Dice Game: 6-sided die vs 20-sided die

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In the discussion about a game involving a 20-sided die versus three 6-sided dice, participants analyze the fairness and expected outcomes based on probability. Both dice sets have the same expected value of 10.5, but the variance differs, with the three 6-sided dice having lower variance. The game’s fairness is questioned, particularly regarding the impact of specific winning numbers; the 20-sided die has winning scores (19 and 20) that cannot be matched by the three 6-sided dice. Simulations suggest that while both sets are equal in average outcomes, the 20-sided die has a slight edge due to its higher maximum potential. Overall, the consensus is that the game is generally fair, but the 20-sided die may be preferable in certain scenarios.
  • #51
This thread seems to have gone wildly off-topic discussing a class of methods that are not appropriate for solving the OP's question, which was easily solved in #6 :sorry:
 
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  • #52
pbuk said:
Your argument is analagous to 'I have to bang in a lot of nails so whenever I need to fix a screw or a pop rivet I reach for the hammer'.
Be careful. I have dealt with plenty of analytical methods in probability and statistics (although I admit that I am rusty).
 
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  • #53
Many thanks to all for writing out the responses. It has been interesting to read about analytical and numerical ways of approaching the problem.
 
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  • #54
Thanks @Master1022 !

This sounds like a good time to close this thread before we get busted for gambling without a license.

Thank you all for contributing here.

Closing this thread now.
 
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