Another area in which Snowie 4 became much stronger compared to Snowie 3 is priming games. This article will show with typical examples the 3 main improvements of Snowie 4 in this respect:

• Handling of outfield primes
• Evaluation of priming battles
• Recirculation ideas

Snowie 3 was already that strong, that only top experts had a chance to win against it in the long run. However, it was possible to trick Snowie into a certain kind of position and win a lot against it. In this kind of position Snowie has one checker behind an outfield prime. Snowie would then double, even behind a 6-prime! So a player could try every game to get many checkers hit, play a backgame and eventually (after many lost games) the player would reach this kind of position, where Snowie doubles, and beavers if the player doubles. Very quickly the cube would reach 256 or higher in a very unfavorable position for Snowie, which far more than compensates for the small losses before.
The reason for this strange behaviour is some missing information for the neural network. Snowie 3 could only recognize primes up to the 12-point. Additionally, Snowie 3 very rarely saw for example a 6-prime from the 7 to the 12-point during the training, and has therefore trouble in evaluating the strength of the prime.
An extreme example is position 1:

Position 1

The side on roll has one checker behind an outfield 6-prime. Snowie 3 doesn't recognize the prime characteristic of all the outfield checkers. It sees only the big advantage in the pip count, the strong home board and a few shots on a blot. The good news is: Snowie correctly doesn't double here. The bad news is: It thinks the position is way too good to double and a huge pass!

Here is Snowie 3's cubeless equity: 1.464

A redouble to 4 would cost full 1.1 points and a take even 2.5 points, according to Snowie 3!
Snowie 4 has no problem to recognize primes all over the board. Additionally, it was forced during the training to play positions similar to this one. So it could learn the real value of primes and how to move them forward. As a result its equity in this position drastically changed.

Here is Snowie 4's cubeless equity: -0.415

Yes, there is a minus sign in front of the number! The cubeless equity differs by almost 2 points. Now a redouble would cost almost 5 points after a beaver (in fact, it would be correct to pass the beaver!).
Certainly, since Snowie 3 has no clue about this kind of position, its checker play here is also really bad. If for example the other side is on turn with a 6-5, it is happy to make the 6-point. Snowie 4 however considers any prime breaking play as a blunder.
In a rollout Snowie 3 corrects its opinion about the cube action a bit, but still there is a huge difference:

Snowie 3's cubeless rollout equity: +0.37
Snowie 4's cubeless rollout equity: -0.43

These outfield prime positions appear really seldom during normal games, so they weren't a handicap for Snowie 3's performance. Only on purpose it was possible to abuse Snowie's weakness here.

Also in "normal" prime vs. prime positions Snowie 4's cube actions are superior. In position 2 the side on roll has too strong threats for a take. 2s, 4s and 5s make a 6-prime and 6s escape the opponent's prime.

Position 2

For Snowie 3 it is still an easy take and a blunder to pass.

Snowie 3's cubeless equity: 0.529

Snowie 4 is more impressed by the possible 6-prime and passes. A take would be a blunder!

Snowie 4's cubeless equity: 0.635

Rollouts confirm that Snowie 4's evaluation is much better. Both 2-ply rollouts, from Snowie 3 and Snowie 4 show an equity of about 0.7, indicating a huge pass. Snowie 4 is not perfect here, but much closer to the truth.

Another niche where humans were still better than computer programs are positions with the possibility to recirculate checkers in the hope to pick up a second opponent checker. Position 3 is an example:

Position 3

One side got hit during the bear-off and the other side has the possibility now to complete the closed board. Snowie 3 wouldn't refuse this opportunity. It closes the board without seeing that otherwise it could perhaps hit a second checker, almost guaranteeing the victory.

Cubeless equities for Snowie 3:

Snowie 4 notices that no damage can be done and it's a free shot to go after the second checker.

Cubeless equities for Snowie 4:

Rollouts of both Snowie versions confirm Snowie 4's ranking and equities. Since Snowie 4 plays consequently to hit the second checker and often doesn't close the 1-point in the next few moves, its equity for 19/13 is a bit higher in the rollout than Snowie 3's (0.02).

Snowie 4 has made a big progress in all kinds of priming games. It will be very difficult to find a systematic weakness in Snowie 4's Backgammon skill.

Johannes Levermann
SnowieGroup SA