Is Backgammon trivial compared to Chess and Go?

 Some time ago, in a social media service that doesn't exist anymore, I made a bold claim. I claimed that Backgammon is as complex as Chess and Go. People didn't agree, and without evidence I found it difficult to make my point. 

Let me try this again, here in this blog :-). In Backgammon you come across several kinds of complexity, like making the right strategic decisions.

Making the right strategic decisions

Let's look at a few tricky positions in my recent (lost) match to 13 against Extreme Gammon Mobile (print and analysis by XG for the PC, Roller+) and see how tricky things can get in Backgammon.

 

 

Here I'm white and rolled 63. I have a couple of issues: there's the blot on 21 that I want to save before B hits it and occupies more slots in its home board. I've got no good home board whatsoever, and an awful stack on 6 that I need to shrink. So I thought it would be logical to play 21/15, 6/3, getting my blot in a safer place where XG can only hit it with a 3, and go for the 3 point with limited danger (only a 2 can hit me). Okay, in most cases it will hit me, but I hope to achieve one of my goals: save the blot or make an additional point.

I was wrong, but not by much (0.1 points of equity). The best play is more conservative: 21/15, 11/8. Probably my mistake was that if I get hit on the 3 point, both parts of my plan are moot - I have not made a point in my home board, and I have another blot left behind that it can attack.

 Same game, one move later - XG rolled 63, hit my blot with 12/15, and moved 4/10. I rolled 41 and found myself in this tricky position:

Black has a lot of blots that I might want to hit. 20 with Bar/20*? Looks solid, lets me attack the blot on 15 in the next move, but weakens my blot on 3 even more (any 3, any 2 will hit it). Or hit on 10 with Bar/21, 11/10? I have nice builders on 11 and 10 then, my blot on 21 can hit its blots on 20 and 15. Or maybe I play conservative Bar/24, 7/3, have a 2-points board, save my blot on 3, and look which of its many blots I can hit on the next move?

I decided for Bar-20*, and yay! I was right. Actually my move and the conservative Bar /24, 7/3 get nearly the same score by XG, although they will lead to very different games. My other candidate move, Bar/21, 11/10 gets a beating by XG - it loses nearly 1/3 of the game (-0,29).

Calculating risks properly

A part of Backgammon where I really suck is calculating risks properly. Take a look at this position.

That's a fairly easy one, you would guess. And I still managed a major f..k up. My reasoning was: yes, this is my chance to fill my 1 spot, make a 5 board by playing 8/1, and all for the minimal risk that he might hit me on 8. XG tells me I lost half a point with this decision. The best move is the simple and conservative 13/8, 13/11. Why is my move so bad? You have to look at the dice distribution for black's next roll to understand:

 

 The first image shows how the game will evolve after the best move. The second image shows my move. Two things can be seen: first: I underestimated that clearing the 13 point and keeping the 8 point is really important. All my followup moves are some 0.3 worse than necessary. And if it hits me with 11 (which it can also use to make the 21 point, I've moved my chances from 0.6 to -0.7. Keeping track of such "anti-jokers" is really important, because they can turn around the game in a single move.

That doubling cube

The doubling cube is a fiendish addition to Backgammon. I'm losing much more points by messing up my doubling than I do with poor moves. There's a couple of reasons: I forget to double because the action is so intense. I take where I should pass because I underestimated "anti jokers" like the one above. And I pass where I should take because I'm worn out and just want to stard a fresh game. Let's see a few examples.

 For me, the situation was clear. There is a good chance that I can't enter my stone against XG's 4-point board. And if I do and hit at 23, I have this blot on 7, need to get 3 stones back. Pipcount is nearly equal. A clear "no double". 

XG says I should double. I'm still confused why, when writing this. Probably I didn't consider that this is a match to 13, and in this position I'm trailing 4-10. If I double and can't enter, re-doubling is not as grave as normal because 4-14 is the same as 4-13. And as the AI believes I'm slightly leading, and have a few killer moves (2 + anything, 11), I should double.

Let's see another one:

 

 Here I didn't double. I'm well ahead, but I'm scared of moves like 21 that would give XG two shots at my poor blot, while having a 5 point board. XG tells me the correct cube action actually is "double/pass".

It's roll distribution looks like this:

 Yes, there are a number of really awful rolls for me. I didn't even think of the horrible 6-6 where I can't move at all, or 6-4, 4-4 where my blot not only stays in danger, but actually has to stay at its current spot, 4 and 6 points away from black stones, very likely to be hit. But most moves bring me to certain victory, and if your winning chances outrank your losing chances like that, you should double.

Stamina

Now this has nothing to do with the game itself, but I notice that in a match to 11 or 15 my performance degrades as we progress. In Backgammon, about half of the positions you get are totally straightforward. Some are immediately visible as tricky, and some look straightforward but you manage to not see an important move. And I, personally, manage to often miss important moves less later in the game.

