July 2016 Archives

On South Seas Roll 'Em

The Baron's latest game consisted of up to four turns throwing a pair of dice and cost nine coins to play. After each turn Sir R----- may have elected to stop playing and collect their sum as winnings.
On hearing these rules, it immediately occurred to me that he should only continue the game if he has thrown a sum less than that he might expect to win in future turns.
We can thus reckon the expected winnings before throwing the dice by considering the expected winnings after throwing them, conditional upon the cases of having done better and having done worse than expected in future turns.

I explained this insight to the Baron, but fear I may not have done so with sufficiently clarity since I was struck with the impression that he had not fully understood me. Hopefully I shall do better with this exposition!

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