Yeah, Godlike, based on your assumptions, I think you're spot on.
But, as I said above, I didn't think he was pushing with a big pair because I saw him limp earlier w/QQ from EP. If he's not pushing with a big pair, would he push with a medium/small pair? I decided probably not, so I’m assuming he does not have any pair in the hole.
If I'm right, then I'm up against big unpaired cards, and
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
is a favorite over any of those except AK, which will
usually split the pot.
If the only non-pair hand he will push with is AK,
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
is expected to win 7.2%, tie 89%, and lose 3.8% of the time, a push with virtually no downside. If he will also push with AQs, it changes to 22.6% win, 67.8% tie, and 9.5% lose. Add AQo and it changes to 44.3% win, 40.7% tie, and 15% lose. The wider his range, the better
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
’s chances become.
On the other hand, if I’m wrong about him not having a pocket pair, then
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
’s chances are 45.3% to win, 0.5% to tie, and 54.2% to lose (against 22+).
Clearly, if he does not have a pair,
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
‘s chances of losing decline dramatically while its chances of winning stay about the same. The chances of a tie against a non-pair basically become chances of a loss against a pair.
So, the correctness/incorrectness of the call depends on the probability one assigns to (a) whether he has a pair in the hole and (b) the likely range of unpaired hands he will push with.
Assuming he will push with AQ+ (not too unreasonable since many poker authors recommend re-raising with these hands and many players use that recommendation as a proxy for which hands to push with), then the over-all chance for
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
to win is the chance that he has a pair *
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
’s win % against 22+ PLUS (100 – the chance that he has a pair) *
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
’s win % against AQ+. The numbers for ties and losses calculate similarly.
For this particular situation, I had to call $25.10 to win $25.45, so I was getting 1.014 : 1 from the pot, even money. In order for
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
to be indifferent to calling, its (over-all chances of winning * $25.45) + (over-all chances of tying * $0 [I’m neglecting the affect of rake as it’s messy enough already and will not materially change the nature of the results]) – (over-all chances of losing * $25.10) must = $0. In this case, my calculations (if anyone is interested, I can email you a spreadsheet) indicate that the indifference point is at a 78.5% chance that he has a pair, so
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
should call when there is less than a 78.5% chance he has a pair when his likely non-paired pushing hands are AQ+.
While I obviously did not know all of the percentages while I was in the hand, I understood what the removal of pairs from his range of pushing hands did for my
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
‘s chances and felt that a call would be worth it. To be honest, I felt that the chances of him having a pocket pair were lower than 78.5%—if I’d known that the indifference point was that high, I wouldn’t have sweated the decision so much.
Having said all of this, it is certainly legitimate to question my assessment of his chances of having a pair in the hole and his likely range of non-paired pushing hands. Maybe there was really only a 1% chance he didn’t have a pocket pair and I was really just trying my damnedest to give my money away and just couldn’t pull it off. Maybe that 1% chance that he would push with a non-pair was only for AK and nothing lower. I admit, I could have been WAY off, but at the time, I just didn’t think so, so I called him. Believe me, it wasn’t easy.
I happened to put a low value on the chance he had a pocket pair and felt that the potential gain was worth the risk that I was wrong. Turned out I was right and in the situation against AKo, we will split the pot 89% of the time...I just got lucky that my flush filled up to put it in the 7.2% of occurrences in which
![The King of Spades [Ks]](https://www.pofex.com/images/smilies/Ks.gif)
beats AK.
Did I take a larger than normal risk for a big pot? Undoubtedly, as I indicated at the end of my previous response to drogga. That's why I took so long to call because I had to figure out how sure I felt that he didn't have a big (or by extension, small) pair in the hole.
Am I going to start making this call on a daily basis? Only if my roll is 100,000x the buy-in I'm playing at...or if the right situation presents itself and I think I can rule out the hands I'm a dog to.
I think in the end we're both right. In the vast majority of cases, I side with you...ditch the AKs. On this one, I differed. But I'm probably just nuts anyway...I do play poker after all.
The real reason I posted the hand was more because (a) I had just won the hand an hour before and was still pretty happy about it

(b) I thought others might enjoy the exploits of a semi-decent player beating someone in a very lucky and ugly way...everyone likes to rubber-neck at a big pile up. I suppose going through and analyzing it like this is good exercise, but like I said above, this is a call that I almost never make, so it's more academic than anything else.
Anyway, I thought it was a fun hand to post, so I put it up.
(All hand percentages calculated with PokerStove v. 1.2)
PS Re: Zuccala’s comment about making different decisions based on whether you are up or down is correct, but I’d been making good decisions and plenty of money all day and felt I’d follow the rush. True, this bias toward calling is not mathematically sound, but I doubt it skews the results of the math in any meaningful way and I stand by my analysis.