Backgammon, Stakes, AI

by Darius Kazemi on August 28, 2006

in Uncategorized

Backgammon is a favorite game of mine. A lot of people don’t like the game (Americans, at least–the game is incredibly popular in the Middle East).

I think I know why it gets a bad rap. Most people learn to play the game of Backgammon by learning the rules and playing a few games against someone. Then they decide it isn’t fun.

This sounds reasonable until you realize that there’s a meta-game involved. When you sit down with someone to play Backgammon, you play a series of games, and you set a point value. “Let’s play to 10 points today,” you might say. Games are typically worth one point–you win a game, you get a point. Except for this thing called the doubling cube.

The doubling cube is a six-sided die with the numbers 1, 2, 4, 8, 16, and 32 on it. This represents the point value of the game. By default, the 1 is facing up, and the cube resides next to the person who went second in play order. The person with the die next to them can, right after their opponent has moved, double the number of points that the game is worth. The opponent can then choose: accept the doubling, or reject it and forfeit the game. If the opponent accepts, the die doubles, and then it gets passed over to their side–now the opponent has the right to double the value.

A smart player offers to double when they’re ahead. This makes sense: either the opponent rejects it, in which case you win, or the opponent accepts it (stupidly), and you have a better than 50/50 chance of doubling your point score. Part of the skill of being a backgammon player is knowing (a) when to double so your opponent really has no choice but to forfeit, and (b) when your opponent doing the doubling has misread their game and you can take the die, redouble, and kick the crap out of them.

It’s this meta-game of knowing exactly how ahead you are, bluffing opponents, and raising the stakes that makes Backgammon interesting. But, like poker, these mechanics are only fun when you’re playing against other humans.

Which leads me to playing Backgammon against an artificial intelligence. The problem with an AI is that it always knows exactly when it’s ahead and exactly when it’s behind. It will always forfeit when you are at an advantage, and it will always double the moment it’s ahead. The only way you can effectively play against this and keep a point lead is to try and keep track of the same information, and play the way it does. The main problem with this play style is that you must quit while you’re ahead.

(EDIT: Ian has helped me realize that it’s pretty much my version of computer Backgammon this applies to. Other versions are probably better. See comments below.)

Now parse this for a second: imagine you’re playing Red Alert 2, or Rise of Nations, or whatever it is the kids are playing these days. Now imagine you’ve spent a while building up a killer army, and you’re 80% sure that you can take out the enemy base if you strike now. You select your battalion, send it into enemy territory, and… they surrender. You won. Next level.

Where’s the fun in that? You don’t get the visceral, long-delayed thrill of crushing your enemies. The payoff just isn’t there, aside from the abstract notion of “winning.” In fact, the only time you get to battle anyone is when you’re almost certainly going to lose, or when it’s a neck-and-neck battle of attrition. Not once do you get to stomp all over your enemies.

As a result, playing against an AI causes the main game to be subsumed by the meta-game. The main game functions as the inner loop of a more important outer loop, and all of a sudden 80% of games you play involve one side or the other surrendering early on. If the meta-game were super interesting, I could see how this might work, but when the fun loop is the one being short-circuited, everyone loses.

End result: Backgammon against an AI is not fun by design. Unless you don’t mind losing all the time, in which case you can play every game all the way through to the bitter end.


Ian Schreiber August 29, 2006 at 3:46 am

Wow, Darius, it’s extremely rare that I disagree with you so much.

