Strange (and probably stupid) pot size control question

[mvdgaag]

Hi all,

I've come up with a rule of thumb for pot size control, especially for valuebetting draws. I was quite wondered to find out you want to create a bigger pot with 7 outs or more!!! I must be mistaken somewhere in my assumptions.

Assuming a pot sized bet: When you are getting better than 1 to 2 odds (33%) of improving to a winning hand you should bet.

This is, because if you miss it cost you one pot sized bet at the flop ($1), but if you hit you can make a pot sized bet that is 3x as big (pot + bet + call) ($3).

If you are called twice you win $4 more than when you've checked
If you are called once you win $1 more than when you've checked
If you miss you lose $1 more than when you've checked.

- It is 0.33 * $4 - 0.66 * $1 = $0.66 if you get called twice.

- And 0.33 * $1 - 0.66 * $1 = -$0.33 if you get called once.

Assuming your opponent folds twice as often if you have hit than calls. And you always give up the pot is you've missed you are expected to break even -> -2*$0.33 + 1*$0.66 = $0...

Of course this is only one card and you'll need at least 16 outs to get these odds. So this is something we all knew and I'd even raise more often for other reasons.

Now let's take the turn and the river together and see what strange magic appears in the expected value. Where am I mistaken or have I been way too passive all the time?!?

If you bet the pot (whatever happens) up to the river. The pot will be (at least) 9 times bigger at the river than at the flop (pot sized bets, one opponent calling), so if you get called all the way to the river and make your draw along the way you can bet 1/2 pot at the river and hopefully make $18

If you miss: at the turn it'll have cost you $1 and at the river it'll have cost you $4. So if you miss all the way it'll have cost you (at least) $5.

Of course your opponent can fold before the river, but lets assume he has a hand and gets all the way there (worst case scenario). Let's assume he calls to a river bet as often as he folds it (maybe this is where I'm very far off).

You win $18 compared to losing $5 so that is better than 3-1 on your money (if your opponent calls your riverbet).
You win $9 compared to losing $5 which is a bit less than 2-1 (if your opponent folds to your riverbet).

With equal chances on both situations you need on average 2.5 to 1 odds (from flop to river) to break even, which corresponds to 28% or 7 outs (to the absolute nuts). You also give your opponent a chance to fold before you get to the river, which is more reason to bet. If he reraises you it's going to cost a bit more but your river bet (if you hit) will also be larger and it's a bit more likely that he calls that bet.

Another way to look at it: Since the size of the pot tripples everytime you bet and get called by one opponent (pot sized bet) you are always getting two (pot + call) to one (bet) on that money when betting pot sized and being called on the next street. This explains why you can call a pot sized bet with 33% or more chance to win. Why not bet it yourself? In terms of equity on that bet you just gave away the equivalent of 1/3 pot. Do the implied odds make up for this?

[Tjorriemorrie]

Sorry but im new, can you explain the 33%? im getting for say a flush 19% (or 5.22:1) and for open-ended straight 17% (or 5.88:1). So I must have a flush AND straight draw for a total of 15 outs?

It looks like you used 15 outs. that's quite a lot. did you assume pairs as well or only nuttish draws like straights and flushes?
thanks

edit: was just pondering: if i have a straight AND flush draw i'll probably go AI at the level i'm playing, haha

[mvdgaag]

Yes, the first example shows this and it is only about one card to come. I'd probably be allin as well...

[ QUOTE ]
Of course this is only one card and you'll need at least 16 outs to get these odds. So this is something we all knew and I'd even raise more often for other reasons.

[/ QUOTE ]

The strange thing is the second scenario with the turn and river together, if you choose to bet them both all the time you'll only need 7 outs to break even... There must be a mistake somewhere, but I can't find it myself.

[bbartlog]

The only mistake is in your assumptions about how often you can get paid off. While your exact figures are open to question, though, I think the general principle you're describing is valid. It often makes sense to build the pot because you think there's a good chance that a later street will bring you a very favorable situation. Of course, fold equity also plays a role in making betting correct...

[mvdgaag]

Wow, so how many outs to the nuts will be a generally accepted number to be building a pot?

[bbartlog]

Has to be considered opponent-dependent. You need to be playing against someone who calls too much (both before and after you make your draw) instead of folding or raising. But I'd estimate that against really bad players who will call your nuts reliably you can do this with as few as six outs to the nuts, while if you're playing against an aggressive, intelligent opponent who will often raise your bet and/or fold when you make your hand then you need to have ten or so (at which point a lot of your equity comes from them folding to the bet, anyway).

[mvdgaag]

Wow, I'm used to check/callinging my 5-12 out hands in a headsup pot when deep stacked. Is this a big leak? Of course I make cbets when I was the agressor and bluff sometimes at the pot if i was the caller preflop and there is a low coordinated flop, etc. But my standard play is to check call draws where I a bet at this street is not +EV.

For example:

I limp 7h8h. The button bets 3.5BBL, I call.
The flop comes Ah Jh 7c.
My opponent bets 2/3 pot.
I feel another 7 or a heart gives me the best hand.
11 outs: 5-1 odds per card, I check/call.

To the river I have about 44% chance to win. So I put in 50% of the money here, but have approx 45% equity. Assuming my opponent calls a bet itself would be -EV (i'm giving away 56-44 = 8% of the bet), although it might be +EV if I take later streets into account.

[smbruin22]

haven't read the thread closely, but i do think there are mention of it.

betting is probably o.k. heads-up (depending on texture of flop and other factors), but it's not usually to build the pot, it's more to take pot now.

i think you don't want to build the pot with a small # of outs.