 

Tactics - not so much

In my opinion, Backgammon delivers the same challenge concerning strategy, planning and mental stamina as Go and Chess do. But other than chess and go, Backgammon offers only very limited tactics. In Chess you need to play a number of likely move sequences in your mind to see how the game will evolve with this or that move. In Go, this is even more prominent, "reading" a position well is key to win local battles. In Backgammon, there's the dice, and calculating the outcome of the game with every single die combination is not something you can pull off. Really good players can detect critical "anti jokers", and the best bots look ahead 3 plys.

My conclusion

Backgammon is a much faster game than Go or Chess. Tournament chess and go matches use something like 3 minutes per move. Games typically last 6 hours. In Backammon, clocks are set to 2 minutes per match point. A tournament match to, say, 11 points then lasts for max 44 minutes. A single game lasts for something like 3 to 4 minutes. After all, the lengthy calculating of variations is not a part of backgamman, and this is the part of Chess and Go that eats most time.

And that's my conclusion: In terms of strategic complexity, Backgammon is a worthy peer to Chess and Go. But the combination calculations / tactics in those games are just not there in Backgammon...

 

Backgammon Reloaded 3D is actually fun

This one is a serious underdog in the App Store. It has „no graphic designer ever touched this game“ written all over it, starting from the ugly icon to the way you navigate through the UI, and even the 3D rendering. Clearly this is the work of one guy who likes to develop software and not of a team with a UX designer, and it shows everywhere. Correspondingly the game has few downloads and only 3 reviews on the App Store so far.

However, the game is a) absolutely and totally free. I‘ve not seen any ad ever. There is no in-app purchase. It‘s just free for you and me to enjoy. And b) it‘s actually a lot of fun to play for a while. Why? Because the game keeps throwing better and better opponents at you, and you have to beat one to get to the next. Sadly I‘ve beaten all of them soundly, which frankly left me a bit disappointed - neural network AIs normally destroy me but this one still made gruesome blunders, even after 1 million training matches.

The UI. It‘s 3D, it looks and feels fast, but the buttons, the font, everything looks like the kind of app I would design, not the kind of app a UX guru would come up with.

Also, BG Reloaded 3D features pretty much the full rule set of backgammon, including money games, matches (only to 5 points though), doubling cube, undoing moves, confirming moves. I haven‘t come across the Crawford rule yet and wouldn‘t expect it to be there, though. It also offers an online mode but so far I‘ve not tested this one yet.

The only minor issue here is that in BG both players roll one die, and the player with the higher roll starts the game with this roll. In BG Reloaded 3D, the player with the higher roll starts by rolling again. 

I've enjoyed playing the game for a few hours, even if I can‘t really understand why a well-trained neural network starts a game like this:

This is what the second best engine does after an opening roll of 4-1. It plays the beginner move 13-8, which doesn‘t leave a blot but wastes all potential for building a good board. 13-9, 24-23 or 13-9, 6-5 are moves that every reasonably good player prefers.

So if you look for a really free backgammon that offers you a few fun hours, and don‘t expect too strong an opponent, look no further. Particularly if you hate the strong engines because you believe they cheat, this might be a good app for you.

If you look for an app that challenges you and helps you improve your backgammon, this app is not good enough for you. XG ranks me as intermediate (14,21); I played a game to 3 points against every single AI that this app offers, and I didn't lose a single game. Not one. And it never was close - the game just plays way too conservatively, doesn't make points, doesn't advance its back men, so all games ended with some men trapped behind a large prime.

Backgammon Gold (premium) - strong and beautiful but with limited tutor

Summary: world-class engine, beautiful UI, limited tutor, no online gaming whatsoever add up to a package that’s worth the price of admission, if I just knew that price.

Sometimes I feel so sorry for backgammon developers. You build a really strong backgammon, and they destroy your app in the App Store because they feel you‘re cheating. 

So for clarification: in Backgammon, you roll two dice, and as 3/1 is the same as 1/3, there are, overall, 21 different possible outcomes (6/6, 6/5, ... 6/1, 5/5, 5/4, ...). A really strong player, such as Backgammon Gold, will select the move that gives you as its opponent the least number of good rolls of those 21 possible rolls, and itself the most good rolls of those 21. As 99% of us are not good enough at Backgammon to do the same we feel we‘re being cheated. Our rolls so often leave us with only awkward moves. Its rolls so often leave it with great moves. But that‘s because it plays like a world champion. And I don‘t.

