You People Suck at Playing Multi-Way Hands

Go read this week's column and figure out how to stop sucking when you're playing against multiple opponents in the same hand.

Really good post.

Originally Posted by seven-deuce

Really good post.

+1 yep, nice one!

Thanks guys.

Enjoyed the article, attempted to solve the question in OP.

Assuming villains can't raise & can only call.

If the pot is P & our bet size is aP, the two players are called A & B.

Options
1) A & B fold
2) A calls B folds
3) A folds B calls
4) A & B call

EV of each outcome
1) P
2) (0.55)(a+1)P - (0.45)aP
3) (0.55)(a+1)P - (0.45)aP
4) (0.35)(2a+1)P - (0.65)aP

If we say 1 happens W%, 2 X%, 3 Y%, 4 Z% and we know W + X + Y + Z = 1 and each is >= 0

W * P + X * [(0.55)(a+1)P - (0.45)aP] + Y * [(0.55)(a+1)P - (0.45)aP] + Z[(0.35)(2a+1)P - (0.65)aP]

WP + [X+Y][(0.55)(a+1)P - (0.45)aP] + Z[(0.35)(2a+1)P - (0.65)aP]

WP + [X+Y][0.1aP + 0.55P] + Z[0.05aP + 0.35P]

As every variable is > 0 by definition this bet will always be profitable.

Originally Posted by ImSavy

Enjoyed the article, attempted to solve the question in OP.

Assuming villains can't raise & can only call.

If the pot is P & our bet size is aP, the two players are called A & B.

Options
1) A & B fold
2) A calls B folds
3) A folds B calls
4) A & B call

EV of each outcome
1) P
2) (0.55)(a+1)P - (0.45)aP
3) (0.55)(a+1)P - (0.45)aP
4) (0.35)(2a+1)P - (0.65)aP

If we say 1 happens W%, 2 X%, 3 Y%, 4 Z% and we know W + X + Y + Z = 1 and each is >= 0

W * P + X * [(0.55)(a+1)P - (0.45)aP] + Y * [(0.55)(a+1)P - (0.45)aP] + Z[(0.35)(2a+1)P - (0.65)aP]

WP + [X+Y][(0.55)(a+1)P - (0.45)aP] + Z[(0.35)(2a+1)P - (0.65)aP]

WP + [X+Y][0.1aP + 0.55P] + Z[0.05aP + 0.35P]

As every variable is > 0 by definition this bet will always be profitable.

I can very much appreciate your enthusiasm, but for the sake of other players who aren't as inclined for math, I'll say that this is largely overkill. We just need >50 percent against one call and >33 percent against two calls to prove it, etc., like you learn in the article.