Author Topic: Dice: Mechanical Variations and Statistics  (Read 2067 times)

Offline Bauglir

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Dice: Mechanical Variations and Statistics
« on: November 10, 2012, 01:33:55 AM »
Just a sort of general thread for discussing the impact different ways of rolling dice can have on the way a game plays out, and for asking questions about how the statistics play out in some situations.

Starter question: Let's assuming you're building a system with variable dice size and exploding dice (if you roll max, roll again and add the result to the original roll). Is there a situation in which the d2 is worse than the d3, if you can only keep some number of dice (finding the sum thereof)? My current empirical results (running from a roll of 1 die to 10, keeping only one) suggest that there is not. Currently debugging the program, which I somehow broke since the last run, to get higher numbers of kept dice.

If you keep more than one of the dice you roll, you do better with d3s. Hypothesis holds only with 1 die kept.
« Last Edit: November 10, 2012, 01:49:19 AM by Bauglir »

Offline Garryl

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Re: Dice: Mechanical Variations and Statistics
« Reply #1 on: November 10, 2012, 02:29:50 AM »
Exploding dice means that you end on a random non-max value, then add some multiple of the max value. The ending value is evenly distributed (for single die expressions; a hypothetical 2d4 for example where you only rerolled if both came up 4 would have a different distribution, of course), so that simplifies the math a bit. It's that multiple of the max value that's the fun part. You have a 1/N chance of exploding (adding N), that 1/N explosion itself has a 1/N chance of exploding (adding another N on top), and so on and so forth.

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Offline Bauglir

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Re: Dice: Mechanical Variations and Statistics
« Reply #2 on: November 10, 2012, 02:40:00 AM »
Ah, hm, interesting. I just realized I'm not even testing the question I asked in the OP - my test currently provides the odds of getting at least 15 with a given set of dice, so all I'm answering here is which die has a shallower distribution (and therefore a better chance of a roll winding up way on an extreme).