That said, let‘s move on to the review. Backgammon Gold gets a lot of „this game cheats“ reviews, and that‘s because under the hood, the well-known very strong engine BGBlitz is doing its job. Like the strongest AIs, BGBlitz bases on neural network technology and will destroy you and me and probably every other human on this planet. However, I had the impression that it doesn‘t handle the double cube properly - once we came into a weird double-redouble cycle in a position where I was clearly winning, and as a result I won my first 15 point match against BG Gold, something I nearly never pull off against the other top notch AIs (BGNJ, XG Mobile). This observation corresponds to the test “bot games” I did between Extreme Gammon (PC, Roller++) and BG Gold. Extreme Gammon found nearly no flaw in BG Gold’s checker play, but some serious flaws in its cube handling. Correspondingly it rates BG Gold sometimes as world class, sometimes only as advanced. 

But that‘s minor complaints - for 99% of us, the playing strength of BG Gold at expert level is more than enough. 

Graphically, Backgammon Gold is no slouch either - several different beautiful boards, intuitive controls, nice animation, and a great „you win“ dialog. All is great. My only complaint: on the iPad Pro, the checkers are a bit too small for the board.

BG Gold on the iPad Pro

Where Backgammon Gold doesn‘t convince me is in the teaching section. The wonderful thing about a Backgammon that plays on this app‘s level is that you can have a world class backgammon player to teach you getting better at the game. And while BG Gold has a tutor mode, this mode leaves much to be desired. I can either see what move it recommends, or see how it evaluates the move I selected, only with a „green / yellow / red“ lamp. Yes, understanding equities is tricky and the various numbers that e.g. XG mobile throws at you require a bit of learning to understand, but once you‘re there they offer much more value. I would love to have an advanced tutor that gives me all the information the game has.

The Tutor. Before you move you can hit the light bulb for a hint. Once you‘ve decided for your move, you get a little traffic light - here „yellow“ probably meaning „not that good but not terrible“. 

How much does it cost? I don‘t know. Right now there‘s a „Backgammon Gold“ on the App Store that is free with in-app purchases of about 18€. There‘s also a „Backgammon Gold PREMIUM“ which is what I have bought, which costs €5,50, and which gives you every in-app purchase? Strange. 

Like XG Mobile, Backgammon Gold is „you against the strong AI“. No multiplayer whatsoever.

Overall you get a lot of enjoyment with BG Gold; to improve your game others are better.

 

Update (Sep 2022): played a few games against BG Gold and transcribed and analyzed them in XG2 on the PC. In these games, BG Gold - albeit using the same BGBlitz that awards True Backgammon superhuman strength - makes some grave blunders with the doubling cube.

Also, it seems that BG Gold only uses BGBlitz in "low power" mode - like all strong engines, BGBlitz performs some looking into the move tree like chess does (ie it can consider things like "if I now play 64 this way and then opponent rolls a 33 and he plays it this way, then if I then roll 21 and play this"...)

Here's an interesting position that shows that BG Gold only uses BGBlitz's "look 1 ply ahead" setting:

 

Here, it's brown's turn to move (upwards). Should he play one checker on the 20 point all the way to the 9 point, or should he move both checkers to the 14 and 15 point?

The correct solution is playing 20/15, 20/14. Playing 20/9 is a -0.132 blunder according to XG2.

Here's what BGBlitz (PC) would play:

Just like XG2 it would move both checkers.

Only if I only let BGBlitz use the lowly "1 ply" analysis, it suddenly moves this:

Ie. the move that Backgammon Gold made.

In the end, XG2 (Roller++ setting) concludes that Backgammon Gold plays on a strong expert level (PR 5.8), which is good, but given that an AI that can pull off superhuman playing inside I'm asking myself "why the .... did they not allow for a stronger setting?" It's like having a Ferrari and only driving it in 1st gear...

Bg3D - totally cool looking 3D backgammon. If it only were a backgammon.

The doubling cube is the latest addition to backgammon. Its history stays mysterious but it was created about 100 years ago, in the 1920s, and massively increased the complexity and the drama of backgammon matches. I believe I'm fairly good at backgammon except for my cube handling which is still way too conservative. This costs me many matches. Same goes for some apps who play a fair game of backgammon, but still I destroy them 15-3 or so because they have no clue how to use the doubling cube.

Now there seem to be people, even app developers, who seem to believe that the cube is an afterthought, something only there if you play for money, not really needed in backgammon. They don't use it in their games and unnecessarily play a more boring, more peaceful backgammon variant, or they don't include it in their app and unnecessarily ask their app users to play a more boring, more peaceful backgammon variant.

 Bg3D is such an app. It comes with a mindboggingly beautiful animated 3D UI that is without peers on my iPhone. It is simple and plays an okay backgammon. And it even includes a doubling cube in the UI:

 

 

That nice cube on the right side is, unfortunately, just polygons sitting there without any functionality. 

 

Apart from that cube issue, the app is quite nice. Very simple to use, four difficulty levels, and a beautiful, beautiful UI with wonderful animations. For example, when all your stones are in your home board, the game will pan to center on that part of the board in a smooth animation.

