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The 'window' that is not a window..

Posted By: Bob Koca
Date: Friday, 25 August 2017, at 12:50 a.m.

In Response To: The 'window' that is not a window.. (sebalotek)

Here are the basic ideas:

The doubling window is based on an assumption that you can choose to cube right now or forever hold the cube. This is rarely the case of course but it leads to straightforward calculations of when to double and when to take (assuming no further cube use). It gives a starting point.

The reason that you could be in this window yet not actually have a correct cube is due to a lack of market losers. If there aren't any at all there is no reason to cube right away. You could always just cube next turn if you wish, and be in the same situation or if your position gets worse decide to not cube and be in a better situation.

If there are market losing sequences then you couldn't always be in the same situation since if you don't cube and then get a market loser you would cash for 1 point but you would rather be in that position with opponent having cube on 2. Those possible regrets need to be balanced though with the chance of getting worse and regretting the cube.

In general terms the closer you are to the cash point, fewer market losing sequences are needed for a correct cube. If you are at the lower ledge of the window then it would need to be an extreme amount of volatility to make the cube correct. Something like a good roll means you win and a bad roll means you lose.

The actual doubling point is very tricky to determine and the computer really does not know where it is. Trading off the regrets of market loss when don't cube and regrets of getting worse when do cube is tricky. Also, how likely one is to get a good efficient cube in if wait now is difficult to take into account. Also the cash point should take into account the opponent's cube power and that is itself not always easy.

One last cool thing. You could even have a correct cube when even below the window. In match play opponent could have less power holding cube on 2 than if cube is centered and the basic window calculation does not account for that extra reason to cube.

The match play book by Kit Woolsey or backgammon Boot Camp by Walter Trice are good for more details.

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