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Subject: Initial throw of 2 aces rss

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Craig Blumer
United States
Oshkosh
Wisconsin
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Statistically, what is the best thing to do when you throw 2 aces (1's)? It always seems like a tough choice, take the 200 points or just keep 1 and increase the odds for better rolls next time?

With 2 5's it seems a clearer choice to me, keep one and throw the rest.

 
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(ʇllıʍ)
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Spokane Valley
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By my analysis, the average score for rolling 5 dice at once is 215.51 and the average score for rolling 4 dice at once is 141.32. That would mean keeping one ace and rolling once more would yield an average of 315.51 points while keeping two aces and rolling once more would yield an average of 341.32 points. Therefore, you should keep both aces. And, you are correct in keeping 1 of 2 fives, by a 265.51 to 241.32 margin.

However, this simple analysis only takes into account a single additional roll of the dice. When you roll 5 dice, you have a 7.7% chance of "zilching" and when you roll 4 dice, you have 15.7% chance of "zilching". Obviously, if you do "zilch", you not only score zero points, but you lose the potential to score more points with additional rolls.

So, I think the ultimate answer lies in how much of a risk you are willing take, especially within the context of your current game.
 
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