+EV theory question

Yesterday a very rare situation occurred to me in a great LP hold’em game. The pot had been capped preflop by me and capped on the flop by me.


Seven of us saw the turn card. I was on the button with the nut straight draw. board was completely rainbow so all my outs were clean although some were likely dead. They all checked to me.


Not counting bluffing or my image/advertising (I understand there could possibly be great benefits image-wise if I bet here and showed my hand later), what conditions would have to exist to make my betting a more profitable play than checking? I am talking strictly about pot odds and implied odds. Or will checking always be the more profitable play (perhaps infinitely more profitable)? What formula is needed to answer this question?


All I am pretty sure about is that if you don’t expect to be checkraised, the play you make really does not matter much in the long run.


sucker

I'm not sure but, were there any homos there? - Louie

BET your balls off. Two reasons....1, possible free card on the turn. This can be a really easy way to save money on days when your cards are falling. Just think, if your hitting lots, betting draws on the flop with bring free cards on the turn. NUMBER 2, If you have a nut straight draw, it usually means you also have an overcard on the flop. Betting the flop may bring the whole field, great, great odds. But if some fold, you may win with the overcard or set up a potential bluff on the Turn and river.

say you have TJ on a board of


2-8-9--4 on the turn, rainbow.


the odds you will make your straight is 38:8 against


46 unknowns, 8 make your straight.


the odds are 4.75:1.


obviously there is enough money in the pot to call all bets and raises.(28 big bets)


you should bet if you expect to get 5+ callers.


you will be making a small profit because the odds are 4.75:1 against, and you have 5+ callers. your hand will be the nuts, so 5 callers is good enough(you need more if there is a chance you hit your hand and lose).


for example, there are 28 big bets in the pot. lets assume there is no betting on the river and you can only win if you hit your straight.


now we figure your expectation for your choices:


if you check the turn you get 8/46 * 28 = 4.9 big bets.


if you bet the turn and get 3 callers you get (8/46 * 31 [the times you win, you win the whole pot + extra turn bets]) + (38/46 * -1 [the times you lose, you lose your turn action]) = 4.56 big bets, so you lose a little money.


if you bet the turn and get 6 callers you get (8/46 * 34) + (38/46 * -1) = 5.08 big bets, a slight profit over checking


if you bet the turn and it somehow gets capped 7 way you get

(8/46 * 52) + (38/46 * -4) = 5.74 big bets


the large pot and the likelihood of getting many callers probably calls for a bet, especially if there is reason to believe pairing one of your overcards is also an out(with a capped flop its not likely).

nf,


Thanks for your help, it's easier than I thought it would be.


So if I got it right, theoretically speaking, it doesn't matter what's in the pot (except for how it will affect the other players). All I need is five or more callers to show an immediate profit, in other words I need to be getting better than 4.75 to 1 on my bet. And even if I only get, say, three callers, but make my hand on the river and can get two or more bets out of them when I bet then, then it's still more profitable than checking if I understand correctly. In real life, either one of the above two scenarios is very likely to happen when I bet the turn here. Combine that with the effect my bet may possibly have on future hands.


Next time I will bet.


Regards, sucker

From the real Louie:


This is a great post. Notice the excellent evaluation strategy of COMPARING the EV of betting vrs checking.


Yes, from a pure bet-for-value perspective the size of the pot is not a direct issue; although the size of the pot indirectly affects your chances (big pots usually mean someone has a good hand) and affects your chances of getting the value calls you need (big pots attract callers).


How many callers you can expect vis-a-vis your chances of winning is, of course, the primary consideration when considering a value bet. But there are other issues at work here: [1] Your presumed overcards MAY win the pot if you snag a pair, and your bet MAY cause someone with stiff over-cards to fold which increases your chances even more (if you have JT you want AJ to fold giving you 2 more outs) [2] With several players calling a capped flop, there is a higher chance that the cards you need are in the other players hands [3] if you check you INCREASE the chances of getting a double bet in on the river when you make your hand [4] you may get check-raised by the other good hand resulting in an undesirable narrowing of the field.


All-in-all I'd bet without hesitation against this many callers.


- Louie

Without knowing the hand, I'd say there is a fair chance you are only drawing to a split. Capped 5 ways with no flush draw means that is almost certain someone else is drawing to your straight 2.


Danny

Hardly. Another player would need to havet the same exact value cards as you to be drawing to the same straight. This is very unlikely, especially in capped pot (are people more likely to play JTo in a capped pot or for just one bet?). The fact that there is no flush draw out there is irrelevant to whether someone has the same straight draw as you (suits and ranks are independent variables).

Actually, calculating your odds of making the straight for one card is highly misleading when figuring out whether a bet is profitable in this situation. The relevant number to find is your odds of making the straight in 2 cards. Because you won't be folding on the turn (very rarely) you will in fact have better than a measly 4.75-1 chance of winning the pot. It's more like 3.25-1 (I'm not exactly sure what it is...).


Another reason to bet the flop other than letting an overcard of yours win by driving out a hand with a better kicker is to knock out players with runner-runner flush draws. Wouldn't it suck if you checked and someone who would have folded catches that runner-runner while you hit your draw?


Reasons to bet:


1. Knock out hands that contain one of your cards but a better kicker so that you might win if you pair.


2. Knock out hands that contain one of your cards so that you win the whole pot if it comes runner runner straight.


3. Knock out hands that might catch runner runner flush in order to beat your straight when you make it.


4. Value (4 callers)


5. Free card on the turn.


6. Possible bluffing opportunity on the turn or river.


Reasons not to bet:


1. You might get check-raised and have only a couple players call.


2. You might be up against a set, in which case your chances of winning are much lower and betting will likely be very expensive (via check-raises and reraises).


3. You might not get as many callers as you would like but this is unlikely and even then it is probably posEV because you might be able to check the turn for a free card.


That's all I can think of right now but regardless, I think betting is clearly correct and you will be making a fairly large mistake by not betting in this situation.

he asked if he should bet on the turn, and it is a rainbow board. there is only one card to come. the pre-flop and flop rounds were capped 7-ways.


the chances of making the straight in 2 cards is:


1-(%miss)


1-(39/47*38/46) or


2.2:1 in 2 cards.

"The fact that there is no flush draw out there is irrelevant to whether someone has the same straight draw as you (suits and ranks are independent variables)."


It is very relevant. These players need to have some reason to put 4 bets in on the flop. If there is no flush draw that eliminates one reason. This makes another reason, namely straight draws, more likely. I dont think it is likely that someone has the same draw as him, but it is possible. It is more likely there are various overcard/gutshot and pair/gutshot draws out that use some of his outs.

Absolutely correct. I misread the original post.

Once again, you are correct. I misread the original post and though it was flop action rather than turn action we were discussing.


Regardless, the chances of an identical straight draw are still pretty unlikely.


I would not bet the turn in this situation. The chances of getting enough callers to make the bet posEV plus the small chance you are drawing to a split means it's pretty likely you will be losing money on a bet in the long run.