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last roll situation

Posted By: Bob Koca
Date: Tuesday, 8 July 2014, at 2:21 p.m.

In Response To: last roll situation (scotty)

You got the main tricky idea correct. The doubling window is for a last roll situation which you were not in and it does not take into account the additional value of lowering the opponent's cube value.

You made a routine counting small error in the calculations. When counting the misses you errored with number of misses leaving 100010 position (13 misses).

There were two conceptual errors. The first is that non doubles need to be counted twice. What I suggest is to the doubles first and get that total, and then count up misses from non - doubles all together and double that and then add. I get 13 misses from the 11. Then a total of 46 x 2 = 92 misses from non doubles for a total of 105.

The other is that often those misses never get a chance to matter. You need to have one of those 105 out of 1296 sequences but also have opponent miss. Probability of opponent winning is (5/6) x (23/36) + (13/36) x (105/1296).

Just looking at the next roll and comparing the gains and losses of doubling in terms of MWC can short cut most of the above calculations. You are pretty glad to have doubled when you get one of your 6 good rolls and regret doubling (but just by a little bit; essentially you are taking a cube you would rather drop but the drop is very close) on the 30 misses.

If you double you have gained an extra point when you get the 6 good rolls. Doubling is now + 6

If you miss with one of the 30 bad rolls then instead of losing a single point for sure by dropping opponent's cube you are usually taking a double when you have 36% and need 37% (note that if only have a few misses can cash if get one more turn so lump those in with cases where would definitely get off next roll). 1% of the time there is a 4 point swing. 30 x .04 = 1.2 games lost. So far this ignores that we do not have a cash on our worst misses. If we get to 100010 position we will only have a strong cube instead of a cash. If we get a 12 and reach 010010 we will have a double that is an easy take. How much does that adjust things? If we don't even give ourselves any cube power at all then in those two games we essentially took a cube (that we could have dropped if had not initially doubled ourselves) needing 37% and having about 20%. Adding in an extra 2 x .16 x 4 gives an additional 1.28 games lost. for a total of 2.48. 6 > 2.48 so double.

One last note: All points are not worth the same in match play but close enough here to overcome such a big difference.

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