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Match Play. Red leads 10-8 to 13. Should Red redouble? If redoubled, should White take?
Using match equity tables, you can calculate the doubling window for this position. That window turns out to be 77%-85%.
Is Red within that window, then the correct action will be double/take. Using Trice’s formula for this type of position White’s point of last take in a money game would be 38 pips. His adjusted pip count is 43 pips. Each extra pip is worth about 1.5%. Therefore, I estimate White’s winning chances to be 75 + 5x1.5 = 82.5%. The rollout gives 81.4% so I am in the right ballpark.
Thus, this position is double/take. Now all you have to is adjust for the relative strength of the players, but I would only do that if there is huge disparity in the skill levels. Otherwise, I would just ship it as Red. Remember, that in any event a weak White might pass anyway.
You need to understand match equity tables and racing formulae to evaluate this position correctly but that is precisely what the best players are capable of and why they win more matches than their opponents.