 

 

Bg3D also features online playing, but probably due to a lack of users I could never establish a game between me and another player.

 

The other major problem for some of us is the lack of playing strength. On its hardest level it makes horrible mistakes; I win something like 4 out of 5 games against it, and I'm only an intermediate player. I fed half of a game of me against Bg3D into Extreme Gammon (PC) and it rated Bg3D "distracted", finding 6 grave mistakes that cost it over 1 game's worth of equity.

 

Summary:  "I felt like destroying something beautiful" (Tyler Durden, Fight Club).

 

That pretty much sums up what this app is to me. Bg3D is free, it's beautiful, but it doesn't play backgammon, and the cube-free backgammon variant it plays, it plays poorly. If you're a backgammon beginner you will enjoy this beautiful app a lot. If you're better, go somewhere else (unless you look for a beautiful app to destroy).

 

 Update 08/2022: played another game with it (a match to 1 pt, the only kind of game this app can still play). Graphically, this is SO BEAUTIFUL. And again it made the most horrible blunders you can imagine. Here's what XG2 has to say about it (I'm white, XG3D is blue).

And this is a kind rating; in the second half of the game the AI was facing very simple positions where you can't go very wrong. In the first half its rating was "distracted" with a PR of over 40. I feel this is its real rating, but can't make myself play and transcribe more matches... Needless to say I won.

 

The Backgammon to rule them all - XG Mobile

Well, "to rule them all" applies to the AI point of view. The thing is, Extreme Gammon Mobile (XG Mobile) doesn‘t feature any multiplayer mode. It‘s you against the strongest mobile Backgammon on this planet, an engine of superhuman strength, even stronger than Backgammon NG and True Backgammon HD, although somebody like me probably won‘t notice the strength difference - they all destroy me. 

As there are only so few, let‘s start with XG Mobile‘s weaknesses: it has no multiplayer, the board doesn’t look as crisp as in some competing products and has some rendering glitches, and it has, well, let‘s call it „the infuriating toolbar“, a toolbar that is both very ugly to look at and hard to open if you choose the auto-hide option. 

Here it is (took me something like 20 attempts to get it to show up on my iPad Pro).

Unfortunately this is the toolbar you have to open to get access to XG Mobile‘s options. But it‘s distractingly colourful, features stupid social networks buttons (including G+ which is out of business for over a year). It‘s ugly to look at, and the place where I have the best chances to get it to open is right next to the doubling cube. I‘ve ended up with some really stupid involuntary doubles.

BTW note the rendering issue on the „five“ cube. It does that when waking up. Killing the app and restarting it helps.

So much for the complaining. On the positive side, you get a world champion backgammon teacher.

To understand how strong XG mobile plays you need to know about the BMAB/PR rating system. In this system you get a rating between 0 (makes no mistakes at all, ever) and something like 100 for total newbie. I’m intermediate, around 14. The best players on this planet are in the 2-4 range “super grandmasters”. 

Just today I let XG on the PC analyze a 9p match I did against XG mobile, and while it rated me intermediate with a performance of 14.5, it gave XG mobile a performance rating of 0.19, which means “ten times less errors than a super grandmaster”. Gnu Backgammon consistently rates it as "superhuman".

 

Here's the statistics of XG for PC on this match.

 

Also interesting: the total equity that XG mobile lost in 9 games was 0.075. This means that in the nine games we played, all mistakes it made added up are less then 1/10 of a point. Shockingly good backgammon.

 

Apart from the best engine that‘s out there, XG Mobile also has the most helpful and sophisticated tutor and analysis features to be found on a mobile device.

In tutor mode, you get immediate, wonderful feedback after a move or cube decision.

 

First it will show you a dialog that it believes you‘ve made a mistake. If you want to see details you get a larger dialog that shows you the best moves and how much off yours was in terms of equity and winning chances. You can then click on the „eye“ button and the app will show the selected move on the board for a few seconds. Extremely helpful.

 

And after each game you get the (often disastrous) summary of your and its own performance.

XG Mobile offers to export matches, e.g. for analysis on the PC, the full backgammon rule and feature set (matches to any length or money games, Jacoby rule, adjustable playing strength, game modes from tutor etc).

 

When it comes to options, XG mobile is well-equipped: full control over all kinds of aspects of the game and backgammon rules are there. And a couple of different designs offer a nice board for every taste.

 

 

A nice leather layout

 

The premium version offers stronger tutors, different board designs and a few other cool features at $10. Considering that there was a time, not long ago, when such a full-featured backgammon would cost you $100-$300 this is a bargain :-). Supposedly the premium version includes multiplayer. No clue where this is supposed to be.

All in all: if you want to improve your backgammon, XG Mobile is the best backgammon you can get.