First: Knowing when to double (and accept/reject) isn’t the cut-and-dried probability equation that you make it out to be; there are other factors that extend beyond how “ahead” you are in the current game. For example, suppose I have 4 points and you have 6, and we’re playing to 10. I’m ever-so-slightly ahead; do I double? Not a chance; you instantly redouble, and now a slightly fortunate roll on your part wins you the match. So I might have to be “more” ahead in a case like this, than if we were just starting out. As another example, suppose I’ve decided that you’re simply a more skillful player than I am, hands-down. Then I should be MUCH more liberal in when to double (and accept your double), because I’m gonna need some extra luck on my side to counter your extra skill anyway, so I’m better off reducing the number of games in the match so that luck plays a greater role in the outcome. Note that deciding “how much better” a player you are than me is something that can’t be done with math, unless we’ve played each other a LOT :)
And of course if there’s a possibility of a gammon or backgammon, doubling may actually benefit your opponent by reducing the cost of their loss…

Second: You say that an optimal AI is no fun to play against, which is true, but then you add a corollary that therefore playing against a computer is Not Fun. Who said the AI has to play optimally? An optimal AI for “Pong” isn’t fun either, but a suboptimal AI that can be outplayed is certainly possible to build. What if your backgammon AI had certain probability thresholds, where it won’t double unless it’s ahead by a fair enough margin that you don’t feel it’s premature? What if its doubling/accepting/rejecting decision has a random element built in, so that there’s a chance it will double when it isn’t quite as ahead as it should be, and now you (the human) have to decide if the CPU is “bluffing” or not?

Third: comparing Backgammon to an RTS is a bit of a stretch. In an RTS, that final clash of units is visceral specifically because of, well, the viscera. Blood flying everywhere, death, carnage, all in one massive winner-take-all battle. Now compare with the endgame of Backgammon, where after it’s a running game and there’s no more interactivity, it’s mostly a tedious chore to roll your dice and bear off — there are few interesting decisions at this point, and if one player is far ahead it’s an act of mercy for the winner to double, allow a concession, and get past the boring endgame into the interesting start of the next game. A better comparison would be if you’re allowed to concede in that RTS *after* you lose all your forces in that big battle, so your opponent doesn’t have to go through the motions of mopping up what’s left.

Darius Kazemi August 29, 2006 at 12:51 pm

On your first point, I guess I forgot to mention that in the version of Backgammon I play (for PalmOS), you don’t play to a number of points. You play FOREVER, accumulating points. Which is weird. Right now the score is AI: 2640, Darius: 1958.

Second point: you’re right, a suboptimal AI would be more fun. This version of Backgammon has an optimal AI.

Third: I actually think endgame in Backgammon is really fun. But that’s because I’ve taken advanced probabilistic signals courses. I could write another essay about this (and I probably will), but I have a strategy for the endgame of backgammon based on laying out your pieces in a modified probability distribution function. I also think endgame is really visceral, but that’s because I always abstract everything while playing–so endgame for backgammon might as well be endgame for an RTS.

And maybe it says something about my RTS play style that the endgame is always a forgone conclusion by the time I send my troops in. (I’m a builder.)

Thanks for the hefty response. I was afraid that nobody would want to talk about Backgammon!

Mai October 15, 2007 at 8:41 am

Try playing against real people, Darius. There’re loads of good online multi-player sites these days. Granted, some of the ‘real’ people are in fact bots – but check out the forums and you’ll see real players ratting on them, so you’ll know which games to avoid. Here’s some good multi-player Backgammon games you might enjoy

Mai :-)

Darius Kazemi October 15, 2007 at 1:20 pm

Hi Mai,

I play backgammon exclusively on my Palm phone. As a result I only play against AI.

When I’m at my computer I almost never play backgammon because I have thousands (literally) of other games I could be playing. However, I will give online backgammon a shot, just to see how I like it.

Anonymous February 26, 2009 at 2:25 pm

The fun of backgammon, I think, is that when you are sure to win, you are forced to open, and your opponent lands right on top. The game is reversed. Good players know how to use their defence for possible exploitation. I think this makes the game addictive, especially when you are playing face to face with someone, and see his sad face after throwing a 1-6 to land on his guy waiting at 7.

I use AI to improve my game, but in order to win against humans, just AI is not enough.

And I like the saying “luck is a residue of design”


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