this mighty analysis mission were: 

 

1. "if I can choose, which back game should I go for?"

2. "is this a backgame worth playing (or e.g. dropping)?"

To answer this question, let's have a look at the equities in our test positions. In normal games you only have limited control over how your timing evolves (and then you get that 66 when you really don't want it). Therefore I've simply taken the average of the equities of the three positions A, B, C. Here they are.

"What is this supposed to mean?" you ask? 

It's simple. To find out what average equity you get for a 42 back game, look at the row labeled "2" and the column labeled "4" and you'll see the figure 0.71 (it's German excel so you see a comma instead of a dot). 

 

This means that if you take the equity for position "A" (low timing), and the equity for position "B" (much timing), and the equity for position "C" (in between), then their average is 0.71. A 42 back game is not the worst you can have. You might even take a cube.

 

Result: 

• The worst five back games here are the 61, 51, 41, 31, 21 backgames.
  Probably you don't want to play a backgame involving your ace point.
  
• your best chances with a back game are the 43, 54, 53 back games.
  Good back games: two consecutive points in the middle of your home board.

If you're at the end of a match and gammons don't count, then not this equity but the pure winning chances for white (and blue) are most interesting:

The situation is similar, but not entirely the same.

Again: don't play a back game with your ace point.

Best: go for the 3 point if you can. 32, 34, 35 are all good.

If you have A LOT of timing, go for at most 1 point between your points

Let's have a look at the equity for only the "B" position in which you have 5 checkers to move home, plenty of timing.

 

Please note: timing is relative - the pip difference that is great timing in one position might be too little or too much in another position, so please take this with a grain of sault.

First you notice that all 65..61 back games are poor here. But as the 6 point is and stays in white's hand in pretty much every game, let's mark them in a greyish pink and ignore them.

Results:

• The best back games are 31, 32, 42, 43, 53 - go for adjacent points or for points with only one point in-between.
• The worst back games are, again, involving the ace point - 21 and 51 (and 61 which we ignore)

The full monty

If you want to do some analysis on the raw data as well, here's a link to the excel (hopefully will easily open as a google table):

The spreadsheet with all the info

 

Disclaimer: I am not good at back games. Watched Michy vs. Dirk yesterday playing a back game on Backgammon Galaxy's YouTube channel. Had no clue why they made some moves. XG2 knows back games, but if I asked it the wrong questions, it certainly gave me the wrong answers.

If you're good at back games and think all this is nonsense, just drop me a comment.

The tutortorial - how to improve your game with the tutor of one of the top backgammon apps

Please note: this blog entry is for beginners who want to improve, not for serious players who know what equities are and how to use them.

Recently on Twitter I suggested to a newbie to use the tutor of True Backgammon to improve his playing strength. And then I realised what a difficult task this will be - the tutors of True Backgammon, XG Mobile, Backgammon NJ all work by throwing a huge number of numbers at you. And you‘re left alone interpreting these numbers.

This is why I‘m writing this tutortorial, a tutorial for the usual tutor. I‘m using True Backgammon and XG mobile as examples. Probably will add other apps (Backgammon NJ in particular) later.

A tiny bit of Backgammon terminology and strategy

It‘s hard to talk about how backgammon tutors work without clarifying some basic terms.

Race: Backgammon is a „racing game“: you roll the dice and race your checkers home, your opponent does the same, and who has them home first wins. If you have less points to cover to come home you‘re ahead in the race. If not, you‘re behind in the race.

Points: a lot of strategy depends on how many checkers you have on a point.

• No checker: both players can still occupy this point.
• * one checker: your checker is a blot that can be hit by your opponent. If he does, it moves to the BAR point, losing all race value it has gained. A blot can be a good thing you create on purpose: if you want to make a point (see below) you can either be lucky and roll a roll that moves two checkers onto that point. Or you risk slotting the point, putting a blot there. If the blot isn‘t hit you can later add another checker to make the point
• * * Two checkers: you have made that point. Your opponent cannot move there, which may hinder him in the race. As you cannot move a checker away from this point without creating a blot such a point is called stripped. 
• * * * three checkers: good to have that - you can use one of the checkers to move to another point without giving up that point. This gives your game flexibility.
• * * * * four or more checkers: this point is too crowded, you should think moving checkers away because they serve no purpose in hindering your opponent‘s race.

Pip Count

As the race is so important, the first figure you need to know is not actually a tutor feature but something that almost all backgammon apps show you: the pip count.

True backgammon doesn‘t show the pip count continuously. You have to touch the menu button to see it In this position my pip count (Mensch - human) is shown as [154], the computer‘s pip count is shown as [142]. This means that I have 154 pips to cover in my race, while the computer only has 142 left. I‘m behind in the race by 12 points. 

