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Thursday, January 15, 2009

Aha moment

Lying in bed tonight, thinking about poker and how I keep paying off calling stations who hit their draw. I asked myself a simple question: What would I need to charge someone on the street before to be neutral EV if I paid off their made flush/straight river bet.

After fooling with numbers, I came to a startling conclusion that I was way underestimating implied odds and the so-called fish/calling stations that I often was angry with (calling my almost pot size flop bets!) had very good implied odds to do so.

Let’s play out a hand with bet sizes. Let’s, for now, say that the bet sizes are 2/3 pot always. And see how that bet size deals with implied odds.

Preflop: Hero bets 3.5bb. Villain calls 3.5bb

Flop: (pot 7bb) Hero bets 4.7bb. Villain calls 4.7bb.

Turn: (pot 16.4bb) Hero bets 11bb. Villain calls 11bb.

River: (pot 38.4bb)

So on the flop our Hero bets a standard 2/3 pot size bet. Villian has a flush draw and will hit his flush 1 in 6 times. He will MISS 5 times and he will HIT 1 time. How much does he need to win that 1 time to make up for the 5 times he missed? The answer surprised me.

Cost of Misses: 5 x 4.7 = 23.5

So when he hits, he needs to win this much back to be neutral in EV. But wait, the one time he does call and hit it, there was already 7bb in the pot, plus the Hero’s 4.7bb. So we must subtract that from what he needs to bet and win in the future streets.

23.5 – 7 – 4.7 = 11.8

He needs to bet and win 11.8bb more. Go back and look at the turn pot size. It’s already at 16.4bb. And he has two streets to try to win 11.8bb.

Let’s say Villian called the flop bet and missed on the turn and now faces the Hero’s 11bb bet. Using the same math let’s find out what he would need to earn on the river to justify the call.

Miss: 5 x 11 = 55

55 – 11 – 16.4 = 27.6

With the river pot size at 38.4, this is very reasonable, but Villian will only have 1 street to get his full value. If the villain hits his flush and you pay off more than this number, Villian has made extra money off you from his implied odds motivated call on the turn.

In the examples above I did the calculations assuming there was a 2/3rds pot size bet. But what happens if you charge them more?

Lets say it’s the turn again, and this time, you decide to bet 13 into 16.4, instead of 11.

Miss: 5 x 13 = 65

65 – 13 – 16.4 = 35.6

It turns out there is a good short cut to estimate:

Villain needs to bet the same percentage of the pot on the current street as Hero did on the previous street. So that means if you bet half pot on the turn. Villain would need to bet and win half pot on the river to make his call neutral.


If you are protecting:

1. There is so much implied odds during the flop (because they have 2 streets of implied odds) that protecting it is more difficult than it’s worth since by betting pot or over betting will get folds from hands dominated or weaker one pair hands. Just bet a moderate amount.
2. The turn is actually the most crucial street in planning because it sets up all the justification for folding or calling on the river. Preflop and flop is the time for speculation and mixing up of play and the mistakes are minimal. But once you get to the turn, it’s business time.

If you are drawing

1. On the flop, if you have a good draw you can call really large bets, even pot size. If the player is really bad, you probably can call overbets. You really just need to hit it that one time and then you have two streets of value to win it back.

This is the MAIN point of my realization is a formula similar to calling with pocket pairs preflop if you think you can win 10x your call:

2. Call with your draw (this goes for flush and OESD) when you believe you can make back the same percentage of the following street. For example, call a pot size flop bet if you think you can win the turn’s pot size (from the turn AND river). Or call a 3/4th pot size flop bet if you can win 3/4ths of the turn’s pot size eventually.

If flop pot is 10 and they bet 8 (4/5ths). Call if you think you can win 21 additional bb (pot = 28) after the turn AND river are done. Not too difficult in position.

2a) You can make adjustments if you have more or less outs. This is an example with 8 outs. This is why with even only overcards, a flop call can still be very profitable still if you are sure that they are all clean outs. This is why “fishes” who call with bottom pair vs me when I have tptk can still make a healthy profit from me when they hit.

2b) This is why pairs and suited connectors have so much value in position.

Tomorrow when I wake up I'm going to see if 6 outs (just over cards) and what the rule is for them, if there is a nice neat shortcut to see for them.

EDIT 1: azn cutie alerted me that for FD it's 1/5 times, which is even better for the drawer.
EDIT 2: if you have just overcards its not a 1:1, but instead approximately a 1 : 1.5. You can call with your overcards (when you're sure they are clean outs) if you can win 1.5 times the percentage of the following street's pot size, after both the turn and river are done.

posted by joe | permalink | 1 comments


At 5:53 AM, Blogger Azn_Cutie said...

Hey Joe,
It's nice to see you thinking so much about the game. Just a few points:

-9 out draws like flush draws are going to get there 1 in 5 times, not 1 in 6 (~20% to hit on the river), 8 out draws like OESD draws are going to hit about 18% of the time, or 1 in 5.5 times.

-This point you make:

Cost of Misses: 5 x 4.7 = 23.5

His "cost" of missing is actually significantly higher than 4.7BB. He is probably going to incur cost calling a sizeable bet on the turn if he opts to call 4.7BB on the flop. Thus, the call of 4.7BB is actually implicity higher because it prices him into larger bets later when he is a bigger dog.

This is kind of a weird concept and Barry Greenstein describes it well. The point is you cannot look at bets at individual streets in relation to pot odds strictly unless all the money is going in because there is always a higher implicit cost associated with calling. By getting a good price on earlier streets, you are just forcing yourself into being priced in for bigger bets in later streets.

This is the thread that BG talks about it in:


If you are having trouble with paying off draws that get there, one thing to consider might be checking the turn more often, which sounds counterintuitive at first.

I don't know about the players you're up against, but full ring plays generally tighter than 6max and the hand ranges are a lot more polarized. It's tough to get value on all 3 streets when you flop a big hand. Checking turn controls pot size for your 1pair type hands and gets you an extra street of value on the river from mediocre hands and busted draws. The added benefit too is when the draws do get there, you can pay off smaller bets that don't hurt you quite as much. Once again, this may not quite be applicable to your 6max games since the bluff frequency is probably a lot higher and you can get value more easily from strong hands.

Interesting post though, I like the way you're thinking. I feel like I explained this in a really convoluted way, sorry.


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