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What is the lowest winning % for Too good?

Posted By: Rick Janowski
Date: Wednesday, 10 July 2013, at 1:43 a.m.

In Response To: What is the lowest winning % for Too good? (rambiz)

Please clarify which equity you are talking about. If you mean cubeful equity taking into account cube vig, then clearly you are correct. However, if you mean cubeless equity, ie, equity from a dead cube, then I am sure you are mistaken. Consider the rollout data from Xavier's position. Although the rollout indicates the position to be marginally too good, the cubeless equity at 0.964 is less than the value of the cube. Although there isn't much cube vig in this or mochy's example there is still some, and this will have the effect of reducing the too good point cubeless equity below 1.000, in a similar way as how cube vig means its possible to take positions with cubeless equity considerably less than -0.5 (ie, cubeless equity than -1.000 holding a 2 cube). Other more natural too good positions may well have greater cube vig than the two examples in these threads.

I agree that cubeless winning probability values such as 3/8, 4/9 or 1/2 are completely unrealistic but that is because it is impossible to find positions where W is close to 3 that still lose enough games to be close to these lower probabilities. To lose from such high backgammon rate positions it is neccessary to be hit in the bearoff and then contained. Because when hit it is highly likely that many men have already be borne off (otherwise the backammon percentage wont be that high) it is usually neccessary to contain, blockade and close out the hit checker (with many men still in his home board) before then bearing off sufficient men to make an efficient redouble (unless a second checker is sent back). This means that in those games where a checker is hit there will be a significant proportion of games still won (could easily be half of the games) but with a significantly reduced gammon and backgammon rate. Consequently the overall average gammon/backgammon rates will cause W to be significantly less than 3, with a value nearer 2 much more likely.

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