Big Hands and Keeping a Clear Head

One of the biggest challenges for amateur players is maintaining an emotionless approach when picking up a huge hand. I cannot count how many times I've seen someone pick up a premium hand and play with little to no regard for the actions of the other players at the table. Playing live gives some insight into the mental state of these players and their thought process goes something like this:

To piggyback on my post from Tuesday, if and when they end up losing their loss is often followed by a lamentation about one or more of A) their terrible luck, B) the inconceivable play of their opponent(s), and C) how they had "no choice" but to play the hand the way they did. "C" is where large amounts of money are needlessly lost. To demonstrate, let's look at a hand I played a few days ago:

Seat 1: Donzo ($50.85 in chips)
Seat 2: UTGplus1 ($39.82 in chips)
Seat 3: UTGplus2 ($70.73 in chips)
Seat 4: Dealer ($52.99 in chips)
Seat 5: Small Blind ($68.21 in chips)
Seat 6: Big Blind ($50.50 in chips)
Small Blind: posts small blind $0.25
Big Blind: posts big blind $0.50
*** HOLE CARDS ***
Dealt to Donzo [Ac Ah]
Donzo: raises $1.50 to $1.50
UTGplus1: calls $1.50
UTGplus2: calls $1.50
Dealer: folds
Small Blind: calls $1.25
Big Blind: calls $1
*** FLOP *** [3s 7d 4c]
Small Blind: checks
Big Blind: checks
Donzo: bets $4.50
UTGplus1: folds
UTGplus2: calls $4.50
Small Blind: folds
Big Blind: folds

We're dealt aces UTG and make a standard 3x raise. Four people call, which is more than we're hoping to see, but we're still the overwhelming favorite heading into the flop.

The flop comes 374 rainbow (all different suits) and the blinds check to us. Although this is a low flop that initially looks ideal, it's actually not great for our hand because A) there are no larger pairs that could have hit, meaning hands that pair the board are going to have a hard time paying us off, B) there are no potential flush draws, and C) there are only gut shot straight draws, as 56 already has a straight on the flop. That said, we're still usually going to have the best hand and want to bet to get value from hands like A7, a pair with a gutshot (e.g. 45), and inferior overpairs to the board. We bet $4.50 into $7.50 for 60% pot and get one caller.

*** TURN *** [3s 7d 4c] [2s]
Donzo: bets $8.50
UTGplus2: raises $17 to $17

Unless the villain floated us with A5 or 22 (or inexplicably was in the hand with 72), the turn is effectively a blank. We again bet for value and are quickly min-raised.

At this point it's helpful to talk about the Baluga Whale Theorem. If you don't want to click the link, it's the idea that when faced with a turn raise, the strength of single pair hands must be seriously reevaluated. When an opponent just calls the flop and raises the turn, they're saying "my hand was strong enough on the flop that I wasn't scared of anything and was willing to let another card come so that I could win more money from you firing a second barrel." It is of course possible that some villains will float with air on the flop and raise the turn, but that's generally a more sophisticated play and not one that you see often at lower limits. Do some players know the Baluga Whale Theorem and use it to bluff? Absolutely, and it's something I expect to see more as I move up in stakes.

Furthermore, if a player is on a draw and is inclined toward playing draws more aggressively, the likelihood of a raise happening on the flop is much greater because A) there is less money invested on the flop than the turn, making a bluff attempt less costly, and B) a raise on the flop, if called, has a strong chance to induce a check on the turn from the original bettor (particularly if the original bettor is first to act), leading to the option for a free card for the raiser.

So, to return to our hand and our villain, what are the reasonable hands for him/her to have? If we consider the hands that had us beat on the flop, there are 9 possible set combinations and 16 straight combinations. Let's also include the 1 combination of A7 of spades, as that's a hand that might've originally called for value, but wants to turn the hand into a bluff now that we've fired a second barrel. If we assume that the villain is only raising those hands and we plug them into Equilab, we have an atrocious 7.5% equity with one card to come. But what if they're sometimes raising worse overpairs for value? If we add 88-KK into the villain's range, our equity skyrockets to 58.6%. But if we just take a moment to review the preflop action, we will see how unlikely most of those hands are. The villain is in the cutoff and there was a caller prior to the action getting to him/her. While a flat call with a big pocket pair sometimes happens in response to just the original raiser, it's something one rarely sees when a third person is involved in a pot, not to mention the dealer and blinds who have yet to act. Consequently, the likelihood of KK or QQ is slim to none, as is the likelihood of JJ or TT, although I'll leave a slightly possibility for those to the arbitrary tune of 25% of the time. 99 and 88 are believable calling hands both preflop and on the flop, but what would the purpose of the turn raise be? Value raising my extremely specific UTG betting range of A7, or just hoping for a tilted call with AK? It doesn't make much sense, but allowing the possibility that the villain also plays those hands that way 25% of the time, and factoring in our removal of KK and QQ and the reduced likelihood of JJ and TT, we come up with equity of 24%.

The last factors to take into account are the raise size and pot odds. As the villain min-raised, we are getting excellent pot odds of 17%. However, considering the strength indicated by the villain's line, we are looking at a strong-to-inevitable chance of facing an all-in on the river. That means that we're not actually looking at calling $8.50 to win $42, we're calling $36.35 (our current stack size) to win $69.85 (what the pot will be after the villain's shove for my remaining $27.85 after I call $8.50). That gives us odds of 34%. If our above range assignment is accurate (or close to it), we don't have the right odds to make the call and should therefore fold, which I did.

Donzo: folds
*** SUMMARY ***
Seat 3: UTGplus2 showed [3d 3h] and won ($31.85)

The villain didn't show at the time, but we can see now that he/she had 33 for a flopped set. Does that mean that the villain will NEVER have a worse hand? No, but the point is to determine how likely that is, and without a read that the villain is extremely aggressive or willing to raise lighter for value, we can't assume that they're taking that line with only a single pair. And because we didn't allow ourselves to become emotionally invested in our aces and left our brain in the "On" position, we were able to escape the hand losing only 29 big blinds instead of 100.