This is a first tutor-ish feature as the player who is ahead in the race has to do nothing but bring his checkers home safely to win. He should play conservatively, not risk leaving blots. The player that is behind in the race needs to risk something to catch up. He wants to hit a blot or block to the opponent so he can‘t use a roll and falls back in the race.

Now let’s a look at the actual tutor; here‘s a position in which True Backgammon tells me that I‘ve made a mistake.

Tutors are all about equities and probabilities

White to play 51, not a great roll.

I played 24/23/18. My reasoning was that red has stripped 17,14, 12 points so if the computer hits me it will weaken its position.  Also I have no offensive plan. However, the tutor tells me that I made an „medium mistake“ (sorry for the German texts).

Which brings us to the question: when is a mistake medium? When is it a blunder? When a minor mistake? And how do you measure mistakes at all?

This is an important question because as a beginner you might particularly try to understand why your really big mistakes are such really big mistakes, while giving medium or small mistakes a nod and continuing without digging into them.

Suggestion 1: focus on the serious mistakes, blunders first. You learn most from them.

All serious backgammon programs use the so-called equity, which is a number typically in the range between -1 and 1. 0 means an even game. 1 means you‘re certainly winning a point. -1 wins you‘re certainly losing a point. The equity can be any number in between, and you can imagine that it is determined by playing a large number of games from this position:

Suppose, in your position, you let a strong bot continue playing and finish the game for you. If the bot wins for you, you write down 1 point for you. If the bot wins for your opponent, you write down -1 (if you win gammon, you note 2 points etc).  Now let‘s supposed you do this 10 times and end up with 1, 1, -1, 1, -1, -1, 1, -1, -1, -1. Then you can estimate the equity of your position as 1+1-1+1-1-1+1-1-1-1 = -4/10 = -0.4. And as you know that single games go from -1 to 1 you can conclude you are quite a bit worse off.

Race vs equity

Maybe you‘re rightfully confused now: first I wrote that the race shows who is leading, now I write that the equity shows who‘s winning. It‘s important that both factors count. Have a look at this position.

A position with hugely different pip count and equity (XG mobile)

Here, white has still 135 pips to go, while blue is almost home with only 43 pips remaining. But if you take a look at XG‘s evaluation, you see that white is clearly winning - the equity is 1.013 which means something like „wins for sure, with a small gammon chance“. Why? Because blue can be far ahead, but he won‘t ever get his lone checker on 1 over these six consecutive points blocked by white. White will now continue by slotting and then making the 3 point, the 2 point, the 1 point, and blue can only wait for a very lucky 66 when white starts bearing off. 
 

So the pip count is often a good first approximation of who‘s winning, but the equity is the real thing.

The value of a move is how it affects your equity

If you know the equity of a postiion you can determine the position’s equity before and after different moves. Let‘s take our position with equity -0.4. Assume our superhumanly playing bot would play move A, which changes the equity to -0.3, while it estimates the position after your move with an equity of -0.6.

This means the best move in this position would win you 0.1 points of equity (one tenth of a single game), while your move lost 0.2 points of equity. Your move is 0.3 points of equity worse than the best one (which is a big blunder). And this is exactly what backgammon tutors will show you, along with more figures.

Let‘s examine the True BG tutor for my medium mistake.

True BG stays silent as long as your moves are good. If it believes you made a mistake it will show you a line at the bottom, moving the board up a tiny bit. Hit „details“ for the actual tutor.

Oh man, what a sh…load of numbers! Let‘s examine them one by one. 

Tutors usually show the best moves in a position in a list. They mark the best one and your actual move, and they will throw a lot of numbers at you to find out what the differences between moves are.

First we zoom in on the best move I should have played, which is shown in the top lines of the list, marked blue.

The leftmost number is the most important one: -0.729. It‘s the equity of my position after the best move. Meaning I‘m significantly behind, even if I play the best move, which is 6-5 8-3 (shown in the first row, right part)

As people are better with probabilities than with equities, you get a large number of probabilities below that explain the situation in more detail: 

• I will win roughly 1 in 3 matches from this position (31.1%). 
• The computer will win the other 68.9%. There is no draw in backgammon.
• A number that is often helpful is the one named „G+BG“. This number tells you how likely you and your opponent are to win with a gammon or even backgammon. Here, my opponent is fairly safe from gammons, I will only win 6.3% or one out of 15 games by gammon/BG. My opponent is starting to build up some gammon potential with a 16.7% gammon chance, he will win one in 6 games by gammon.
• Ignore the MWC figure for now - these are the match winning chances for me, which is important for match play, because the evaluation of a position might be different if you‘re playing a long match and leading by far or if you‘re playing a normal game.

You can already learn a bit here, make some interesting observations. If you scroll way up to the position in the first figure, you see that my opponent already made two additional points that my last two checkers have to pass, while I have not yet succeeded to do so. This difference turns into a significantly higher chance to win, and in twice as many gammons.

