• Bronze
Joined: 15.06.2009
[Edit: Intro + fixed link + emphasizing key text]
I may be incorrect. That has happened before. But if I am correct, then I am correct by quite some margin. It would be nice if some guru could have a look at the article and the rest of my post.
[End Edit]

I believe that there is an error in the section "When exactly is a river bet profitable?". In particular, when we are out of position, the logic fails a bit in my opinion.

The context: We are out of position.
Our read (read 1) is that if we check, then our opponent will bet if and only if he has us beat.

The question: Is a bet better than a check-fold?

The article claims that the anwer depends on the calling range of the opponent.
I too claim that the anwer depends on the calling range of the opponent, so all is well so far.

The article then claims that if the opponent calls and then loses with a probabiliy p that greater than (bet size/pot size in bets), then we should bet.

Our read is this (read 2): He will call with every hand (b of those) that he would have bet with had we checked. He will also call with c of the hands that he would have checked behind had we checked.
Moreover (read 3): Our opponent will not raise if we bet period.

I claim that our bet is profitable in this situation if and only if the probability p as defined above is greater than 1/2.

Statement: We beat the c hands and lose to the b hands.
[You can't argue with this. It is consistent with our original read 1 and read 2 about what happens if we check.].

My claim: We should bet if and only if c>b. The size of the pot is irrelevant in this situation.

It is a different matter when our bet will make hands fold that would originally have bet (or more generally hands that beat us) but this simply is not the case here.

One could speculate about the origins of the reasoning in the article (or better, ask cornolio). From the opponents perspective, the pot size is involved. He should base his call decisions based on the pot size. We should still ignore the pot size since we are not bluffing here. We are making a thin value bet.

To be specific: The article presents an example where we have KK oop. There is an A on the board. The action goes bet-call (flop), bet-call (turn).
In the article it is estimated that the opponent will call with all Ax remaining in his range (AQ+), and also with QQ. [He will also bet all A if we check and check worse hands if we check.] The article says (correctly probably) that we lose 4/5 if we bet, but maintain that the bet is correct because the pot is large.

Sure, betting is better than checking and calling. But checking and folding is best given our reads.

/Johan =
• 4 replies
• Bronze
Joined: 15.06.2009
In the real world, it is very hard to get off KK in a heads up pot.

It should thus be mentioned that if you don't have the guts to check and fold (even though you trust your reads), then you should bet-fold which is cheaper than check-calling. If you don't trust your ability to fold to a raise, then the check-call might be cheaper than a bet-call.

But this is not what that section in the article is about really. It's about wheter betting (and presumably folding) is better than checking and folding given our reads. It is not.

/Johan =
• Bronze
Joined: 15.06.2009
If your primary line of though is "I am not folding" and "My opponent will bet if i check if and only if he beats me" and "My opponent is not raising if I bet", then you should bet if there is a single hand that you beat that would have checked behind, had you checked, that will call.

This is even looser (thinner) than in the article and definitly thinner than I argue in post#1 (where the primary line of thought is different). Note that the pot size still doesn't enter. This is due to the fact that the primary line of thought here is internally inconsistent (rather, it is, taken as a logical statement, decidedy false).

If the rake is taken into consideration, then the extremely thin bets should go out. If your future image is a concern then you have a desicion to make based on the meta-game wheter to bet extremely thinly.

/Johan =
• Global
Joined: 23.11.2009

In the interest of time, lets just re-evaluate each decision made in the example for When exactly is a river bet profitable?.

For instance, if the pot is 9 BB big before your bet on the river and the opponent calls better hands in 60% of the cases, calls worse hands in 20% of the cases and folds worse hands in 20% of the cases, you still have to bet.

Recall that: EV is the SUM of the result of each event * the probability of each event.

So from Corns example, when our opponent bets we fold and when he checks we win (because he bets all hands better than ours). He has better hands 60% of the time on the river. Therefore:

EV(check/fold) = Result(check) * Probability (check) + Result(bet)*Probability(bet)

EV(check/fold) = 9*(1-0.6) + 0*(0.6)
EV(check/fold) = 3.6

Again, in Corns example, we win 10 bets when called and win. This happens 20% of the time when we bet. When we lose we always lose 1 bet because he never raises us. This happens 60% of the time when we bet. When he folds we win 9 bets and that happens 20% of the time. Therefore:

EV(bet) = R(call&win) * P(call&Win) + R(call&Lose) * P(call&Lose) + R(Fold) * P(fold)

EV(bet) = 10*(.2) + (-1)*(.6) + 9*(.2)
EV(bet) = 3.2

Check/Fold is higher EV than betting in his example.
• Bronze
Joined: 22.09.2010
If you x/f with KK in that had I want to be on every table you are becasue you're check-folding everything in your range which doesn't hit the Ace which is way too many hands in a pot that big.

So really I'm taking issue with the original assumptions as well as the mathematics, becasue in today's games I think the assumptions are pretty much false, the fact our opponent hasn't raised us at any point despite 3-betting a MP raise and there being an Ace on the board pretty much locks me into the fact he doesn't have a big Ace so I'd actually lean way more towards this being a bet for value than otherwise.

Of course someone super good will recognize this and maybe even delay action until the River with a hand like AK or AQ in which case we are probably bet/folding the river (Since KK/QQ is probably the bottom of our V-Bet range off the top of my head) but either way I don't believe I'm a fan of checking this river with KK.

To me this hand is a really straightforward bet for value, if we had TT this might be close.

The size of the pot in this case means pretty much everything in terms of protecting yourself from being exploitable. If you check and he bets you will be getting almost 10-1 to see whether your hand is good or not, that means folding the bottom 9% of your capping range which here probably involves KQs and 88 or something along those lines, KK is way too strong.

If you CAN make these assumptions about your opponent then you have a MEGA-read in today's games and therefore you take the correct exploitable line as displayed by dats but otherwise I'm pretty sure this is a super easy VB