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Paired Boards
Both players have 30 bb.
Suppose you raise from the button to (3 bb) with pocket JJ and the big blind 3bets to (10 bb).
You assume that the bb 3bets with a range of [AA-22, AK, AQs, AJs, KQs].
option – 4-bet Raise to 30 bb
When you 4-bet, the hands that call you are likely [AA, KK, QQ, AK, AQs]. This represents (6 + 6 + 6 + 16 + 4] or 38 combos. The opponent will fold 56 combos from the range [AA-22, AK, AQs, AJs, KQs].
Because the opponent folds 56 combos and calls 38 combos, the %F = 59%
foldEV = (%fold)(amount win if they fold)
foldEV = (56 combos / (56 combos + 38 combos) * (0.5 bb + 10 bb)
foldEV = (59%) * (10.5 bb) = 6.2 bb
Hand Equity (pre-flop)
— The over-pairs AA – QQ are 80% to win against you — (18 combos)
— The over-cards AK, AQs are 50% to win against you — (20 combos)
%call = (38 combos / (38 combos + 56 combos) = 61%
%win =
— (20% against over-pairs) with 18 / (18 + 20) or 18/38 or 47.4%
— (50% against over-cards) with 20 / (20 + 18) or 20/38 or 52.6%
amount win = (0.5 bb + 30 bb) = 30.5 bb
amount lose = 20 bb
callEV = (%call)[(%win)(amount win) – (%lose)(amount lose)]
against an over-pair (AA, KK, QQ)
callEV = (61%)[(20%)(30.5 bb) – (80%)(20 bb)] * (47.4% weight))
<b style=”background-color: var(–bb-content-background-color); font-family: inherit; font-size: inherit; color: var(–bb-body-text-color);”>callEV = -2.8 bb against over-pairs
against over-cards (AK, AQs)
callEV = (%call)[(%win)(amount win) – (%lose)(amount lose)]
callEV = (61%)[(50%)(30.5 bb) – (50%)(20 bb)] * (52.6% weight))
callEV = 1.7 bb against over-cards
totalEV = foldEV + callEV = (6.2 bb) + (-2.8 bb + 1.7 bb)
totalEV = 5.1 bb
This means, 4-betting all-in against this 3-betting range isn’t bad at these stacks.
option – call and see a flop
Instead after you open to 3 bb, 3-bet to 10 bb, you decide to call 7 bb more with JJ.
Let’s assume the flop is (AA4) and again an assumed 3bet range of [AA-22, AK, AQs, AJs, KQs].
When the flop is AA4,
you’re beaten by these hands [AA, KK, QQ, 44, AK, AQs, AJs] = 37 combos
you’re beating [KQs, TT – 55, 33, 22] = 52 combos
Now, the hands that you’re beating have no reason to invest further on this flop. Some of those hands might c-bet the flop since they have the initiative but their real intentions is to give up if you show interest. If you continue and they don’t hit the Christmas miracle, they will give up with these hands.
Another point is that our opponent might not always c-bet it when they flop trips on a paired board. They clearly have the best hand and their mission with the strongest hands are to figure out how to extract value from weaker hands that are likely strong on this board (like JJ, strong 2 pair). In this spot, the opponent has options to c-bet small, c-bet large, or check to induce. Other hands in this range are not as confident but still ahead of you (KK, QQ). If you were to get aggressive with JJ on this board, hands like KK and QQ would be in a tough spot.
With 20 bb behind for both stacks, the possible lines are to
— check
— c-bet 7 bb
— c-bet 20 bb all in.
If they check, my assumption is that they are very strong or very weak. Hands like AK, AQ will check to induce and hands like 22, 55 will check to give up.
Should you alway bet the pocket JJ when they check and how much of your 20 bb stack should you bet?
If they c-bet 7 bb, my assumption is that they have a mix. The stronger hands (AK – AJ) know they are ahead. The weaker hands (KK, QQ) are not sure but will likely give up if you get aggressive. This smallish bet is designed to extract thin value from hands that might call by disguising it behind hands that can easily bluff and get away with it. By betting 1/3 of your opponents stack on the flop, you can limit their options to push/fold mode. With a hand like JJ on this flop, I’m not sure I like jamming all-in into a big pot when my opponent is betting.
Do you think that c-betting small is better or worse than checking the flop?
If they c-bet 20 bb, the question is what can you beat and would they play it this way? I think most of the hands containing an Ace will want to put more chips in the pot. I’m not so sure KK or QQ will push all in on this flop since you opened for 3 bb and you have still have some ace X combos in your range after calling the 3-bet. This is a very polarized bet that is designed to extract max value when they have it and maximize fold equity when bluffing.
If you have AK and you know your opponent has JJ, what is your go-to-play?
a) check to induce
b) bet small (7 bb)
c) bet all in (20 bb)
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