Playing vs. grandmaster (checker play and cube decisions).

Match is to 7. I'm losing 3-2.

Is this a good spot to double? If not, why not?

not even close. If you miss your shot you lose the game. If you double and miss your shot you lose the match. Even if you do manage to hit here there is still a good chance you could lose. After you hit here you can cube and take the 2 points when gnubg declines.

What would be your reasoning for cubing with very little chance of winning this game? Especially since it will most likely end the match if you miss?

First thing you need to realize is that you're a big underdog in this position. True, you virtually always win when you hit, but you only hit about 30% of the time (11/36). When you miss, you have just a few extra winning chances. You could roll a number that lets you stay back in red's home board, and then red could leave a shot, and then you could hit, and then you could win. All of those events happing together is a pretty slim chance, probably about another 3%. Or you could win the race despite being 35 or so pips behind, which adds maybe another 1-2%. So your winning chances are in the 34-35% ballpark, and you don't want to double.

There are backgammon positions which work a lot like semi-bluffs in poker. You get a shot, you're an underdog to hit, but if you hit your gammon chances go way up, and if you miss you still have reasonable chances and can take a double. We call those 'action doubles' but they usually occur in volatile middle games where the guy thinking about doubling has a strong home board and the other guy has no anchor.

In an endgame position like this one, it's very very unusual to be able to double as an underdog.

I would class myself as a learning 'new' player and upon arriving at this position I thought this may be a good spot to double.

Yes, there's a good chance of me losing the game and therefore the match if I double, but a number of reasons come to my attention:

1) I need to NOT roll a 6, otherwise I lose. Chance of this happening is 66.66%. Also, any rolls that don’t give me a 6 let me have a strong chance to let me close up my home board.

2) Providing 1) is true, I can hit with any ‘1’ one the dice. That’s a 33.33% chance of hitting.

Combining both 1) and 2) (0.6666 * 0.3333 = 0.2222) gives me 22.22% chance of hitting and having a high enough chance of closing my home board, thus winning the game at 4 points.

3) Say I miss with the shot I have on my roll now (66.66%) and do not roll a ‘6’ (66.66%), my opponent has 10/36 (or 27.77%) rolls that leave me with a second shot.

Combining 1), 2) and 3) I have 12.34% of altogether hitting him and therefore, winning the game as my home board will more than likely be closed.


In summary, is a 22.22% chance really not worth the risk? Obviously the 12.34% chance is not worth taking but I did it to point out that even if I don’t hit the first time, there is still a chance of hitting a second time.

Slow down, aao, your probability is all crazy. You are multiplying probabilities of events that aren't independent to get numbers that don't mean what you think they mean. If you really want to get down and dirty and do this, you need to explicitly count where each of these rolls leaves you.
You have 11 hitting rolls: 12, 13, 14, 15, 16 (two ways), 11 (1 way). These are fantastic and leave you a huge favorite, maybe 90-95%. For generosity we'll say 100% (which it would be if you kept the cube). So that gives you 11/36 chances of winning the game.
Any other six, of which there are 9 (26, 36, 46, 56, 66) leaves you in pretty bad shape, except for 66, which leaves you in just kind of bad shape. You also have to run with 55 and should probably run with 44, so that's 11 rolls that you run with. Let's say you win 10% from here: this gives you 11/36*10%, which we'll call about 1/36 winning chances.
With the remaining 14 rolls (14/36), your opponent does leave you a shot after 65, 64, 63, 62, 54(I think that's all), which is 10/36, and then you have to hit the shot (11/36). This is about 1/3^3=1/27.
This gives you winning chances no bigger than 11/36+1/36+1/27 <= 14/36, which ain't too great. None of the mitigating factors (the fact that he can't redouble you, or you win a gammon a *tiny* fraction of the time) are close to giving you enough for a double here.

Despite all this, you shouldn't get the idea that backgammon is a game of mental probability calculations. Otherwise it wouldn't be any fun! But in a situation like this, where the game almost entirely hinges on whether you hit or not, you should at least know how to figure that out (11/36) and realize that your overall chances of winning aren't too far from that. Obviously Mr. Robertie said it better than I did.

Okay, that's fair enough. I just thought that this situation might get some different views about doubling here or not, but it appears that it is not as close as I had thought it was.

And yeah, I have some probability calculations to learn lol.

Not particularly relevant to this exact situation but quite a useful rule of thumb i read about a while back is as follows:

When considering a double, you should way up 3 factors:

1)Net pip position (i.e how far ahead/behind you are), 10%+ is a tick
2)Strength of your position relative to opponents
3)Proportion of dice roles which allow you to dominate your opponent and open up gammon/backgammon possibilities

The general rule is that if you are ahead in 2 or more of these then you can probably double if you discount your double equity position.

obviously the second point is a matter of judgement but quite often you will be ahead in 1 and 3 meaning its a double anyway. Also, there is a correlation between 2 and 3 so quite often a strong position opens up a lot of dice opportunities to dominate your opponent. Thats is really, I find it helps during the tricky middle stages of a game.

This is almost a swing double...but not quite. However, it really depends upon the skill differential between you and gnu (most world class players would disagree, but they are wrong). If you are an intermediate player, go for it!