Module 5 · Lesson 25 of 39 · Free
Bet sizes as a share of the pot
A bet of half the pot asks the caller to win 25% of the time; a bet the size of the pot asks him for 33.3%. Players speak of bets as shares of the pot because the share, not the number of big blinds, decides what a call must win and how often a bluff must work.
The hand
The turn. 30 bb are in the pot and you hold Q♥ J♥, top pair. You will bet, and you choose how much: a third of the pot is 10 bb, half is 15 bb, two thirds is 20 bb and the pot is 30 bb.
Predict first
You double your bet from half the pot, 15 bb, to the pot, 30 bb. What happens to the share of the pot he must win to call?
- It doubles too, from 25% to 50%
- It rises from 25% to 33.3%
- It stays at 25%: the pot grows as much as the bet
Show the answer
Answer: It rises from 25% to 33.3%
Against 15 bb he calls 15 bb to play for 30 + 15 + 15 = 60 bb: 15 ÷ 60 = 25%. Against 30 bb he calls 30 bb to play for 30 + 30 + 30 = 90 bb: 30 ÷ 90 = 33.3%. His own call goes into the pot too, so his share grows more slowly than your bet.
Working it out
Work out each size in three steps. The bet: half of 30 bb is 15 bb. His price: if he calls, the pot holds 30 + 15 + 15 = 60 bb, and his call is 15 ÷ 60 = 25% of it, so he needs 25% equity. Your bluff: you risk 15 bb to win the 30 bb already there, so it must work 15 ÷ (30 + 15) = 33.3% of the time. A third of the pot, 10 bb, asks him for 10 ÷ 50 = 20% and needs a bluff to work 10 ÷ 40 = 25%. Two thirds, 20 bb, asks for 20 ÷ 70 = 28.6% and needs 20 ÷ 50 = 40%. The pot asks for 30 ÷ 90 = 33.3% and needs 30 ÷ 60 = 50%.
Small bets are cheap for both players: a third of the pot asks the caller for 20% and needs a bluff to work only 1 time in 4. Big bets charge more for the next card and win more when a worse hand calls, but a bluff that big needs more folds: 1 time in 2 for the pot, 2 times in 3 for twice the pot. So choose the size for its job: one that worse hands can still call when you bet for value, one that asks a draw for more than its chance when it must pay (a later lesson works this out), and the smallest that still makes better hands fold when you bluff.
Formula
Caller's price = bet ÷ (pot + 2 × bet). A bluff must work bet ÷ (pot + bet). Half the pot: 15 ÷ 60 = 25% and 15 ÷ 45 = 33.3%
Check your understanding
The pot is 40 bb and you bet three quarters of it. How many bb do you bet?
Show the answer
Answer: 30 bb
40 × 3 ÷ 4 = 30 bb.
He bets 24 bb into a pot of 32 bb. What share of the pot after your call must you win, in %?
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Answer: 30%
If you call, the pot holds 32 + 24 + 24 = 80 bb, and your call is 24 bb of it: 24 ÷ 80 = 30%.
You bluff two thirds of the pot. How often must the bluff work to break even, in %?
Show the answer
Answer: 40%
Say the pot is 3 bb: you bet 2 bb to win 3 bb, so the bluff must work 2 ÷ (3 + 2) = 40% of the time.