Now let‘s compare my mistake-ish move.

• My move is only the 6th best move. I managed to not find one of five better moves. Good job.
• The leftmost figure, -0.798, is the equity of the position after my move. In brackets it shows (-0.069) which is the difference to the equity of the best move, ie the equity I‘m losing because I picked the wrong move.
• It then shows my move, 24-23, 23-18
• Below it shows my new winning probability, 32.2%. I‘m 1.1% less likely to win now.
• Also it shows gammon/backgammon probabilities. You can see that my opponent‘s gammon chances have climbed by 10% from 16.7% to 26.4%. That‘s because I‘m leaving two blots for him to hit and build a strong board.

Tutors are no teachers

That‘s pretty much it. That‘s what you get out of a tutor. And if now the realisation dawns upon you that tutors are just a large bunch of numbers that a perfectly playing computer throws at you, and that it‘s hard work to interpret these numbers, then you‘re 100% right. A tutor is no teacher. It won‘t tell you about backgammon concepts like priming, blitzing, back games, flexibility, pure plays. It will just tell you for your current position and for every single move how it affects your winning chances and gammon chances. The rest is up to you.

How to work with a tutor

First, let‘s get this out of the way: a very good way to improve your backgammon is to get a human teacher, or read a good backgammon book that explains what‘s going on in the mind of great players when they look at a position.

An incredibly valuable and totally free starting point is the wonderful annotated match between Kit Woolsey and Jeremy Bagai that you can find on bkgm.com. Two top players and the back then best bot explain why the players made the moves they made and why alternatives would have been worse or better.

Also, please note that even after years of playing backgammon I still sometimes end up in positions where the computer tells me „this was a shitty move, you should have played that“ and I just don‘t find out why. The tutors are valuable tools but won‘t help you always.

With that said, that‘s what you can do with a tutor‘s analysis:

• If you‘re a beginner, I suggest you focus on blunders that cost you more than 0.3 points of equity. It‘s far easier to find out what you did wrong than in moves that only cost you 0.05 points of equity.
• Tutors often allow you to click on a move and see it on the board. Look at the position after your move and after the bot‘s move. What are the key differences?
• Maybe look at other moves that are also close to the equity of the top move. What do they have in common that your move doesn‘t have in common with all of them?
• Look at the gammon/backgammon percentages. Sometimes a key difference is that you greatly increase the chance of losing two points.
• Oh yes, and please trust the computer‘s evaluation 100%. If you‘re a top player you might know about very, very exotic positions where the bot misanalyzes the position. But a beginner can blindly trust the evaluation of a superhumanly strong player like True Backgammon‘s BGBlitz engine or XG mobile. If the bot says your move is shit, your move is shit. :-)

XG Mobile‘s tutor (which is really the same thing)

Here‘s what the same figures look like in XG mobile.

XG Tutor tells me I made a serious blunder

Like True Backgammon, XG will remain silent as long as you‘re making good moves. If you blunder (like I did here with a blunder that cost me 0.12 points of equity) you get this dialog. Hit „show best choice“ for the tutor‘s overview and you see this:

Again, you see a list of the best moves; your move is sorted at the second position. You see the moves and the associated equities; if you click on a move the tutor will show you the winning/losing/gammon/bg probabilities. Click on the little eye and you‘ll see the move on the board.

As you see, it‘s pretty much the same data, visualised slightly differently.

That‘s it for now. I hope you enjoyed reading this and it can help you a tiny bit to improve your backgammon.

Next up: how Tutors help you analyze your cube decisions. I was considering adding this here, but the post is very long already, and cube handling is way more intricate than normal checker play, so maybe beginners should first not worry too much about the doubling cube, maybe even play 1pt matches where the cube doesn‘t play a role.

 

Hardwood Backgammon for iOS - very close, but still no cigar

Imagine you‘re listening to a really beautiful song, and just when it‘s all perfect, the singer takes out his mouth organ and plays a really ugly mouth organ riff. That‘s a bit how I feel about Hardwood Backgammon (HW BG). It has many great features, and should stand out of the large sea of backgammon apps. But one issue nearly kills it for me.

Let‘s start with the positives. HW BG has nice 3Dish visuals on iPhone and iPad, different boards, backgrounds, checkers and dice (and more for money) to choose from, features everything a full backgammon app needs (matches, doubling cube, Crawford rule), and a strong bot to play against.

Hardwood Backgammon in action (iPad pro)

It also has online play, but online I‘m so happy with DailyGammon and Backgammon Galaxy and Heroes that I just don‘t try it out.

