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"On-roll advantage" rules of thumb

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12-30-2022 , 08:36 AM

sdfsgf

grinder

Join Date: Aug 2019 Posts: 667

It's common to have positions where both players need to roll one specific number (either to jump a prime or enter from the bar or whatever) and the player who rolls first obviously has an advantage because they get the first crack at it. Are there any rules of thumb for how big of an advantage the on-roll player has in these positions? (I'll spend some time working out the math, but figured this had to have been done before, I just haven't figured out the right keywords to locate it).

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12-30-2022 , 10:09 AM

sdfsgf

grinder

Join Date: Aug 2019 Posts: 667

Actually this worked out relatively cleanly. If both players need to roll a number with probability p, the probability of the on-roll player rolling the number first is just 1/(2-p). So if p = 11/36 (a single number) then the on-roll player rolls it first 59% of the time.

There may be some useful extensions eg needing to roll two numbers before the opponent rolls one.

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