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  • arw

    July 9, 2020 at 2:49 pm

    <div>You have AK on a A63 rainbow flop.</div>

    Before the flop, the small blind 3-bets your min-raise to 8 bb.

    You call with AK

    Pot Size is about 18 bb.

    On the flop of A63 rainbow, the villain has 36 bb and he decides to lead out 4.5 bb. You have about 77 bb left in your stack and you have 3 options:

    • Fold
      • before you fold, you need to consider the pre-flop range of the opponent. They just 3-bet you from the small blind and c-bet on an ace high flop. Maybe it’s something like (AA, KK, QQ, JJ, TT, 99, 88, 77, AK, AQ, AJ, KQ, QJ, JT) where you can also add some bluffy hands like weak aces, small pairs, and other suited connectors. The villain has enough chips to still play a wider range and isn’t in push/fold mode yet.
        • Does this opponent c-bet 100% of the range on ace high flops?
      • Call
          • calling 4.5 bb instead of raising would help you control the pot size with a one-pair hand. The straight draws are present but the villain rarely has low suited connectors or low cards when he/she 3 bets from the small blind pre-flop.
        • Raise
            • You decided to raise on the flop to about 18 bb or about 1/2 of the villains stack.
              • What hands will call you that you can beat?
              • 87% to win against <b style=”font-family: inherit; font-size: inherit;”>weaker aces like AQ, AJ, AT
              • 85% to win against <b style=”font-family: inherit; font-size: inherit;”>weaker aces w/ straight draws like A5, A4, A2
              • 66% to win against <b style=”font-family: inherit; font-size: inherit;”>straight draw hands like 54… we can ignore 52, 42
            • What hands will call you that have you beat?
              • 2% to win against <b style=”font-family: inherit; font-size: inherit;”>sets like AA, 66, 33
              • 16% to win against <b style=”font-family: inherit; font-size: inherit;”>two pair like A6, A3…we can ignore 63

              It’s a stretch to say that all of these weaker hands will jam over your small raise on the flop. I think that some of them will fold but the math is easiest for me when I look at the combinations.

              • AQ, AJ, AT — each have 8 combos — (2 aces * 4 kickers)
              • A5, A4, A2 — each have 8 combos
              • 54 — this hand has 16 combos…I question whether this hand is even in the pre-flop range.
              • AA — this hand has only 1 combo. You have one ace and another ace is on the flop.
              • 66, 33 — there are <u style=””>3 combos for any set that doesn’t have another blocker.
              • A6, A3 — there are 6 combos — (2 aces * 3 kickers)

              The value range has 19 combinations and is heavily favored by two pair hands where you are 16% to win.

              The bluffing range has about 16 – 24 combinations of strong aces and weak aces with a draw. You are about 86% to win against this range.

              Expected Value

              When you’re up against the value range, you should calculate the expected value. Let’s assume that you’re only 16% to win against these sets and two-pair hands. If you can somehow get your opponent to call less often than 62%, you will have positive expected value. I used this applet to map out the poker hand.


              • Calling on the flop might be the best play. The c-bet range is very wide. By raising, you will narrow that range considerably but only the strongest hands will remain…like two pairs and sets. I’m not sure you are gaining a ton of value by raising here unless there is a decent chance that your opponent will fold the best hand. By calling, you allow your opponent to possibly bluff again with the wider c-bet range that includes (KK, QQ, AJ, AT). Calling also allows you to control the size of the pot when you only have 1 pair.
              • Raising in this spot causes your opponents range to shrink considerably. He/she will call with all the monsters (AA, 66, 33, A6, A3) and likely fold out the medium strength hands like (KK, QQ, AJ, AT) that you want to stick around. The flop doesn’t have a ton of straight draws that connect to your opponents pre-flop action.
              • Folding is not ideal. You have a strong hand but not the nuts. As my boy Walter from Breaking Bad says “Tread Lightly