Walter Montego: Loadsaquestions!

Sometimes playing for a long shot is so much more worth it than playing safe. Which way will a computer decide?

You might be surprised to hear this but the computer doesn't care about the odds of a shot and never calculates them. The same goes for the odds of a leaving a blot and having it hit, closing a prime, etc. It doesn't a care. In fact it doesn't even know what odds are!

What it does is make each of the possible moves and then evaluate the resulting position. The one with the highest evaluation is the winner and the move that got to that position is the one that gets made. The computer's database is all about knowing the value of every possible position to a reasonable degree of accuracy. How it gets to any position (eg. through a long-shot hit or just by moving pieces) is irrelevant. A backgammon program is very much more a stats machine than a conceptual player.

I'm sure you've made a move that you know was not as good as a different move, but if your opponent doesn't get the roll to make you sorry for taking the chance you will win the game. So, do you go for it, or not?

Unlike the computer player, a human player will often consider the odds. That's because we don't have quite the same kind of calculating ability for comparing moves. Our intuition is the best match to the system that the computer uses but we have much, much less experience. We do know, however, that the position evaluation is related to the odds of various shots. (The computer doesn't need to know this as it can compare exact(ish) outcomes directly). The other thing that we do that the computer doesn't do (and really cannot do), is think conceptually.

I might know, for instance, that, being behind in the race, I must hit my opponent, despite the risk of being hit back. For example, hitting might leave a blot in my 5-point home table. In a case like this I'll know that the chance of being hit is 11/30 but if I don't hit then a 5 or 6, at odds of 20/36, would let my opponent escape with a most likely win resulting. I don't need to know the equities of the positions, I can compare the odds and they dictate the hit. The computer goes straight to the equities, compares those and comes to the same conclusion.

So, do you go for it, or not?

Having said the above. There are times when I don't play rationally but play "psychically", ie. I try and second-guess the dice. And hey, sometimes it works! And sometimes I might do the incorrect move just for the hell of it, because getting the luck would give me a buzz. (For some players that's their predominant style, especially cube gamblers). By and large, though, I try to play what the backgammon programs (mainly GnuBg) and my own experience have taught me over the years is the optimal move.

the rating points for Backgammon on this site. Single games seem disproportionally in favor of the player who is rated lower when his rating is more than 60 point

Absolutely. The chess rating formula used for backgammon makes a mockery of the rating system. The risk/reward ratio is totally wrong for high rated players. It's impossible to consistently win as many matches as needed to maintain your position unless you go for longer match lengths which reduce the luck element. A 60% winning ration for single pointers is very good but the chess rating formula means that you might need to win 75% in order not to be penalised.

Is a person that uses a computer to help with his moves on this site play noticeably different from someone that doesn't use it?

Anyone whose rating chart has anomalies is worthy of suspicion. The rating cheats who have opponents dropping like flies for them can be spotted by sudden streaks of wins. A person using a bot to determine their play is less noticeable but, unless they really are good, they'll progress too easily.

What would be an example of such play?

Usually you can't really tell but a good player can sometimes spot moves that are unusual or advanced. Moves that wouldn't occur to most players, such as hitting in their home table and leaving two blots. That's more risk than most players can accept but there are times when it's definitely the right thing to do.

Then there are other occasions when a bot-trained player will spot something that only a bot would do. In some circumstances, for example in a holding game or anchor game, when there will be a few moves before there's any chance of hitting action, there's time to build one's home table. Doing that efficiently might mean making a vulnerable-looking mess (that will suddenly firm up into a solid board). The bots have a particular way of doing this at times, maybe having three blots in their home table. Human players tend to be more cautious and/or neater in how they do it. Seeing a player do such a bot-style spread suggests that they're either good, and bot-trained, or using a bot.

Is it something noticeable at once, or is it much more subtle that it takes many games and certain move situations to notice or even have a suspicion that it might be going on?

Both nabla and I spotted the bot-player that I mentioned before. I seem to remember seeing some of the bot-style moves and being suspicious. I was also suspicious of the rather too perfect rating climb. nabla and I analysed some his matches using GnuBg. Initially it looked suspicious but not conclusive because there were still mistakes being made. However that analysis was done at 2-ply, which is a strong setting. nabla had the idea of redoing the analysis at 0-ply and then the mistakes vanished and the player was show to be playing exactly as the program dictated.

Since he was exposed, he plays all of his matches in private mode so that nobody can see and analyse his moves!

Does the computer ever conclude that that the winning player made the most mistakes or the worst of them?

Absolutely. Almost every time you beat a bot then you'll have played mistakes against an opponent that made none, yet you won. Similarly, good players who lose to lower rated players will usually have played better but still lost. That's how powerful a factor luck is in the game, and what keeps people coming back for more, even if they're rubbish players.

What's a mistake?

When a bot analyses a position and a roll it will create a list of the possible moves and an evaluation for the resulting position. The top move, the one with the best evaluation, is the best move and all others are mistakes. - according to that bot at that analysis level

But how do we know whether that list of moves, and in particular the top move, is correct? The only way to know is to analyse even more deeply.

Thus the 0-ply analysis, used by the bot cheat mentioned above, showed mistakes when the matches were analysed at 2-ply. As 2-ply is more accurate than 0-ply, we can assume that 0-ply's mistakes are mistakes. (or at least very probably)

However, it's important to note that the bots evaluate moves and positions as if they are playing themselves at that same analysis level. In real play, with a human opponent, you can be sure that your opponent has weaknesses. A bot will never play to exploit its opponents weakness. It can't, because it has no such concept as "opponent", let alone "weakness". The computer knows how *it* would play a given position and roll and that's all it needs to know. When I said "as if they are playing themselves" just above, what I mean is that their statistical database (ie. the neural network) has values that only reflect play against itself.

And what happens if it is the winning move despite being a mistake? A move is a mistake because on average it produces a suboptimal outcome (the lower evaluation mentioned before). But you can often make a mistake and get away with it because, in any given game, the dice are being themselves, not trying to be average.

I've many times made a move and clicked Submit just fractions of a second before realising that it was the wrong move, and then breathed a sigh of relief because my opponent didn't get the roll that could capitalise on my mistake. Similarly, when analysing a match, the computer will show me many mistakes that I didn't realise (or wondered about) at the time and the follow up shows that I got away with it.