First you need to invest a few bucks (don‘t remember exactly, something like 2€) to get a “world class” level AI. I couldn’t resist, and yes, this got me a world class AI. The bot plays an aggressive, very strong game. Sometimes it makes small mistakes, particularly it’s a bit too fast at the doubling cube, but in the two 5-pt matches I played against it while transcribing in XG2 (Roller++ level), XG rated it at PR 3.0 and 5.3 (the later due to one too aggressive double), which is world class level, definitely. 

A different board (cost me a few bucks)

When you start a match, the app selects a virtual opponent for you. I have no clue what this is about - you get a random name, but there doesn’t seem to be any playing character or something similar associated to it. Lilly seems to play exactly like Joan d’Arc, and you neither can get separate statistics or anything else.

Moving is enjoyable, both double-tapping (click on source checker, click on target location) and drag&drop is supported. It’s not totally up to the best (can’t undo a move by moving the checker back to where it was, like in True Backgammon), but very pleasant. I also really like the nice 3D look and feel. Very professional.

BUT… and here’s the big but. Two things nearly spoil the app for me. They are small issues with a big impact for enjoyment.

First, when you have made a move, you see an “end turn” button like this: 

The “end turn” button of anger

This button will stay there for five seconds. Then it will automatically vanish, your move is made and it’s the opponent’s turn.

Now if you’re a beginner, five seconds sound like a long time. But sometimes, in difficult situations, I want to spend much longer looking at the position after a move, weigh different alternatives, before I commit to this or that move. Five seconds is just nowhere enough. These five seconds cause a lot of stress and frustration.

Second, the app doesn’t store its game state when you do something else. If you move to a different app and iOS decides to close HW BG, your match is gone and you have to start a new one. Never had this, ever, in any other top BG app.

Oh yes, and while we’re at it, the app also has a fairly minor bug. 

THE BUG

In post-Crawford games, the app is so eager to do the automatic double that it will double right at the beginning of the game, in the initial position, before the first roll. Not an issue at all. But still a bug.

These are minor issues, but in an app space that is as crowded as Backgammon, where an app competes with wonderful apps like XG Mobile, True Backgammon, Backgammon NJ, these are showstoppers.

Still, go ahead, try it, if you’re moving fast and not playing long matches with long breaks, there’s nothing wrong about this good app.

Update Sep 2022: after laborously playing a number of matches and at the same time transcribing them into XG2 I found that the "world class" AI plays indeed on world class level (PR 4.8 so far). Will continue some more.

The Backgammon by UNBALANCE

 I was looking forward to playing “The Backgammon”. After all, it’s by UNBALANCE, the company that created “Crazy Stone Go”, which was the best Go-playing app for Android/iOS before the AlphaGo clones came. I’m still playing most of my Go games with UNBALANCE’s nice app, and so I expected a lot from a backgammon of these developers.

To some extent I was not disappointed. “The Backgammon” is a solid implementation of Backgammon; unlike many of its competitors it features money games and matches up to 15 points, correctly implements  everything including the Crawford rule, allows to try out different moves before committing to one etc.

I like “The Backgammon”’s presentation. Two different nice boards wait for you, nicely rendered on phone and tablet. The menu system is easy to understand and has a clean, professional look.

The wood board on an iPad Pro 

The app offers both online playing (which I haven’t tried - there’s backgammon galaxy and backgammon heroes with XG-based analysis features) and playing against an AI. This AI offers five difficulty levels from “gruesome gruesome beginner” to “beginner”. 

I must confess I’m disappointed by UNBALANCE’s effort to build a Backgammon AI. Other than their Go this is no master. Even on its hardest level 5 it makes obvious beginner mistakes, like doubling with a checker behind a 6-prime, just because it’s 10 pips ahead in the race. Also its checker play is doubtful at times. I haven’t fed a match into XG, but I am very convinced it plays not better than a PR of 20 or so. Here’s a few examples:

Beginner cube handling at work

In the example above, black has a checker on the bar, behind a 5 prime, and has nothing. But because I’m only 9 pips ahead in the race, it accepts my double.

A horrible double blunder on (iPhone)

To increase longevity and give you a challenge, “The Backgammon” includes a “challenge mode”, in which you have to beat every level at 5 different match lengths to earn medals. Unfortunately, though, Level 1 is so incredibly weak that I can’t get myself to try out what happens if I win all medals (it leaves direct shots without any reason).

The challenge mode (iPad pro)

So, if you’re an intermediate player or better, you probably won’t find an opponent that can offer you exciting matches here. But for beginners, this is an acceptable Backgammon that you can have a great time with, for free. “The Backgammon” is purely ad-financed. It shows you ads on the top of the screen, and will show you an ad movie after each match. There’s no in-app purchase to get rid of the ads.

