[binkley]

The fact that you believe that this wasn’t an angle means that the middle position player meant to 3bet. Any 3bet of an UTG open indicates strength. Doing it from middle position shows more strength than if it can from CO for example. Both players have strong uncapped ranges when the action gets to you. AQo doesn’t feel strong enough to shove in this situation.

3betting in live play isn’t as common as online. Live players are not as practiced in 3betting and may use non-standard sizes and ranges. I think it’s very risky to use your observation of open raise sizing to guess the meaning of the player’s 3bets.

[arw]

@Binkley @Stoyvind

This seems like a shove to me but it’s also very close.

1) By shoving, you will win (0.5+1.0+2.5+2.5) = 6.5 bb if both opponents fold. A stack increase of close to 50%.

2) You would be offering direct pot odds of (20.5 / 11.5) = (1.8 to 1) because your opponent needs to call (14 bb – 2.5 bb) = 11.5 bb to win (6.5 bb + 14 bb) = 20.5 bb. To break-even, the opponent would need to win about 35.7% = (1 / 2.8).

3) Find the %call and %fold when you shove.

Assume that the utg opener folds if you shove.

Assume the accidental limper wanted to 3-bet with:

——– has a monster (AA, KK, QQ) — (3 + 6 + 3 = 12 combos)

——– has a smaller pair (JJ – 22) — (6 * 10 = 60 combos)

——– has a stronger ace (AK) — (12 combos)

——– has a weaker ace (AJ, AT) — (12 * 2 = 24 combos)

——– has speculative hands (KJ, JT, T9) — (16 * 3 = 48 combos)

Identify which of these hands will call a shove.

My best guess is something like:

——– AA, KK, QQ, JJ, TT, 99, AK, AJ, KJ

——– (3 + 6 + 3 + 6 + 6 + 6 + 12 + 12 + 16) = 70 combos

This means that the opponent will 3 bet with (12 + 60 + 12 + 24 + 48) = 154 combos and will only call with 70 combos.

The %call is 45% (70 / 154) and the %fold is 55% when you shove.

Calculate the hand equity

— AQ vs. AA = 12%

— AQ vs. KK = 32%

— AQ vs. QQ = 33%

— AQ vs. JJ = 46%

— AQ vs. 22 = 49%

— AQ vs. AK = 27%

— AQ vs. AJ = 68%

— AQ vs. KJ = 60%

— AQ vs. JT = 61%

4) Find the Expected Value

foldEV = (%fold)(amount win by shoving)

foldEV = (54%)(0.5 + 1.0 + 2.5 + 2.5) = (0.54)(6.5 bb) = 3.51

callEV = (%call)[(%win)(amount win) – (%lose)(amount lose)]

callEV vs AA = (45%)[(12%)(6.5 bb + 11.5 bb) – (88%)(14 bb)] = -4.57

callEV vs KK = (45%)[(32%)(18 bb) – (68%)(14 bb)] = -1.69

callEV vs QQ = (45%)[(33%)(18 bb) – (67%)(14 bb)] = -1.55

callEV vs JJ = (45%)[(46%)(18 bb) – (54%)(14 bb)] = 0.324

callEV vs TT = (45%)[(46%)(18 bb) – (54%)(14 bb)] = 0.324

callEV vs 99 = (45%)[(46%)(18 bb) – (54%)(14 bb)] = 0.324

callEV vs AK = (45%)[(27%)(18 bb) – (73%)(14 bb)] = -2.41

callEV vs AJ = (45%)[(68%)(18 bb) – (32%)(14 bb)] = 3.49

callEV vs KJ = (45%)[(60%)(18 bb) – (40%)(14 bb)] = 2.34

foldEV = 3.51

positiveEV = 2.34 + 3.49 + 0.324 * 3 = 6.802

negativeEV = -4.57 – 1.69 – 1.55 – 2.41 = -10.22

totalEV = (3.51 + 6.80 – 10.22) = 0.092 bb

Based on my assumptions and calculations, this seems like a marginal shove.

[binkley]

I was guessing that the accidental caller would be 3betting with a tighter range. This decreases a lot of V auto-folds. Would V really want to min 3bet with pairs 66 through 22? I think not, but maybe I’m projecting my own strategies.

[stoyvind]

Thanks for your interesting and thorough comments! Much appreciated.

