re: Poker & Diminishing Value of AK
This is a concept many people don't seem to understand. Of course it's good to isolate with a hand like AA because I want to be able to put opponents on a range of hands. But I would gladly go all-in PF with 9 other players with AA. Someone said the equity of hands goes down with each person enterring the pot. That's false. The equity of AA goes up as each additional player enters the pot.
Let's pretend everyone has 100 chips for simplicity.
From pokerstove: (I'll round)
AA vs. single random hand, 85%
pot equity = 200*.85 = 170
AA in 4-way pot, 64%
pot equity = 400*.64 = 256
AA in 9-way pot, 33.5%
pot equity = 900*.335 = 301.5
Don't know about you, but I'll take the 301.5 chips over the 170 chips on average any day.
Now let's test it for AKo
heads up, 65.5%
pot equity = 200*.655 = 131
4-way pot, 38%
pot equity = 400*.38 = 152
9-way pot, 18%
pot equity = 900*.18 = 162
So especially since this is a ring game, you would rather have AKo vs. a random hand 9-way than 2-way. Of course as mentioned this is a random hand. The hands that would push like that are not random hands. I'm going to be a little bit liberal on the hands they may hold, say TT+, AJs+, KQs, AQo+.
heads up: 51.64%
pot equity = 200*.5164 = 103.28
pot equity = 300*.30814 = 92.422
pot equity = 400*.18 = 72
So yes, if you have AKo and think the others are pushing with legitimate hand, not only does your equity decrease, but your ev becomes negative with a straight up PF all-in. Pot odds
may dictate a call anyway, let's look at the example given:
I was thinking of using pokerstove, but it won't give you how often one player will beat another heads up given that the third player has one of the predefined "legit" hands as well. If we consider the side pot ignoring the third hand (meaning if the results come out close we should fold, because we are boosting the value of our hand with every A or K the other person holds.
He has to pay $88 to get in on the pot. He wins the side pot 51.64% of the time, $110 in that pot ($55 from him and bigger stack of the 2).
110*.5164 = 56.804
Main pot is $135 ($45*3), he wins that 30.814% of the time
135*.30814 = 41.5989
Total win = 56.804 + 41.5989 = ~98.4.
He's paying $88 to win an average of $98.40. Good play based on that criteria of hands, not adjusting to the lesser odds of winning the heads up.