Let’s follow our usual format :
1) It is double match point – there are no gammon or cube considerations, we just want to win this specific backgammon game.
2) We trail badly in the race, but the opponent is on the bar. That’s all this is about – what is our plan? Slot the 5-point now and hope to cover it? If not, how do we play to contain the white checker after it enters?
3) At the table, our hero played 12-10 6-5.
4) Was he right? Snowie does not excel at containment positions, but it still plays pretty well. However, if Snowie does not contain well, it certainly will bring the position home just fine after a closeout. So rollouts would tend to be biased toward the slot and immediate closeout.
The two slot moves are both better than the best non-slot moves. As far as non-slotting plays go, 12-10 8-7 gives 1s, 2s, and 6s to hit or cover the 5-point, while leaving only 52 and 55 as enter-and-hit numbers.
What are the key features here? Well the main issues are:
a) The racing deficit – if the race is close, we should chose the play safe and come home without taking risks. If the race is lopsided, we will need to close out the opponent or hit him in the outfield.
b) The strength of our board and the opponent’s board. In this position, our open point is the 5-point, making it easy for the opponent to hop into the outfield once he enters. If we have a deeper point open, we have more opportunities to safely put checkers in place to make the point or to hit if White enters. If we have more than one point open, we lose as much from being hit but gain less from being missed.
c) Our covering numbers. The chances of being hit on the first roll are 31%. If we have to stay for two rolls, the chances go up to 52%. If we can’t cover in two rolls, the odds are 67%. If we are going to slot, we have to cover.
The real question in positions like this is, how do the individual factors weigh? Would the slot be correct if we were 10 pips closer? If the opponent had a stronger board? Let’s look.
Here we move just 5 pips closer, and the slot becomes wrong by a fair amount. I was a little surprised by this result. Notice that safety is not especially called for – the correct play still involves moving closer with 12-10, not going safe with 8-6.
This tells us that “life after death” is important in this position. Unless Black is in such deep trouble that he cannot win without slotting, he should only slot if he has win chances after being hit.
As we tighten up the position by another 5 pips, our win chances get a little better, but unsurprisingly, the slot remains wrong, and it is still right to play 12-10 for an extra builder and leave the back checkers split. Notice throughout these variations that 12-10 will always be right.
If White rolls 55, he will have a huge racing lead, and gammons do not matter. Black would prefer to be hit if white rolls 55.
Suppose we have only one direct cover. What now? I also found this a bit surprising, and of course the decision gets a bit closer. But apparently the race is more important here.
Note that Black still has 20 numbers to cover next roll. So it’s the equivalent of a double direct cover.
Can it be right to slot against a 5-point board? Yes it can. Here, Black has 35 covers after the indicated play (only 44 fails), so this game comes down to basically a one-roll proposition.
It’s fair to say that White will win if he hits here, and lose if he doesn’t.; (In fact, Black has a bit more “scramble vigorish” than White, so he wins a bit more than 69.4%.) If Black makes the best non-slotting play, he still has 5 losing shakes (52, 55, 56 from the bar), and the gain on 51, 53, and 54 must be less than the loss from the 25 misses which all but gin the game for Black.
This particular play becomes easier if you reason it through as follows:
a) Break it into slot plays, building but not slotting plays, and safe plays
b) Compare the slot plays to the building plays
c) Compare the building plays to the safe plays
Once you realize that the slotting plays must be better than the building plays, and the building plays can’t be much better (if at all) than the safe plays, the right decision becomes easy.
Finally, what if we move up the checker in White’s board? Unsurprisingly, it makes little difference. It makes the slot a wee bit more attractive, because after a hit and a return enter, Black is a little better positioned. It was at least possible that the slot would be less urgent if Black was going to need time to dig out of White’s board, but Black rates to have plenty of time to do that.
Black will have 20 escaping numbers each shake, and the ones that don’t escape are small numbers. Once Black slots and covers, he is a big favorite to escape off the 23-point, coming up to the 21 doesn’t matter much.
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