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For some reason, this topic has spurred a lot of thought on my part... when I started writing this, I intended to write a short analysis, but that's not going to do. I'll be back later with more analysis in a part 2.
I'm going to attempt to attempt to analyze floating the flop. Even though we had to make a lot of assumptions for flop analysis, it gets much hazier, and much less mathematical.
Just a point for thought here, before we delve into the turn play. If the above min raise can be profitable... do your cards matter? Does it make a difference that you hold 77 as opposed to pure nothing? Other than the 8 percent chance we're going to improve, our hole cards are irrelevant. We're not playing the strength of our hand... we're playing the weakness of theirs, and the strength of our position.
Now... let's assume we've floated the flop. As a side note... I don't know if this is the right play or not. I'll find out when you do. We've spent 1.50 to call, and created a pot of 5.00.
Our first problem is: What is the turn card going to be?
I'm not writing a novel here, so we're not going to analyze EVERY situation, and we can more or less throw most of the math out of the window. Now we're playing poker. We can group the cards that are going to come into a few groups.
Cards that help our hand.
Cards that don't hurt our hand (undercards), but may complete a draw
Cards that scare us slightly (overcards)
Cards that create a new draw
Cards that scare an opp who has an ace.
We also have to figure out our opponent's likely course of action. We're still dealing with your AVERAGE uncreative opponent who won't fire a second shell out of position. Let's assume that he can still bet if he thinks he's ahead, will check if he thinks he's behind, and lets throw in the quirk that he'll bet if he picks up a draw.
Cards that help our hand:
There are two... the other two sevens. This is an unsuspecting card on the board. You can raise in any situation, or slowplay the turn and raise the river. The world is your oyster, and we're going to the felt on this board.If he has AA and we're set over set... *shrug*. This is going to happen around 4 percent of the time on the turn.
Cards that don't hurt our hand much, but may complete a draw.
These are (discounting potential scare cards for opp), a 3, a 4, or a 6. Anything else is an overcard. There are technically only 3 of these cards in the deck, since we'll be counting suited cards as cards that create a new draw. Opp can really only raise here with an ace, or an ace that makes two pair, or an ace with a straight that was made. Let's assume the card is a 4d.
Opponent can't really put you on a straight draw here, given your call preflop, in most cases. Opp can only bet (if he's uncreative) with A9o+, AA, A2s+. That's 77 times he's going to bet again. Let's assume he's going to make a 3.00 bet into the 5 dollar pot. If he's missed, you can bet the same 3.00 and take it down. So now, you're investing 4.50 to win 3.50, but you can pretty much tell exactly when it's going to work. Let's assume this works 85 percent of the time, and 15 percent, opp gets tricky and either calls or reraises.
So 140 times, we've invested 1.50 to float the flop. 63 times, we can invest an additional 3.00 when he checks.. so 54 times, we're going to win 3.50 (+$189). 9 times, we're going to lose 4.50 (1.50 on flop, 3.00 on turn.) or 40.50. If he checks the turn, and we bet, we have an expectation of around $2.36.
What do we do if he bets? If we're taking this flop 140 times, and he's checking 63, he's betting 77. If we just flat fold, our loss is 115.50 when he bets.
Sorry if my logic is kind of skewed here...
54 times, we win 3.50
9 times, we lose 4.50
77 times, we lose 1.50
The net value of straight forward play here is $33, or about 0.24 per play. Probably, looking at it, it's a marginal play.
What if we raise his bet? What can we make him fold. This is a two pair/set representing play... let's assume opp can fold all Aces except AJ+, Or aces that make two Pair, or a straight. We're eliminating pretty much any value of any kind of gutshot.
He can now call with AJ, AQ, AK, AA, A2, A3, A4, and A5. This eliminates a lot of mid range hands. He can only call with 27 of the hands he can raise with. So if he bets 3.00, and we raise to 6.00... what happens?
50 times, he raises, and we reraise to 6.00. We win 3.50 + his 3.00 bet. so 50 times, we win $6.50, or a net value of 312.50.
27 times, we lose 6.50, or a loss of 175.50.
So let's assume we're going to bet and raise every time in this situation.
Now:
54 times, he checks, we bet, and win 3.50. (+189)
9 times, he checks, and we get checkraised, and lose 4.50 ( - 40.50)
50 times, he bets, we raise, win 6.50. (+312.50)
27 times, he bets, we raise, and he calls or raises, and we lose 6.50. (-175.50)
Total value of this play is 285.50, or approximately + $2.03.
Aggressing the turn in this spot has an EV of +2.03, as opposed to aggressing the flop, as opposed to +0.81for the flop.
Back later with the next type of turn card.
TO be continued.
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