The alternative green board, also nicely rendered

Please note, though, that an app playing on this level cannot teach you to become a better player. Not because there is no tutor mode, and also not because it just doesn’t play well enough to be a good teacher. For this you need e.g. XG mobile, True Backgammon, Backgammon NJ.

Yes! My first 7-point match played with "world champ" rating

 Okay, you probably couldn't care less, still I'm proud as hell.

Played a 7-pt match against XG mobile today, managed to win and not mess up too badly; finished with a PR of 2.03.

Here's my single blunder. Would you have done better?

White to play 42.

It's fairly clear that the 2 should hit with 16/14*. But what to do with the 4? Move on with 14/10 and minimize risk, or play bold and slot with 8/4?

...

Honestly I should have seen that. I'm 62 pips ahead and should have played safe. 16/14*/10 only leaves two shots - 44 and 64. I went for 16/14*, 8/4 and blundered 0.18 of equity.

Still: YAY WORLD CHAMP MATCH! :-)

A seemingly easy position (or: why I love backgammon)

Came across a wonderful backgammon position today (on DailyGammon). At first glance, it is totally trival. All the complications are gone. In three rolls the game will be decided. 

Still I managed to squeeze a blunder of nearly 0.2 equity out of it. After 10 minutes of thinking. With a piece of paper. And a calculator.

That's how mysteriously complicated backgammon can be, even in its most simple positions.

Here we go:

 

White's turn. Cube action?

 

This is a match to 15, score is 2:2.Should white double? Should black take?

I have still not figured out how to solve this one.

What's your suggestion?

 Spoiler starts here.

The trivial part is: 

• if white rolls 44, 55, 66, white wins (1/12 probability)
  
• if white rolls something else, and black rolls a double, black wins (11/12*1/6 probability)
• if white rolls something else, black rolls no double, then black has only a single checker on 1 and will win for sure. Unless white can bear off the three stones in two rolls.
  But how likely is this?

I was black, my opponent (correctly) doubled.

I arrived at the conclusion that I need 25% wins to take, the second dot gave me only 15%. So I need to win about 10% of all games in case 3. Since even with a 21 roll, white still has many combinations to win, I concluded that nearly all 2-roll combinations will bring the three checkers home and passed.

Tuns out, the correct cube action is double/take. In this position, black will win almost 30% of games (28,97%, actually; I even did a rollout).

I still have no clue how somebody might solve this OTB. And I'm still amazed that such a simple position is so difficult to solve.

My first Android review :-) - Backgammon by AI Factory

 Okay, it's time to also review Android Backgammons. I wiped the dust off my old trusty Galaxy Tab S2, and installed my first Android Backgammon in a long time: Backgammon by AI Factory. 

 

Backgammon by AI Factory in action

There's this urban myth about Albert Einstein. It says that he has received poor grades in school, particularly in physics. Actually he has received a grade "6" in physics, but while a "6" is a poor grade in most European countries (an "F"), it is a very good grade in Switzerland, where Einstein went to school.

I had to think of this myth when playing a match against Backgammon by AI Factory (henceforth BGAIF) at its supposedly strongest play level "7". Is this all a big misunderstanding? Is the strongest level maybe "1"? But no, even the text explaining the levels goes into great depth about the two new levels 6 and 7 which use a different, very strong AI.

But look at this, for example (NB this is a screenshot from XG2 that I used for expert analysis):

 

Blue to play 22

 

In this position, a blue checker is trapped behind my 5 prime. It's not so important what blue does with three moves of checkers in his home board. But blue MUST move one 2 as 23-21, hoping to roll a 6 later and get behind my prime. Unless you're a total newbie you immediately sees this necessity.

It turns out that BGAIF didn't. It moved 6-2(2).

 

Blue to play 22, with analysis fro XG2

Not unexpectedly, XG2 considers this a horrible blunder, losing nearly a full point of equity (-0.894, to be precise :-) ). And if you look at the move list on the left side, you see quite a lot of BGAIF's moves marked in red color, because they are blunders.

At the end of my match, XG2 awarded BGAIF the poorest of all ratings: distracted (PR 41,8). This means that you cannot hope to improve your backgammon skills by playing against BGAIF and learning from its moves. You can also not hope to enjoy playing against it if you're not a beginner. It's not playing like the poorest AIs that I've seen, but it's nowhere near the same league as Backgammon NJ, for example. 

I'm a bit mystified how an app can offer seven (!) levels of difficulty, using two different AIs, and the top level plays like a beginner.

For completeness sake: yes, I won the match, even though I played poorly (Intermediate) and luck was on BGAIF's side. 

That said, let's cover the basics of this app: BGAIF offers quite a lot, everything that a newbie to Backgammon might want for playing casual games. It doesn't offer enough for anybody to improve her backgammon skills.

