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Real Backgammon

Posted By: Timothy Chow
Date: Tuesday, 27 April 2010, at 2:53 a.m.

In Response To: Real Backgammon (Daniel Murphy)

There are two different questions floating around here. The first is whether you'd rather make a correct play or an incorrect play. That seems to be the point of your suggested Game A and Game B. The second question is whether ten 0.010 errors are equivalent to one 0.100 error.

The second question is what I took you to be asking in your previous message. My answer is that they are equivalent only in terms of equity, not necessarily in terms of the results you will probably observe.

For the first question, I would agree that all other things being equal, it makes sense to make the play with higher equity. However, again the issue of how long it takes for the long run to kick in comes into play. Let's try this one: Would you prefer $1 million in cold hard cash, or a 1 in a million chance to win $2 trillion? The second option has higher equity, but frankly I'd prefer to settle for $1 million unless I get to play the second game on the order of a million times.

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