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.