Backgammon Articles

Beating Snowie
by Bill Robertie
From the Two Plus Two Backgammon Forum, December 9, 2009.

Here's some positions that shed light on a technique for beating Snowie. It's possible to trick Snowie by going into a massive backgame, hitting a checker, and eventually reaching positions where Snowie will let the cube get very high because it believes it's a big favorite whereas in reality it's a huge underdog.

While you can do this, it's a bit more tricky than you might think. Let's take a look at a series of positions. Each position comes about after this scenario:

  • Black played a massive backgame and got all 15 checkers sent back.

  • White came home and bore off 1 checker.

  • Black then hit a shot.

  • Black then built a prime somewhere.

In the first four positions, Black is on roll and owns the cube. What happens if he doubles? How does Snowie evaluate the positions? Let's take a look. (Throughout this discussion, we're talking about Snowie's 3-ply evaluation, not rollout results. We want to know what Snowie would do over the board.)

Position 1.
Black on roll.
Black's prime spans the outer boards.

Snowie evaluates this as redouble for Black and take for White. It thinks Black is an 80-20 favorite, while White wins a few gammons among his 20%.

It's redouble-pass of course, since Black's winning chances are upwards of 90%. However, Snowie understands that he's a big underdog, so the cube won't be bouncing around much. Snowie is close enough to a correct evaluation that his only error will probably be a single bad take.

Position 2.
Black on roll.
Black's prime is entirely in White's outer board.

This is a little more peculiar. Snowie evaluates Black's winning chances at 79%, almost identical to the last position. He also believes that of his 21% wins, almost all will be gammons. As a result, he evaluates this as no redouble and take.

Snowie's evaluation is further off now but he still only wants to take, not beaver. Again, no back and forth with the cube is likely.

Position 3.
Black on roll.
Black's prime now extends a little in White's inner board.

This is basically no different from (2). Snowie has Black a little weaker at 77% winning chances, and still evaluates this as no double, take. Double-pass is correct, but Snowie's still not in danger of losing a huge cube.

Position 4.
Black on roll.
Black's prime is one pip further back.

Oops! That extra point back made a huge difference. Snowie now has Black's winning chances down to 69.7%, and thinks White will win 30.3% games and 32.6% (!) gammons. White is winning more gammons than total games, which is a clear bug. Snowie also evaluates this as no double-beaver, which means there's a real possible the cube will go to the limit.

Now let's look at what happens when White is on roll in similar positions. Things get a little murky again.

Position 5.
White on roll.

Snowie thinks it wins this position 53% of the time, with 48% gammons. However, its evaluation is no redouble and take.

Position 6.
White on roll.

Snowie thinks it wins this position only 27% of the time with 20% gammons. It doesn't double here and thinks this is a beaver for Black.

Position 7.
White on roll.

Snowie thinks it wins this 51% of the time with 47% gammons. Now it thinks the position is redouble and take.

Conclusion

It's pretty easy to get Snowie to beaver a Black double, as long as Black's prime is backed up into White's inner board with a bunch of checkers. That will get the cube from 2 to 8. The tricky part is getting Snowie to redouble again. Snowie evaluates apparently similar positions quite differently. In Position 7, Snowie was willing to double when it saw a few clearly winning variations (6-2 and 5-3, followed by a miss). It's possible that good technique for the Black player actually involves not making a full prime to fool Snowie into thinking that it's still in the game.

Remember, however, that you actually only need to hit one position where Snowie redoubles to make the trick profitable, not a whole series. If you (Black) own a 2-cube, then the following sequence could occur:

  • You hit a shot and double to 4, Snowie beavers to 8.

  • Snowie doubles to 16, you beaver to 32.

  • You then redouble to 64, and Snowie beavers to 128.

Snowie only had to make one bad double to get the cube to 128, which is certainly big enough if you can create this position even one time in 50. (Remember that when the trick fails, you're still just in a bad backgame with plenty of chances to win or save the gammon.)

Interesting stuff all in all. There's a clear bug in the evaluation of Position 4. I've heard that the Snowie folks are back working on a new release, maybe sometime next year. If that's true, here are some positions that need a little work.


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