Chapter 2 had a moment where it got interesting and then simply moved on: on the turn you were one card short of the flush. In that hand both players checked, so it cost nothing.
Now it costs something. Your opponent bets, and you have to decide — not by feel, but by a price. This chapter shows you how to work it out.
An out is a card that turns your hand into the winning one.
Back to the turn from chapter 2. You hold the ace and king of diamonds, and four cards are on the board — two of them diamonds as well:
There are 7.5 bb in the pot. You are exactly one card short of the flush.
Count, do not estimate:
Nine. That is not an estimate, it is a count: there are thirteen diamonds, four are visible, nine are left.
The rest is division. You see six cards — your two and the four on the board — so 46 are unknown. Nine out of 46 is 19.6 %.
Just under one time in five the river brings the diamond. Four times in five it does not — and that is exactly what happened in chapter 2. The two of clubs came, no diamond, and you lost. That was not a mistake. Needing a card nine times out of ten and not getting it means nothing was done wrong; it simply did not hit.
Nobody works out 19.6 per cent at the table. You do not need to either:
For the nine outs on the turn: 9 × 2 = 18 %. The exact figure is 19.6 % — the rule is a point and a half off, which makes it as precise as a decision at the table needs to be.
If the seven of diamonds had already fallen on the flop, you would have nine outs there with two cards to come: 9 × 4 = 36 %, exactly 35.0 %. That is close enough too.
The rule is why this chapter is useful at all. You can count outs. You can double a number. That is all there is to it.
Now the other half. On the turn there are 7.5 bb in the middle, and your opponent bets 4.
It costs you 4 to stay in. What you can win is what is already there — the 7.5 plus his 4, together 11.5. The question is not “how much is that”, but: how often would I have to win for this call to pay off?
And that is a division. You add 4, and the pot then holds 15.5:
You would need 25.8 %. You have 19.6 %. So fold — and that is the answer that surprises people: a flush draw is not automatically a call. It depends on the price.
Because the price changes with the bet, and with nothing else:
| He bets | You need |
|---|---|
| a quarter of the pot | 16,7 % |
| half the pot | 25,0 % |
| three quarters of the pot | 30,0 % |
| the whole pot | 33,3 % |
These four numbers are the whole chapter. They hold always, at every table, in every hand — it is the same division. Once you know them, all that is left is to count your outs and compare.
If your opponent bet only 2 into the 7.5 instead of 4, it would look different: then you would need 17.4 % and you have 19.6 %. The same draw, the same card, a different price — and the fold turns into a call.
Not every out is a whole out — and sometimes there are more. You counted nine because every diamond brings you the flush. But an ace or a king would also give you a high pair. Whether that counts depends on what he holds — and you cannot see that.
In chapter 2 you saw it in the end: he held the queen of clubs and the jack of hearts, a pair of queens. Against that hand every ace and every king is an out as well:
With 15 outs you need 25.8 % and you have 32.6 %. The fold turns into a call — and all you did was look more closely.
The reverse holds too: your opponent can improve as well, so hitting does not mean winning. This sum is a tool, not an oracle — it tells you whether the price is right, not whether you win. But it is the first decision in poker you can work out instead of feeling your way to, and over a thousand hands that is the whole difference.
Six questions, one answer each. It is the same board as above — look at it while you count instead of relying on memory.
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