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BGonline.org Forums
leaving shot #1
Posted By: Daniel Murphy In Response To: leaving shot #1 (maxim)
Date: Friday, 7 October 2011, at 9:21 p.m.
To be hit is to lose. The 6-4 play must leave a blot. Generally, immediate shots outweigh subsequent shots because every turn lengthens the parlay required for a shot to be left. Most obviously because we don't have to worry about shots we leave two turns from now, whenever our blot is hit one turn from now. But sometimes we can win more often by leaving more immediate shots, if that creates a position so much safer that, if we're missed now, we're much less likely to be hit later. For the more immediately dangerous play to be better, the reduction in later hits has to outweigh the increase in immediate hits. Usually, we need not (and most of us cannot) look further ahead than what happens on our Opponent's next roll and the one after that, since hits after that become increasingly less likely.
Here we have a choice of minimizing shots with 8/4 8/2, or playing either 13/7 13/9 or 13/9 8/2.
8/4 8/2 gets hit 11/36 = 30.55% immediately. The other two plays get hit 13/36 = 36.11% immediately.
Suppose we play 8/4 8/2 and are not hit on our Opponent's first roll. If we look at all of our next 36 rolls and our Opponent's responses, we find that our chance of being hit on our Opponent's second is about 15%. But that is not 15% of all games, but 15% of the 25/36 games in which we were not hit on our Opponent's first roll. So our chance of being hit in two rolls (by my calculations) is
30.55% + (25/36 * 15.2%) = 30.55% + 10.5% = 41.05%
Suppose instead we play 13/7 13/9. We lose 36.11% immediately. That's a lot more -- 5.5% more is a lot. But if we are missed, our position is much safer than after 8/4 8/2. Particularly, notice how differently our rolls 64, 62, 61, 52 and 51 play. It turns out that our chance of being hit in two rolls is
36.11% + (23/36 * 5.47%) = 36.11% + 3.5% = 39.61%
I did a similar calculation for 13/9 8/2 and that play leaves a blot for our Opponent to hit on his second roll slightly more often than after 13/9 13/7. More important is that the play doesn't look right. It doesn't solve the problem of clearing the midpoint, fewer of our followup rolls allow us to solve our second most dangerous problem, which is filling in the 4 point gap, and it appears to make our third biggest problem -- clearing the 9 point -- harder to solve.
So ... 13/7 13/9 should be best here. A clue to realizing that leaving 2/36 more shots might indeed be best is that 8/4 8/2 leaves a naked 9 point with gaps on 8 and 7, in addition to leaving 3 checkers to clear from the midpoint. Whereas after 13/7 13/9, we can hope to clear the 9 point with some help from the made 8 point, and also from a made bar point, if we cover our blot there next roll.
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