AKs UTG

[Rastapopoulos]

Ok, since I either way DON'T wan't to be studying to my statistics exam, let's calculate a bit on this hand... [img]/images/graemlins/wink.gif[/img]
My reasoning could be totally messed up here, if so please
<font color="orange">flame me </font> so I learn.

Oki, considering the pot odds, after his all-in bet on the turn, you have the following three outcomes:
(never mind money already invested)

1. You bet $31 that you will have the strongest hand after the river and win a total amount of $103 - $2 (party rake) = $101. Outcome: <font color="green"> Win $101 </font>

2. You bet $31 that you will have the strongest hand after the river and loose. Outcome: <font color=" red">Loose $31</font>

3. You turn down the offer to play the game, and fold. Outcome: +/- $0

If we divide option 2 with option 1 we get: 31/101 = ~ 0.307 = 30.7%
... that is how often you have to win in order to go break-even on the game.

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Assumptions:

5 times out of 10 villain will have A[img]/images/graemlins/club.gif[/img] K[img]/images/graemlins/diamond.gif[/img]
3 times out of 10 villain will have 5[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/heart.gif[/img] (to make it harder for you, villain is holding one of your outs)
2 times out of 10 villain will have A[img]/images/graemlins/diamond.gif[/img] 5[img]/images/graemlins/diamond.gif[/img]

thus: 50% AK, 30% Set, 20% Top Two
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According to Pstove,
A[img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/heart.gif[/img] will hold up against:
- A[img]/images/graemlins/club.gif[/img] K[img]/images/graemlins/diamond.gif[/img] 21.6% of the times
- 5[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/heart.gif[/img] 60.2% of the times
- A[img]/images/graemlins/diamond.gif[/img] 5[img]/images/graemlins/diamond.gif[/img] 28.4% of the times

So accordingly, if we calculate your weighted probability by:
P = { (Probability for that villain is holding option A) * (Winning percentage of option A) }
+ { (Probability for that villain is holding option B) * (Winning percentage of option B) }
+ { (Probability for that villain is holding option C) * (Winning percentage of option C) }

we get:

P = (0.5 * 0.602) * (0.3 * 0.216) * (0.2 * 0.284) = ~ 0.423 = 42.3%

Conclusion:
Since 42.3 % &gt; 30.7 % you should play the game and have +EV.
(Read Criticism below)

Criticism:
Well, it all depends on the range of hands you put villain on. Now, in this situation I didn't count in AJ, AQ since I don't believe villain would play them so aggresicely. I didn't count in the straight since it seemed so remote, with a raise pre-flop.

So I let AK represent the best case scenario, and assumed the best case scenario would occur more often than the worst case scenario of a set (with a heart). Two pair seems more remote than a set, but let's say villain raises with A5s pre-flop.

Additionally, the pot-odds gets somewhat distorted when villain has AK, since you will only win the pot 20% of the time, and split the pot 40% of the time (when no heart comes on the river). You can of course calculate the correct pot odds for this, but I don't do it this time to keep the post more simple.

I still however think that it suggests a line of action and that you would only have slight if any -EV by calling.

Comments appreciated. They don't have to be nice. [img]/images/graemlins/smirk.gif[/img]

[MarkL444]

given the way you played it, that river fold sucks. the odds youre getting, youre nut draw, and very possible best hand at the moment are just too much.

[xorbie]

I think your assumpts are off. Villian is way more likely to have AK than 55 with a raise in such early position. Also, your pokerstove statistics seem way off.

[Rastapopoulos]

[ QUOTE ]
I think your assumpts are off. Villian is way more likely to have AK than 55 with a raise in such early position. Also, your pokerstove statistics seem way off.

[/ QUOTE ]

[img]/images/graemlins/blush.gif[/img]
Heh... I wrote off the figures I had jolted down on my lecture notes in the wrong order. The Pstove percentages of AK against set, and AK against another AK should of course be replaced with each other.

Nevertheless, the math is the same, since I calculated it with the correct weight, I just posted a mixed-up formulation. Thanks for pointing that out.

And yes, AK, AJ, AQ are the more likely holdings, but it's this thing with statistics and assumptions: Rather than calculating optimistically or taking LEAPS with assumptions, it is better to be quite certain of what you're saying.

Through this calculation I show that if anything, a call will definetely not be very -EV. If you like, just alter the hand holding assumptions, and you'll get only an increase in the positive EV. I'll try to calculate with respect to the splitting of the pot against AK as well later.

[swolfe]

raise or at least limp/re-raise preflop
bet the flop

[antidan444]

Thanks for all the responses, guys.

Sometimes, I trust general guidelines of good NL play over my read on a particular hand. In this case, what happened was I kept thinking about the "don't spend more than 50 BB on TPTK" generalization I read about five or six months ago, and played scared poker. Reflecting on the hand, I think the most likely hand villian held was another AK and I was freerolling (and I think AQ is his next most likely hand). He could have AA but the percentages say no, and most players don't raise preflop with 55, 22 or anything with a 3 in it. I just didn't pull the trigger on the read because of that 50 BB rule.

This thread helped me realize that every situation is different and must be evaluated seperately, and also that I really need to work on and trust my hand reading.

Thanks, guys.

[orange]

Raise pre-flop, bet the flop, call the turn.

[soLit]

If he raised preflop, Either he hit a set ( i dont think so ) or he has a/k or maybe a/q a/j I think your still ahead.