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Accounting For Value In A Poker Hand

I was in a live(in a casino) $1-$2 blind no limit cash game. My position was in the big blind(NYSE:BB). The player utg+2 raises to $15. He has played very tight, so I give him a range of AQ,AK,JJ,QQ,KK,AA. Four other players call before it gets back to me.

My pot odds are 5/1 or 16%. Given that i most likely have live cards(someone not having Q5 etc), unlikely to have reverse implied odds(The event that even if i hit what im looking for, someone beats me), and the unlikely event that the initial raiser will lay down top-top or aces, there is value in the call. The pot is $90.

The flop comes A 3 4 with two clubs.

Being first to act, I check. The original raiser bets $30. Two players call. So, pot odds to me are (90+90)/30 = 6/1 or 14%. In analyzing the value of the proposition, i analyze possible ranges for each opponent. I keep the range for the raiser. One of the callers probably has Ax and the other probably has a flush draw. This is of course speculative, but a probable occurrence.

If a 2 or 6 comes I win. But given the clubs, ill discount the 2 and 6 of clubs as outs to be conservative. So I have 6 outs. Using the law of 4, im approximately 24% to win. I call given a 24% of winning and a cost of 14%. The pot is $190.

The turn is a King non club. The board is A 3 4 K with two clubs.

I check again. The raiser bets $50. The other two players fold. This information is dynamic and changes the valuation.

First, its unlikely he has AA, KK, or AK. With two clubs on the board, and three people who called his flop bet, if he had AA,KK,AK he would bet more than 1/4th the pot to protect his hand. Its unlikely he would keep betting if he had an underpair like QQ or JJ with two overcards and three opponents. Given this, AQ seems likely.

Second, since the other players folded, i can add back the 2 and 6 of clubs to my outs; providing a total of 8 outs.

I am receiving pot odds of approximately 5/1 or 16%. Using the law of 2, I have a 16% of hitting one of my outs. Michael Price has a saying: "I like to buy the steak for 80 cents on the dollar, and pay nothing for sizzle". In this scenario, I was paying face for the steak, but getting the sizzle for free. What was the sizzle? It is the area of speculation. It came in two places in this particular hand.

If the 18% hits, meaning a 2 or 6 rolls off on the river, i will bet something like 1/4th to 1/2 the pot and often get called. Lets make it an even $100 bet. A 6 or 2 on the river looks unlikely to make my hand. This is implied value.

There is also bluff value. If a club comes on the river, which is 11 outs, (but will discount the 2 and 6 because that would be a value bet) then I can bet 2/3 to whole pot to induce a fold. Im able to do this because of perception. A flush is alot more visible of a draw than a strait. Most players in my situation would also be drawing for a flush in this situation, and im certain he perceives that.

Im getting the steak for face but getting another $390 at 18%, and $290 also at 18% for free; with the percentages being independent. The expected value could be calculated as (390*18% + 290*18%) - (50*64%) = 122 - 32 = $90. I call.

The river is a 9 non club. I check and he checks behind showing AQ. Just what i rationally expect to occur 64% of the time. Although the card didnt roll my way, what a wonderful game!