You can play money games or matches, with or without cube. It even supports the Crawford rule of matches. It offers several different board designs, some of which you only get if you have another app from AI Factory installed on your device. While playing it supports you finding the right move by highlighting possible checkers and target points and showing the current pip count. It also features an - unconventional - undo: on the one hand you can completely undo any number of moves, which is cool. On the other hand it doesn't feature the "normal" undo that everybody who plays backgammon seriously needs. Normally, when deciding what to do with a difficult roll, you play around with different moves, do them on the board, examine the position, maybe do some probability math, take the move back, do another one, until you're happy. In BGAIF you move the last checker and your move is done. This is a bit annoying, as the next time to undo is after the computer has rolled and moved.

BGAIF doesn't offer any kind of tutor, but that's okay because the engine's advice wouldn't be too much to learn from.

 

The default wooden board looks fairly good.

 

Ads in BGAIF deserve a special mention: BGAIF is completely free, so it's development is supported by in-app ads. No in-app purchases. The ads are VERY limited to a banner in the top right corner. Kudos to AI Factory for not destroying the game with too obtrusive ads.

Summary: I must say I was disappointed by the AI of this app. 7 levels, and the best one plays like a beginner? That's not good. Apart from that, BGAIF is a fairly decent app with not too many highlights but no critical flaws either. Good for a fun game in-between if you're not an experienced Backgammoner (Backgammineer?).

ps. please note that I don't own an android phone anymore, so I can only review how the app looks on a tablet. A good review should check how the app looks on different devices, sorry, can't do that.

A hidden treasure: Backgammon KG

Apple‘s App Store is like a big ocean. If you‘re a fish who manages to live at its beautiful coral reefs, or at its wonderful famous beaches, plenty of divers will get to see you. But if you live down there in the black depths far below the surface, chances are you‘ll never get into a diver‘s sight. 

Backgammon KG is such a creature from the deepest seas. Unlike companies who have read their SEO (search engine optimisation) books and know how to get their app into your search results, its developer Keith Gould probably just wanted to create a good, free backgammon and nothing else. As a result it is near impossible to get it into your app store‘s view. I‘m regularly hunting for new backgammons, scrolling through long lists of apps, but this one never appeared. Only as a related game to another app it showed up. I downloaded it to my trusty iPhone and was amazed at what a beautiful deep sea fish I had found.

Backgammon KG on an iPad Pro

The thing is: there are many (MANY) backgammon apps on the App Store. But there isn‘t a single one that you can call full-featured without blushing and that is really free. Only this one. Backgammon KG. On the German App Store it has a single (one star “this app is cheating”) rating which suggests that only few people ever tried it.

Graphically it’ fine, but there‘s not too much to write home about; the UI gets the job done, the app has a clean and consistent look, you‘ve got 10 board designs to choose from. But I‘ve seen more beautifully looking backgammon apps. One complaint: sometimes, mostly in the lower row of the board, you have to click slightly left to where your checker should move or it will move one point too far. And a minor complaint: there is no native support of the iPad - it’s using app scaling which makes the app look low-res.

Some of the designs (here: metal) are, well, daring

It’s real strength lies not in its presentation but in its scope and in its price. Backgammon KG is really, actually, totally free. Not free as in “buy 1000 coins in-app to unlock this and that”. Not free as in “whenever you like it least it will confront you with 20 seconds of video to watch or with a blinking ad image. No. Really, actually free. Download it. Play backgammon.

And backgammon it plays. Not the “what doubling cube?” kind of backgammon that half of the apps support. Not the “there is something else than money games?” kind of backgammon. Not the “my developer got the task to build my AI in 10 working days so I play like the ultimate backgammon noob” kind of backgammon. Real, actual, strong backgammon! You can play matches from 1 to 11 points, with Cube, Crawford and everything else working the way it should.

Backgammon KG’s AI uses the same fundamental approach that all the top apps rely on - a neural net based machine learning approach that was trained by millions of self-play games. It shows that the app could have used a few million more of those self-play games. It’s strong, really strong, but not as strong as XG mobile or the BGBlitz inside True BG. I’ve played 4 test matches to 3 points, one myself, one pitting Backgammon KG against the PC program XG2 on an extremely strong level (“roller++”). My conclusion: KG’s checker play is world class level. Not perfect - sometimes an error or even a small blunder creeps in. But good enough for quite everybody to get a good challenge. Cube handling is not as strong; Backgammon KG plays a very defensive cube, missing good cubes quite often. So in the end XG2’s assessment of KG in the four matches was once advanced and expert each, and twice world class. Not bad for a free app.

The little red lamp shows the tutor’s opinion on my move (error!)

Also, the game includes a (nearly) full-featured tutor - great to improve your skills. If you activate the tutor in the settings, you’ll get two things: a little lamp that is white (“perfect”), green (“small error”), yellow (“bigger error”) or red (“blunder”). make a move, see the lamp, and take back/experiment to see what the game recommends. Next to the lamp you’ll find a “Moves” button. Hit it and see all possible moves, ranked from strong to weak, along with two mysterious figures that I haven’t understood.

