Have I been wrong in calculating my outs.....

[Abu Turab]

I've been working through Petriv's book and also read Matros' article on odds in Card Player. Until now I have been doing the following for a flush draw: after the flop 47/9 and after the turn 46/9. But after doing the calcualtion based on Petriv's book, my turn is calc is 1.86/1 vs 4.2/1(47/9) thus I have been pricing myself out of draws. Which is the the correct way to use the calculation?

[Siegmund]

Depends what you are counting.

You have a 38:9 chance to complete your flush on the turn, and another 37:9 chance to complete it on the river (a privilege for which you'll usually be paying an extra big bet.) In other words, no, you aren't miscounting your outs.

However the combined effect of the last two cards is that a four-flush on the flop has 1.86:1 odds of making the flush before the showdown. This means, for instance, you can raise for value on the flop if you are getting 2 or more callers, instead of just calling all the way.

[Mike Haven]

This means, for instance, you can raise for value on the flop if you are getting 2 or more callers, instead of just calling all the way.

Why does it mean that?

[Mike Haven]

You should have been calculating 38/9 and 37/9, or 4.2 to 1 and 4.1 to 1.

[Siegmund]

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Why does it mean that?


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Pot odds tell you when calling is better than folding. They don't tell you anything about whether raising is right, or whether betting is better than checking.

When you have a 4-flush on the flop and have odds to stay in, you expect to be taking down the pot 35% of the time (when your flush comes in.) If you raise and get say 3 callers, you are paying $1 now in exchange for a 35% chance a pot that is $4 larger, a long-run gain of 40 cents.

[Mike Haven]

so let's say it's a 10-20 game and three of us are in for the flop = 30 pot

one bets 10, the other raises to 20 - if i get it right you say we should raise to 30 for value as we are getting 3 to 1 on 20, much better than 1.8 to 1, = 120 pot

but then isn't it the case that when we miss 81 times out of 100 and face a bet of 20 or 40 we are in effect now getting only 110 to our 50, or 150 to our 70, for a 4.1 to 1 shot?

or are you hoping the 19 times out of 100 that we turn a flush, with three flush cards showing on the board, and we don't get beaten by bigger flushes or by boats, we will win enough to make up for those 81 misses and loss of effective odds to catch on the river?

[Siegmund]

In your situation, folding is probably a little bit better than calling (you're getting 6:2 or 7:2 to call now and will be getting 4:1 or 5:1 on the turn), and if you raise the first bettor might fold rather than call two more. The decision is clearer when the flop hasn't already been raised ahead of you.


Let's suppose 3 of you see the flop, it's bet and *called* to you. There is 50 on the table, you can call or raise.

If you call:

3BB on the turn. 19% of the time you'll hit; let's say you are +4BB when that happens. the other 81% of the time, let's say it is bet and folded to you, so you're offered 4:1 to draw again and essentially break even. Your net: you are paying 1SB on the flop to win an average of 0.76 BB = 1.52 SB later. Calling is better than folding, as we know.

If you raise, and everyone calls:

4.5BB on the turn. 19% of the time you will hit, call those +5.5BB profits. 81% of the time let's say it is bet and folded to you and you have 5.5:1 to take another card off, about a +0.3BB position for you. Now you are paying 2SB on the flop to get 1.29BB=2.58SB later. A tiny improvement.

Now let's suppose FOUR people see the flop, and it's bet-call-call to you. 7:1 pot odds.

If you call: 4BB on the turn, 19% chance you hit and win +5BB on average; 81% chance you draw with 5:1 odds, +0.14BB onaverage; net +1.06BB=+2.12SB return on a 1SB investment.

If you raise and it's called around: 6BB on the turn. 19% chance you hit and win +7BB on average; 81% chance you draw with 7:1 odds, +0.52BB on average; net 1.75BB=3.50SB return on 2SB investment.

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Basically there are two decisions going on at each turn: comparing odds against improving on the next card vs. pot odds to decide if calling makes sense, and compaing odds of winning the final pot vs. number of expected callers if you raise to decide if raising makes sense.

[Mike Haven]

i am really trying to follow your calculations, but i keep getting lost, i'm afraid

however, i think that you are including your own money in the winnings you make when you hit on the river as profit

if that's the case, although the money put into the pot on the flop isn't yours any more, neither is it profit to you if you end up winning the pot

i am still not convinced you should raise a draw for value

[Siegmund]

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however, i think that you are including your own money in the winnings you make when you hit on the river as profit


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Yes. I find it simpler to speak of it this way. "I lose $1 65% of the time and win $3 35% of the time" is exactly the same thing as "I pay $1 now for a 35% chance to win $4."

And, frankly, I found the idea of raising draws for value very hard to accept for a long time. The concept of pot equity is very poorly covered in ToP and HPFAP, but discussed in some detail in SSHE. I'd rate it as fully as important as pot odds from a theory standpoint but it seems to figure much less prominently in most books and websites.

[Moonsugar]

you are in the big blind with Ah 2h in a 10 handed game

everyone calls and you check

flop comes Qh 7h 3s

you check

utg bets and all call

you raise for value

i know the example is extreme and there are better ones in the literature just trying to help