Staked players in a game with the staker

[SA125]

I posted this in the Poker Theory forum but wasn't sure whether or not that was the right forum or not. I'm putting it out here also because this forum was my first thought for where the question could best be answered. I'm hoping the sharp guys here can recognize something in it and offer something tangible.

The scenario is this. I play in a full ring game where one of the players sometimes has a piece of numerous others in the game. The staked players varies from one to three and the piece he has of them varies from 25-50% to maybe 100% of one of them.

Forget about possible collusion. There's definitely soft playing and the potential is obvious but isn't part of the question here.

Is it possible to look at this scenario strictly from a math/EV gambling standpoint and see whether or not the staker has an edge in this game?

To break it down further you can take a typical 3 way pot and say it's a 3 handed game where it's you, the staker and the 50% horse. The horse is playing legit and trying to win. Does the staker have an edge in those scenario's?

All comments appreciated as this is an actual scenario in a live high stakes game I've played a lot in.

[DrVanNostrin]

(I'm assuming the staked players are all winners in the game; thus their true win rates are greater than the aveage player in the game.) If this is the case the staker has a smaller edge than he would if all his players were in different games. It's easy to see that replacing an average player with a staked player reduces the win rate of each player at the table.

The staker will also experience less variance than he would if his players were all in different games. That is because one player's success increases the chances of another player's failure (and vice versa).

[SA125]

Thanks for the reply. So you say he has an edge if the players are good?

He has a 40% chance of being invloved in every pot. Up to a 30% chance if he folds.

I'm thinking that if him and his horses were good players, and they all are, there is a definite edge in the game for the staker. How much, if any, was the question here.

[DrVanNostrin]

It depends on how big the rake is and how good the players are. If the rake is large and the players are mediocre his EV could easily be < 0.

I'm somewhat unclear on what comparison you're interested in. Do you want to know whether it's wise to stake good players so they may sit a game with you?

It depends how much of the player you get. The larger the amount you have the more likely you should be to put him in. If the rake is 1BB/hour the aveage player's WR is -1BB/hour. If you replace an average player with a player who's WR is 1BB/hour it will cost other 9 players at the table 2BB. Each of those 9 nine players is likely to lose 2/9 BB/hour as a result of the switch. If you have 10% of this player you'll lose 2/9 BB/hour when he enters the game and will only get 0.1BB/hour back from staking (you'll lose money on staking). If you had 50% of him you'd still lose 2/9 BB/hour but you'd get 0.5BB/hour back from staking (you'd make money on staking).

This isn't exactly right for a couple of reasons:
1) You'll lose less than the average player as a result of the switch because you know more about the staked player than others do.
2) If the staked player's true win rate was 1BB/hour it will be less than 1BB/hour given that you're in the game (I'm assuming you're also a winning player).
3) It's also dependant on seating. Players who sit near the staked player will suffer a little more as a result of the switch. Those who sit on the opposite side of the table will suffer a little less.

[SA125]

[ QUOTE ]
I'm somewhat unclear on what comparison you're interested in. Do you want to know whether it's wise to stake good players so they may sit a game with you?

[/ QUOTE ]

I don't want to stake anyone. As I said in the OP, I play in a high stakes live game where the staker has a piece of from 1-3 players and the piece ranges from 25%-50%.

I'm asking whether or not it's +EV for him to have pieces of other good players in a full ring game and, conversely, whether or not it's +EV for me to play in it if he does. My gut is telling me it does matter, but I can't put anything quantitative to it. So maybe I'm wrong.

An analogy is a 3 handed game where two of the other players are on the same bankroll. Rather than colluding by forcing you out of pots, they can just "best hand" you. They have an edge on you in that scenario.

Is that somewhat the same scenario where a staker has pieces of players, rather than playing from the same bankroll? If so, to what degree and should it effect the decision to play in the game?

[DrVanNostrin]

[ QUOTE ]
An analogy is a 3 handed game where two of the other players are on the same bankroll. Rather than colluding by forcing you out of pots, they can just "best hand" you. They have an edge on you in that scenario.

[/ QUOTE ]
If they're not working together and they're not better players they don't have an edge here. Their combined edge is the same as it would be if they were playing on seperate rolls.

[rufus]

Basically, unless there's some sort of collusive effect between the two players, the player who's doing the staking is a bit silly for playing against a player that he's also staking. Any pot where the two are up against each other is going to be tilted against the staking player in terms of EV.