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Big Pot 4/8 Limit w/ AA
Last weekend,
I was dealt KK on my 3rd hand…flopped top set, hit quads on the river.
The next hand was AA. This is the hand I want to talk about.
The next hand was KK again. The flop was AQX and I ran into a weak ace to lose minimum.
First off
— the chances of being dealt AA are (4/52)(3/51) = (12/2652) = 1 in 221
— the chances of being dealt AA or KK (8/52)(3/51) = 24/2652 = 1 in 442
— the chances of being dealt any pair is (52/52)(3/51) = 1 in 17
— the chances of being dealt AA back to back is (1/221)(1/221) = 1 in 48,841
— the chances of being dealt any pair back to back is (1/17)(1/17) = 1 in 289
— the chances of AA, AA, and AA is (1/221)(1/221)(1/221) = 1 in 10.8 million
— the chances of any pair 3x b2b is (1/17)(1/17)(1/17) = 1 in 4913
9 players, $4/8 limit, blinds $2/4
In the AA hand, I was first to act and I had just shown quad kings with KK. Very few people would assume that I have a monster in this spot. I raise to $8, it ends up getting capped 6 ways for $20 each. Pot is $120. Flop is 874 rainbow.
Blinds check to me and I bet $4, call, call, it gets raised to $8 by (alias The Machine), call, I 3 bet to $12, and we go 5 ways to the turn. Pot is $180.
I 3-bet the flop because I feel like my hand (if not good) has backdoor potential. If it pairs the board, I have the best two pair (when they don’t hit trips). I’m dodging flopped sets and flopped straights. All of which would have likely raised. By investing $4 now, I can see if they raise. If they do, I can likely save bets on future streets when I’m behind. Otherwise, I’m building the pot with the best hand.
The turn is a 2 which is likely pretty safe. I still like my hand given these specific players so I bet $8, call, fold, The Machine raises to $16, call, I call, player between calls. The player after the machine is very transparent. I know when he has it and I know when he missed. The player after me and before the machine is someone I don’t know. Pot is $224 and 4 ways.
The river pairs the board with a 4. The board is 87424 w/ no flush draws. I bet $8 with AA on this river and the transparent player calls. He hit trip 4’s on the river. Pot is $240. This isn’t a bad beat story. Instead, let’s evaluate my play on each specific street. Although the river bet of $8 may seem meaningless when the pot is so big, I disagree…a bet is a bet.
QUADS (44) — 1 combo
FULL-HOUSE (84, 74, 42) — 6 combos each — 18 combos
STRAIGHT (56) — 16 combos
SETS (88, 77, 22) — 3 combos each — 9 combos
TWO PAIR (87, 82, 72) — 9 combos each — 27 combos
ONE PAIR (KK, QQ, JJ) — 6 combos each — 18 combos
I’m beating (27 + 18) combos and losing to (9 + 16 + 18 + 1) combos.
Winning against 45 combos and losing to 44 combos.
This result is misleading. I could stop here and tell a story that makes me look good. Instead, consider the opportunity and potential cost of betting into a monster. I don’t think anyone had a strong hand which is why I bet.
Given the pot size, all the hands above will at least call or raise on the river.
Hands like (KK – JJ, and worse two pair) might call the river and never raise. The other hands like (boats, straights, and quads) should raise to $16 costing me an extra bet (which I have to cry call) given the pot is over $200.
When I check/call river,
Call EV = (45/89)($224 + $8) – (44/89)($8) = 113.34
When they bet/call river,
Call EV = (45/89)($224 + $16 + $16) – (44/89)($16) = 121.52
Overall, this was close. If my calculations are right, it looks like I can beat over half of the combos on the river. Betting is slightly better than check calling given the board texture and my hand strength.
Thoughts??
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2 Replies
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I have some nit picky comments on the odds.
— the chances of being dealt AA are (4/52)(3/51) = (12/2652) = 1 in 221
— the chances of being dealt AA or KK (8/52)(3/51) = 24/2652 = 1 in 442
— the chances of being dealt any pair is (52/52)(3/51) = 1 in 17
— the chances of being dealt AA back to back is (1/221)(1/221) = 1 in 48,841
— the chances of being dealt any pair back to back is (1/17)(1/17) = 1 in 289
— the chances of AA, AA, and AA is (1/221)(1/221)(1/221) = 1 in 10.8 million
— the chances of any pair 3x b2b is (1/17)(1/17)(1/17) = 1 in 4913
— the chances of being dealt AA are (4/52)(3/51) = (12/2652) = 1 in 221
— the chances of being dealt AA or KK (8/52)(3/51) = 24/2652 = 1 in 442
— the chances of being dealt any pair is (52/52)(3/51) = 1 in 17
— the chances of being dealt AA back to back is (1/221)(1/221) = 1 in 48,841
— the chances of being dealt any pair back to back is (1/17)(1/17) = 1 in 289
— the chances of AA, AA, and AA is (1/221)(1/221)(1/221) = 1 in 10.8 million
— the chances of any pair 3x b2b is (1/17)(1/17)(1/17) = 1 in 4913These are the odds with a fixed starting point. In other words, what are the odds I get dealt AA in the next three hands. However we rarely care about when the first instance happens. I think it’s more likely to say, once you are dealt AA what are the odd of getting AA the next hand. (1 in 221) What are the odds of getting dealt AA the next two times? (1/221)(1/221) = 1 in 48,841. So on average, if you are dealt AA 50,000 times, you should get dealt AA three times in a row once.
And it’s not coincidence that it will take about 11 million hands to get dealt AA 50,000 times.
This doesn’t discount any of the analysis, but I think it’s an important distinction between starting with a random starting point, or after a certain event has already occurred.
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Limit hold’em ranges are dramatically different than no limit ranges. And people are often (correctly) much more aggressive with weaker holdings or with draws than when compared.
I don’t disagree with any of your analysis, but I think an argument could be made to check allowing weaker hands to bet without risking the check-raise. I think the situation is close either way. That $8 bet probably is plus or minus $1 of actual equity vs checking.
But I think an understanding your opponents tendencies should really be used as the deciding factor.
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