Sorry for the ambiguous title.
So I was playing Divinity OS when a question popped into my mind about Probability of winning the RPS game.
I gave myself similar question with the following metrics
A and B have a coin
If it lands Head, A receives $5
If it lands Tails, B receives $2
First to reach $10 wins
By manual labour I reached conclusion that B had 7/64 chance of winning (I'm not sure if it's correct)
My question is how do I generalize this, IE, say there are 2 or 3 people playing with a fair die, they receive some arbitrary but different amounts and first to $x wins
And how to extend it to more number people?