#rotatorposting

[regina-bithyniae]

Probability Question

In "Betrayal at Calth", both players roll a number of custom six-sided dice to see who goes first each round. The relevant dice face are two facings with a "hit" symbol, and one facing with a "critical hit" symbol. The other three facings are irrelevant.

The base rules have you roll four of these. Whoever gets more total hits goes first, and you reroll if you're even. We house-ruled in that crit numbers break ties.

It would seeeeeeem right that if you rolled more dice, the chance of a tie and reroll would fall because there are more differentiated possibilities, but as this is a larger sample size it should also more reliably converge to half your dice being hits, and one sixth being crits. So from 1 to 6, what number of dice rolled minimizes the probability of needing to roll again?

@powermonger you might have interest

[regina-bithyniae]

had a series of 4 SVCs running which had to cross validate and append the avg scores to a dictionary, took like 40 minutes,

they were overwriting one another so I've gotta do it again

gonna go kms

[regina-bithyniae]

I gave my 6d6 another look and found where I got it wrong:

I missed the denominator on number of combinations is r!(n-r)! and instead just used r(n-r)!, which is fine for any case where r is 2 or less, but for the r=3 case it meant I overestimatd by a factor of 2.

Doing probabilities correctly, I find 0.225585938 probability of a tie for 6d6, which is much more like your simulation.

Thanks for running simulations. Looks like at least on our domain, more dice outweighs the LLN effect.

Probability Question

In "Betrayal at Calth", both players roll a number of custom six-sided dice to see who goes first each round. The relevant dice face are two facings with a "hit" symbol, and one facing with a "critical hit" symbol. The other three facings are irrelevant.

The base rules have you roll four of these. Whoever gets more total hits goes first, and you reroll if you're even. We house-ruled in that crit numbers break ties.

It would seeeeeeem right that if you rolled more dice, the chance of a tie and reroll would fall because there are more differentiated possibilities, but as this is a larger sample size it should also more reliably converge to half your dice being hits, and one sixth being crits. So from 1 to 6, what number of dice rolled minimizes the probability of needing to roll again?

@powermonger you might have interest