The tutor’s move list

So to find out the best move, click on the first row and behind the semi-transparent list the move is made. Close the list to see the full thing. Undo if you want to still consider different moves.

I can’t stress enough how cool the combination of a strong AI and a tutor is - apart from reading Backgammon books or watching Backgammon videos of pros commenting pro matches this is the best way to hone your backgammon skills. And while I believe the top apps deserve your investment of around 10 bucks, this one does the job really well, completely free of charge.

One minor gripe: the app doesn’t tutor your cube decisions. This is sad because, at least for me, cube handling is the toughest part of backgammon. To make a proper cube decision you have to assess your winning chances, your / his chances to gammon, the volatility of the board, the likelihood of losing your market next turn. After decades of Backgammoning I still regularly make cube errors on the level of “this has cost you half a point”. But then, Backgammon KG isn’t much better in this respect, so a cube tutor wouldn’t teach you that much.

The default board design 

 

A few more words on features: Backgammon KG includes four playing levels, offers statistics on your playing performance, and tries to keep you motivated by gradually unlocking more board designs whenever you win a game on expert level. For the final “Andromeda” design you have to win 200 games. Not an easy job (though you can cheat by stopping and re-starting the app again and again with your last winning move on the board, but that wouldn’t be appropriate, would it?)

My conclusion: this is one of my top three recommended backgammon apps. True Backgammon costs you good money and offers the most beautiful experience. XG mobile isn’t as beautiful but IMHO a tad bit stronger, and an excellent choice for good money. And Backgammon KG is nearly as good without costing you a cent. Now go ahead and download it, what are you waiting for? :-)

 

Update (Sep 2022): as part of my project to have XG2 rank every app in a big table for easy comparison I've played a few matches against Backgammon KG and analyzed them in XG2. Result: it indeed plays quite strong, at a strong expert level, almost world class - PR 5.7. You hardly find a human opponent that is that strong, and gives you free backgammon teaching.

 

A piece of art, but barely a backgammon: Backgammon Machine

The computer game “Doom” kicked off the whole 3D first person shooter genre. In this classic, you start by selecting a difficulty level. On “I’m too young to die” the game is easy, on “Hurt me plenty” it’s fairly hard to beat, but real men (and women) played it on “Ultra Violence” for a real challenge. This analogy came to my mind when thinking about why a Backgammon like “Backgammon Machine” that doesn’t include the doubling cube is fun to play, but somehow stale compared to the real thing. Checker play offers plenty of fun, but by including the cube you turn the game’s challenges from “hurt me plenty” to “ultra violence”. 

That said, Backgammon Machine is a special app. It’s really, actually, totally completely free. No ads. No in-app purchases, no virtual coins, no “watch this video for <feature>”. Free. And beautiful. Man this app is well designed in its pure and beautiful grey look. Steve Jobs would love it. I love it.

Playing a game of backgammon on the iPad

But its beauty doesn’t stop at only visual appearance. Its user experience is also top notch - the way you move your checkers, how you undo is just perfect. For example: you roll 6/3, move a checker by 6 pips. Now if you tap on this checker, the app will highlight two target places - 6 back (to undo the 6) and 3 back (to turn the 6 into the 3). Very clever, have not seen this anywhere else.

The minimalistic options screen

Concerning features, this is pretty much it. You start a game in “match to 1 pt” mode. You make your moves (enjoyable). It makes its moves. You start another game in “match to 1 pt” mode. And so on. No tutor/analysis, no setup, no matches, no doubling, no exporting, no manual dice, you get the picture :-).

Oh yes, and the UI is so clean that it doesn’t show a pip count. The joys of counting pips by hand (strengthening my “criss-cross pip counting skills”).

But maybe that’s enough. Play against a strong, free AI can be fun, at least for a casual backgammon in between meetings or such, even without matches, without doubling. So all boils down to the question: is the AI any good? The answer is yes and no. It certainly plays a stronger game than the AIs that have been hand-crafted in a rush. It certainly plays a weaker game than then high-end AIs of XG, BGBlitz, BG NJ. 

I‘ve played 18 games so far, and lead 12:6 against the AI. I feel I was fairly lucky sometimes, but I‘ve also seen it going for significant blunders. For example, in a situation where I‘m bearing off against 1 or 2 trapped checkers it moves those trapped checkers home far too early (considering it doesn‘t treat a gammon as 2 points it should wait it out as long as possible). Or take this one:

Backgammon Machine playing a 6/4 opening rather … uhm … unconventionally

This 6/4 opening, according to XG2, is nearly a blunder (losing 0.072 equity). This is way too loose, it will be hard for me to roll something that doesn’t hit, and hit on a point I want to make. Not something an app that claims to play at nearly master strength would do.

