Situation: There's a game where each player rolls five dice, comparing totals. They do this until one player rolls the higher number twice in a row. That person wins.
This is a Discord game, so although all the dice one player rolls have the same number of sides, that number can change based on different factors.
Ex.: 5d20 vs. 5d22. 5-100 range vs. 5-110 range.
In addition, in some situations one player can gain an advantage that lets them reroll any and all dice below a certain number (usually but not always 7) as many times as needed until the die is at least that number. So, the range can change from both the minimum and maximum sides.
Ex. 5d20 (rr below 7) vs. 5d22. 35-100 range vs. 5-110 range.
I found another question where the person asked how to compare results between two dice when they each have a different number of sides here: Probability of winning a dice roll when the two players have difference die sizes
That seemed relevant, but on top of having some trouble parsing it (e.g. I know what sigma signs mean, but I've almost never used them, so it'll take time to really understand the formula), I didn't know how using multiple dice might impact things.
In theory, a formula where I can plug in the ranges and find out the odds of either side winning consecutive rolls would be fantastic, but that seems both unrealistic and like it would be over my head if someone did lay one out. I would be fine with just a formula, be it the one at the link or something else, that gives me the odds of each range winning any given roll.
With regards to winning consecutive rolls, I'm pretty sure I can find that by multiplying the odds of the underdog together for two rolls to get their chance of winning (X), then just subtracting 100% - X to get the favorite's odds of winning. The ranges can change with every roll, so this isn't going to be spot-on, but that would also make a formula even harder to create, and this method will get me close enough to where I'm trying to go as long as I can get the % for each side on each single roll.
