Black – Pips 158 (-4)
Black to Play 6-6
Black to play 6-6 in these situations:
(a) Cash game, center cube.
(b) Tournament match, double match point.
(c) Tournament match, Black trails 3-4 to 5, Crawford Game.
(d) Tournament match, Black leads 4-3 to 5, Crawford Game.
We’ll continue the line of inquiry we started in the April 15th blog post with another early game position that might be played differently at different match scores. Here Black opened with a 6-3, running 24/15, and White responded with a 4-1, splitting with 13/9 24/23. Now Black has a 6-6 to play.
Mostly 6-6 is an easy problem in the opening. If the bar points are open, you make them and pick up your dice. But if one of the bar points has been made, or the back men have split, you may have to do some original thinking. That’s the case here. Black actually has four viable plays, two blitzing plays and two positional plays. Let’s look at all four and see which play suits which match score.
The Positional Plays
Play (1): 13/7(3) 15/9, and
Play (2): 13/7(2) 15/9 24/18
The positional plays reject the hit on the 2-point and instead concentrate on priming and escaping. Both involve 13/7(2) and 15/9. Play (1) plays the fourth 6 to the 7-point, giving Black a lot of building potential next turn while leaving the remaining blot on the 24-point, out of danger. Play (2) instead moves the back checker out to the 18-point, into a triple shot, while keeping a spare on the midpoint.
In the pre-bot days, no one would have considered Play (2) as an option. It gives White 33 hitting numbers (everything but 5-5 and 5-4 hits somewhere) and if Black gets hit, he can’t be extending his prime next turn. What’s the point?
But along came the bots, and in many positions they didn’t mind moving the last checker up, even if it meant leaving the checker on the enemy bar-point. So there must indeed be some point to the play. In fact, there are two points:
> If White rolls a 7 or an 8, hitting the blot on Black’s 9-point, Black’s rear checker is much better placed on the 18-point. Black has some rolls that anchor, and many other rolls that hit on Black’s 16-point.
> White’s checkers are now ideally placed to start building home board points. Moving to the 18-point forces White to hit there and ignore the home board. While not a disaster, the fact that White had other good things to do with these rolls lowers the cost of being hit.
None of this means that 24/18 is better than 13/7, only that it’s worth consideration.
The Attacking Plays
Play (3): 13/7(2) 8/2*(2), and
Play (4): 8/2*(2) 13/1*
With these plays, Black abandons the priming game plan and launches an attack on White’s back checkers. Compared to the positional plays, these moves are highly committal, and win more gammons while winning fewer single games. Play (4) wins more gammons than (3), but wins the fewest games of all the four choices.
Now let’s look at our four scores and pick a best play for each score.
Money game. In a money game we’re trying to balance wins and gammons. We’re happy to pick up some extra gammons, as long as we don’t have to pay too much in terms of extra wins. We’re willing to give up winning an extra game, as long as we get at least two more extra gammons as a reward.
The best non-hitting play is 13/7(3) 15/9. Rollouts rate this as solidly better than 13/7(2) 15/9 24/18. The reason is that leaving the spare checker back on the 24-point wins about 2% more gammons, while leaving net winning chances about the same. Getting hit on the 18-point slows Black down and prevents him from launching a blitz or building a prime quickly, thus reducing his chance of a gammon.
So 13/7(3) 15/9 is our baseline positional play. Now let’s compare the attacking plays. For money, 8/2*(2) 13/7(2) clearly dominates the aggressive double-hit 8/2*(2) 13/1*. The double-hit wins 2% more gammons, but loses 4% more games, exactly the opposite ratio from what you want. (It also loses more gammons.) We’re striving for balance in money play, and 8/2*(2) 13/7(2) provides that balance; it gives good attacking chances while still keeping a firm grip on the position.
Comparing the best positional play (13/7(3) 15/9) to the best attacking play (8/2*(2) 13/7(2)) gives a clear edge to the attacking play, which sacrifices about 0.5% wins to gain about 3.5% more gammons. This shouldn’t be surprising, since making any home-board point will boost gammon chances, while Black still keeps a solid grip on the position and retains the option of going either way in the future – blitzing or priming. So for money, 8/2*(2) 13/7(2) is a clear winner.
Double match point. If we don’t care about gammons, the positional play 13/7(3) 15/9 is now the winner. A prime and a racing lead is the easiest way to win a game when gammons don’t count. This play gives Black his solid racing lead, while providing plenty of builders to extend his prime.
Gammon-go. With gammons trading 1:1 with single games, the two attacking plays now move to the top. Extreme Gammon rollouts put 8/2*(2) 13/7(2) on top, with 8/2*(2) 13/1* close behind. Give yourself credit for either choice, as both are preferable to the slower positional approach.
Gammon-save. Here we don’t care about winning a gammon but we don’t want to lose one. Clearly the positional play 13/7(3) 15/9 dominates, winning the most games while tying for fewest gammons lost.
Solution:
(a) Money: 8/2*(2) 13/7(2)
(b) DMP: 13/7(3) 15/9
(c) Gammon-go: either 8/2*(2) 13/7(2) or 8/2*(2) 13/1*
(d) Gammon-save: 13/7(3) 15/9
