Rank: Advanced Bloo Milk Member
Groups: Member
Joined: 8/3/2020
Posts: 73
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I am trying to calculate the probability of winning initiative if you benefit from Recon, but I'm not sure what happens if you roll a tie. Does the person with Recon get to reroll twice or only once? I solved the probability by summing the conditional probabilities given what the opponent rolls (x) and then considering the case of a tie.
If you roll twice again on ties, the probability is equal to the sum from x = 1 to 20 of (1-(x/20)^2)/20, which I will denote as S. Then the probability of winning initiative = S + 0.05 * S + (0.05)^2 * S + (0.05)^3 * S ... = S/(1-0.05) = 0.675.
If you can not use recon on tie breaks and only role once, the probability = S + 0.5*(0.05) = 0.666
Either way it seems to be about a 2/3 chance.
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