Module 6 · Lesson 30 of 39 · Free
Free cards and protection
Check the turn with the best hand, let him check behind, and the river comes for free: a flush draw makes its flush 9 times in 46, about one time in five. A bet does not stop that card from coming. It makes him pay to see it, and when the price is more than his chance, every call loses him money unless he wins more after he hits.
The hand
The turn. You hold K♣ Q♠, top pair, and 20 bb are in the pot. You think the Calling station has a flush draw, like J♥ T♥: nine hearts would give him the best hand.
Predict first
You bet 10 bb. On the price alone, is his call right?
- No: he needs 25% and has 19.6%
- Yes: a flush draw is worth a call
- Yes: he needs only 19.6%
Show the answer
Answer: No: he needs 25% and has 19.6%
His call of 10 bb plays for a pot of 20 + 10 + 10 = 40 bb, so he needs 10 ÷ 40 = 25%. The river gives him a flush 9 ÷ 46 = 19.6% of the time, less than the price.
Working it out
Compare the two plays. Check, and he sees the river for nothing: 19.6% of the time he makes his flush and the 20 bb pot is his, which costs you 0.196 × 20 ≈ 3.9 bb on average. Bet 10 bb, and the same card costs him 10 bb to see. If he calls, he pays 10 bb and takes the 40 bb pot 19.6% of the time: 0.196 × 40 − 10 ≈ −2.2 bb on average for him, and his loss is your gain. Any bet above 20 × 9 ÷ (46 − 2 × 9) = 6.4 bb, about a third of the pot, makes his call a mistake on the price alone.
Betting a hand that is ahead so that draws must pay for their cards, or fold, is called protecting it. Each draw needs its own size on the turn: a gutshot, 4 outs, is priced out by any bet above 10.5% of the pot; an open-ended straight draw, 8 outs, above 26.7%; a flush draw, 9 outs, above 32.1%; a flush draw with an open-ended straight draw, 15 outs, only above 93.8%, almost the whole pot. If he can win more on the river when he hits, he can call a little more, his implied odds. And when you are the one drawing, take the free card when he offers it: check behind and see the next card for nothing.
Formula
Break-even bet against a draw on the turn = pot × outs ÷ (46 − 2 × outs): 20 × 9 ÷ 28 = 6.4 bb
Check your understanding
On the turn he has an open-ended straight draw, 8 outs. You check and he checks behind. How often does the river give him his straight, in %?
Show the answer
Answer: 17.4%
8 ÷ 46 = 17.4%.
You bet 20 bb into a pot of 30 bb on the turn. What share of the pot must his call win to break even, in %?
Show the answer
Answer: 28.6%
If he calls, the pot holds 30 + 20 + 20 = 70 bb, and his call is 20 bb of it: 20 ÷ 70 = 28.6%.
On the turn the pot is 30 bb and he has a gutshot, 4 outs. From what bet is his call a mistake on the price alone, in bb?
Show the answer
Answer: 3.16 bb
30 × 4 ÷ (46 − 2 × 4) = 120 ÷ 38 = 3.16 bb. A bigger bet asks him for more than his 4 ÷ 46 = 8.7%.