Nevertheless this app plays a good game of Backgammon, certainly better than many of the “beginner” level Backgammons out there, and as it’s fast, fun, free and beautiful, it’s great for a fast, casual game of backgammon.

So, just install it and have fun. Just don’t expect too much. I hope the author invests more into self-playing to improve its strength, and into a few more features. Matches would be great.

 

Update (September 2022): As part of my "big table with all backgammon app rating" project I've played a couple of games against the machine, and had them analyze with XG2 on the PC. Seems I was lucky during my review; the app plays a strong expert game, almost world class level. (PR 5.2). Sadly it still has no cube.

 

Strange but fun - Backgammon - offline by SNG CT

This one took me a long time to review. Even after playing 35 games against its four levels of AI, I‘m still unsure what to think about it. One thing is for sure, it‘s not for a serious match of backgammon, one in which you can learn from a superior AI and improve your skills. And it wants to make money by making you watch ads and buy coins. And it doesn‘t shy away from fairly unconventional ideas to achieve this.

But let‘s start with the basics. First off: this is about money games. No matches.

The game pits ou against four difficulty levels. Each level raises the stakes - at the beginning you have to compete with the „beginner“ AI because you can‘t afford the price of admission to play against advanced or expert. After you‘ve selected your level you‘re treated with a screen in which you can enter your bet and your maximum bet. From this it calculates how often you can double. 

It took me a long time to figure this one out. First fun fact: this app called Backgammon doesn‘t know what a Backgammon is. It does know what a Gammon is, though. So it calculates in my example: maximum bet is 50,000 coins, my selected bet is 14,400 coins. If I would double and lose gammon I would lose 57,600 coins which exceeds my maximum bet. Therefore I may not use the doubling cube.

Hint: you want to select a bet that allows you to double because the AI has no clue about how to double well, doubles like a „now I‘ll win for sure“ beginner, accepts doubles it should really, REALLY drop. Easy money.

After these two easy steps, you‘re sent to the actual game.

Two things here: a) for some reason much screen space is invested in showing you and one of many virtual opponents. And b) this layout makes the board tinier than possible,, and there‘s no way of showing it full-screen. No problem on a big iPad screen, but still…On a 16x9 iPhone screen this is no issue.

IPhone.

Apart from this, the user experience playing this backgammon is awesome. Nice undo, unobtrusive  support figuring out which checker can move and where it can move, nice drag-and-drop playing if you wish (I love drag-and-drop in Backgammon because it slows me down a little bit and lets me think if this is really what I want. With click-and-click you move fast. And err fast.. And d&d feels like a real board). The app offers a multitude of beautifully rendered boards.

Part of this game (that I was using only in one game to understand it) is: you can watch an ad to re-roll a poor roll. Yes, seriously. There seems to be a limit to this (3 times per game?), but it tilts the odds massively to your side - getting rid of the two or so biggest anti-jokers will massively make you a favourite.

Here it is: watch and reroll.

If you‘re a reasonably good backgammon player, you won‘t need this feature, though - the AI is nowhere as unbeatable as XG, NG, BGBlitz are. But for mysterious reasons I love playing against those little virtual bots. They cover an interesting “white space”: backgammon apps tend to fall in one of two camps. There’s the bleeding-edge neural network bots that play vastly superior to you, and there’s AIs that some guy had to handcraft by creating a bunch of rules, rules that misunderstand 50% of board positions and play like a beginner. You know, the ones that double against your 6-prime because you’re 10 pips down.

This app claims to use a neural network AI that has been trained a million matches. Maybe that’s not enough, but the AI happens to play well, without the horrible blunders that handcrafted AIs annoy you with, but a bit worse than me (XG calls me “advanced” most of the time, “intermediate” if I don’t focus enough). And strangely, the intermediate AI beats me more often than the expert AI. So, at my level of play, I get opponents that I beat more often than not, but that offer good resistance and challenging games, which probably is what many players want. Your mileage may vary. Oh yes, and I’ve mentioned that it doubles poorly, so the joy (pain?) of figuring out whether to take or drop a difficult double is not something you get in this app.

What else can be said? You can buy virtual chips for real money, and if you’re a beginner you will probably have to do this to keep playing (there’s a daily 1,000 coins bonus, as in many F2P games). You can pay 5 bucks to remove ads or watch a boring ad video after every single game. While playing you’re building up experience, even have an experience level, but I haven’t figured out what this level is supposed to do. The app offers no tutor features of any kind.

All in all, if you like money games, want a good but not too good AI to play casual games against, “Backgammon - offline” might be an app to consider. If you’re a backgammon newbie you might face “out of money” situations, though.