I assume that players at my card room are not properly balanced (and this player in particular), so I would be guessing that he had a narrower range (AA-99; AQo, ATs, KQs). This gives me about 40% equity. In hindsight, I have come to the conclusion that I should have folded and waited for a better situation. I am also going to test @Binkley ‘s observation about the 3-bets, because I suspect that it is correct that frequencies and sizings are different than in on-line games.

[arw]

In the villains spot with 22 – 66, I think he might 3-bet with hopes of getting heads-up and finding out where he/she is at. By calling the 2.5 bb with a small pocket pair, you’re looking to flop a set or usually fold and you’re giving others a chance to raise you out. At a final table, my move is to 3-bet these small pocket pairs or fold them. I think a lot of players call with their small pairs here, I would do otherwise in this spot.

If you assume:

AQ vs. (AA-99; AQo, ATs, KQs)

combos

big pocket pairs — AA, KK, QQ = 12 combos

small pocket pairs — JJ, TT, 99 = 18 combos

better aces (AK) — 12 combos

chop aces (AQ) — 6 combos

suited aces (AJs, ATs) — 12 combos * 2

suited king (KQs) — 3 combos — (since you have AQo, you block one)

You’re losing to 42 / 75 = 56% of the combos

You’re beating 27 / 75 = 36% of the combos

You will chop 6 / 75 = 8% of the combos

hand equity and EV

foldEV = (1 – %c)(6.5 bb)

— AQ vs. AA = 12% — callEV = (%c)[(12%)(18 bb) – (88%)(14 bb)] = (-10.16c)

— AQ vs. KK = 32% — callEV = (%c)[(32%)(18 bb) – (68%)(14 bb)] = (-3.76c)

— AQ vs. QQ = 33% — callEV = (%c)[(33%)(18 bb) – (67%)(14 bb)] = (-3.44c)

— AQ vs. JJ = 46% — callEV = (%c)[(46%)(18 bb) – (54%)(14 bb)] = (-0.72c)

— AQ vs. TT = 46% — callEV = (%c)[(46%)(18 bb) – (54%)(14 bb)] = (-0.72c)

— AQ vs. AK = 27% — callEV = (%c)[(27%)(18 bb) – (73%)(14 bb)] = (-5.36c)

— AQ vs. AJ = 68% — callEV = (%c)[(68%)(18 bb) – (32%)(14 bb)] = (+7.76c)

— AQ vs. AT = 68% — callEV = (%c)[(68%)(18 bb) – (32%)(14 bb)] = (+7.76c)

— AQ vs. KQ = 68% — callEV = (%c)[(68%)(18 bb) – (32%)(14 bb)] = (+7.76c)

-0.88c

Your AQ has an overall -0.88 weight on your Call EV against this range.

Thus,

When they always call (c=1)

foldEV = (0%)(6.5 bb) = 0

callEV = (100%)(-0.88) =

When they call 75% of the time

foldEV = (25%)(6.5 bb) = 1.625 bb

callEV = (75%)(-0.88) = -0.66 bb

When they call 50% of the time

foldEV = (50%)(6.5 bb) = 3.25 bb

callEV = (50%)(-0.88) = -0.44 bb

[stoyvind]

Thanks again! There is so much to wrap my head around in these numbers 😉

[arw]

Sorry,

The numbers can get overwhelming but it’s how I breakdown hands. It makes me consider every pathway of the decision tree and hopefully lead to better assumptions & estimates.

[stoyvind]

Not at all! It was really interesting to see how the hand can be analyzed. Thanks a lot!

[fivebyfive]

My answer here really depends on the table dynamic. 9 left, 5 paid. What do the other stacks look like? Is 14bb really short, average, above average? How many stacks do we cover?

If I’m the absolute shortie, with everyone else 20bb+, we’re still too far from the bubble for me to shut down and try to squeeze into the money. This is too strong a holding and since we’re 4 off the money with 9 left, ICM isn’t that big of a factor yet. I’m getting my chips in the middle.

If there are some short stacks below me or a bunch of 12-16bb stacks, now ICM is starting to play a factor (even with the same number of spots before the bubble). So a fold gets more tempting, even so I suspect this is a marginal shove in a calculator. But still, in this spot, I could more justify a fold.

If there is this one big 35bb stack, us at 14bb, and the rest of the table is really short (say all <10bb), this is a snap fold.

[stoyvind]

What a treat it has been to post for the first time! Great, in-depth comments in the forum and even a whole podcast episode about the hand. Wow! I have learned a lot from this. Thanks a lot!

Results: The MP-player had a pair of tens and knocked me out

[jim]

Thanks for listening, @Stoyvind and welcome to the community!