Hey. I was trying to estimate the average pay from winning a game of Party's SNG Hero, which has a variable element of capturing a bounty. I think I got it, but I wanted to confirm my reasoning is right.

For those who don't know the game is like this. There's 4 players, 1st place gets 3/4 of the prize money. One of the players is randomly assigned to be the bounty target, and whoever takes him out gets the other 1/4 of the money. If you're the target, you get the bounty money by being the last one standing. For simplicity, I'm just considering the case of getting 1st place, and not the off chance of capturing the bounty and then losing.

So my reasoning is this: when you're the one to win the game, half of the time either you or your last remaining opponent will be the target. So you'll get the bounty 1/2 of the time for sure.

If the target was the first one to get taken out, 3 people could have done it. You'll be the bounty winner 1/3 of those times. Same if the target was the second one to go, you get the bounty 1/2 of the time. So,

1P = 3/4 + 1/4(1/2 + 1/4*1/3 + 1/4*1/2)
1P = 3/4 + 17/96
1P = 89/96 or 97.2% the prize money.

Is this correct, or is something in my premise wrong?

Not sure if I understand you perfectly, but you're missing the games when the bounty finishes 3rd or 4th and we have the bounty, right?

No, I considered it. That's the first "1/2" inside the parentheses.