F Paulsson
euro love
Silver Level
Anyone who reads this should be familiar with the concept of semibluffing. For a refreshment course, see: https://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.
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.
