Fire the 2nd barrel with the nut draw.

Anyone who reads this should be familiar with the concept of semibluffing. For a refreshment course, see: http://www.cardschat.com/semi-bluff.php

The problem with that article, as is the case with virtually all articles and posts I've read about semibluffs, is that it builds on a foundation laid down when limit hold 'em was the game "everyone" played. The math assumes limit hold 'em. And today, when no-limit is all the rage, people still calculate values of semibluffs with the same formulas, but the formula does not translate to no-limit without introducing a fatal flaw: Bet sizes are static in limit hold 'em, but pot-dependent in no-limit. Let me explain:

The "cost" of bluffing the turn - barring the event of a raise - is not anywhere close to the bet size we choose times our risk of being called, which is what the classical math behind a semibluff holds. It's much smaller, which people rarely realize. Best shown with an example:

We 3-bet bluffed preflop in the big blind versus the small blind, and c-bet the flop and are called. On the turn, we have 98s on a 2-6-3-T board, i.e. a gutshot straight draw. Stacks are deep. Our opponent's range isn't terribly wide once he calls the flop, but it can certainly still contain medium pocket pairs (although probably not as low as 66) and hands like AK, maybe AQs. He checks to us. Do we bet?

It's borderline criminal not to fire a second barrel here. If the pot is, say, $35 and we each have $100 left behind, we definitely need to bet. Here's why: For all intents and purposes, we have four outs. Our pair outs have some value versus AK and unimproved pocket pairs, but if we check back the turn and hit a pair, chances are we'll just about break even anyway. Our opponent is going to bet into us on the river some of the time putting us to a tough decision that I don't think we'll get right considerably more often than not (sometimes we fold a winner, sometimes we call with the loser) and if there's a positive dollar value attached to checking back the turn and hitting a pair, it's at least very low.

But now look at what happens if we bet $22 into the $30 pot. With the kind of strength we've shown, it's very doubtful that our opponent will check/raise us with anything less than a set, because our line is very consistent with KK/AA. But for the sake of argument, let's say that we end up getting check/raised 10% of the time, which is decidedly on the high end of things; since I'm building a case FOR betting, so I'm using numbers that work against me to prove the profitability. And when we get check/raised, we're obviously folding.

Let's also assume, which I think is fair, that if we get called on the turn, our opponent isn't intending to fold very many rivers. He called two barrels out of position on a dry board after we 3-bet him preflop. I think he almost certainly intends to call almost any river card. Surely, on average, we'll at least win another half-pot bet the times we river the nuts. At least.

So, assuming he check/raises us 10% of the time, and calls off another halfpot bet on the river the times we get there and we never win the pot if we don't river the nuts, how often does he need to fold for the $22 bet on the turn to be break-even?

22%.

Let the break-even percentage be X. Then

0=0.1*(-22) + (0.9)*((1-X)*((0.91)*(-22) + (0.09)*(22+30+37)) + X*30)

=> X ~ 0.22

I want to repeat that this break-even number is counting with a HIGH risk of him check/raising the turn, and a LOW estimate for how big of a bet we'll be able to win on average when he calls the turn and we get there on the river. For most opponents, I believe both of these numbers will be more favorable for us than I assumed here. The key point here is that if you check back the turn and hit your straight, not only have you given up any chance of winning the pot unimproved, but you've also kept the pot sized down, making it harder for you to extract a really big bet on the river the times you get there. Sure, sometimes you're going to hit the jackpot card while simultaneously your opponent has a set and you stack him, but the combined probabilities of those two events occuring simultaneously are very low. Most of the time, you'll get check/called on the river by JJ. Actually, more than 90% of the time your opponent ends up winning the pot. Not fun.

So, if you have a draw to the nuts on the turn in position, very small chance of winning unimproved, there's plenty of money left behind and your opponent is likely to call three barrels if he calls two, don't check it back. You don't need to succeed with your bluff very often at all for it to be so very worth it.

0=0.1*(-22) + (0.9)*((1-X)*((0.91)*(-22) + (0.09)*(22+30+37)) + X*30)

Exactly what I was thinking

Nice post.

I think as a rule most people tend to not fire a 2nd barrel nearly often enough, especially on boards like this. They know to fire cbets but if they get called tend to shutdown too often with their weak draws because they overestimate their SD equity and underestimate FE. It's nice to see the math so clearly laid out.

Nice post, I'm amazed a mere gutshot makes such a huge difference to the fold equity we need.

Really nice post FP - thanks for demonstrating the math.

Totally agree. One of the things I've been doing a lot lately is looking for TAG regs with a high flop cbet/low turn cbet and calling their pf raises in position with a wide range - they don't seem to adjust well.

Of course, after reading FP's demonstration of the math here, I need to re-evaluate my own turn betting with weak draws, I'm sure I don't bet often enough here myself.

i remember back in my sucky days i used to fire the 2nd barrel way too much, but this post indicates when is a good time to actually do it. nice post etc, i adapted my problem by doing more delayed cbetting

Thanks for the article. I usually go whit the situations..every poker hand is different

can you break down the formula?....
i can see this:
.1 = ten percent raise percentage
.9 = 90 percent not raise (call or fold.)
curious about the (1-x), .91 ???
22 = the bet size in this situation
37 = ???
I.e. can you expand a little more on the formula?.....
secondly not to hijack this thread but is there any way you could point me in the direction of more formulas like this? These are areas I would really like to focus on at this point in my poker playing.

0=0.1*(-22) + (0.9)*((1-X)*((0.91)*(-22) + (0.09)*(22+30+37)) + X*30)

We're looking for the break-even point of X, which is the how often villain will fold. Hence "0 = ..."

0.1 * (-22): This is the cost of being checkraised (we lose $22) multiplied by the times that he checkraises us (10%).

(0.9)*: This is the OTHER 90% of the time, i.e. the times we don't get checkraised.

... ((1-X)*: If he folds X% of the time, he will call (1-X)% of the time.

... (0.91)*(-22): Of the times he calls, we will lose $22 91% of the time, but...

... (0.09)*(22+30+37): ... we will win $22 (the money he puts in on the turn)+ $30 (the original pot on the turn) + $37 (the extra bet we win from him when we get there on the river) the remaining 9% of the time, and finally...

... X*30: ... he will fold X% of the time which will yield us $30 when that happens.

Or differently put:

When he checkraises us, we lose $22. When he doesn't, but calls, we lose $22 91% of the time, but win $22+$30+$37 the rest of the time. When he doesn't checkraise us and folds, we win $30.

Hope that clears it up. It's a Expected Value equation, where I look for the value when EV = 0. You can read (a little) more about that here: http://www.cardschat.com/poker-odds-expected-value.php

This is also a valid strategy at micro stakes. The fold equity here is close to 0 when you are up against one of those loose calling stations, but they will almost never raise you, and if you hit the gutshot, even a weak pair will pay you a pot size bet (or more).