The question of whether it is appropriate to pass on a slightly EV+ gamble in a HU match is one that presents itself again and again, under many circumstances. Here is an example:
Example A: 7 minutes into a normal speed HU SNG. Blinds are 15/30, effective stacks of 1200, and your opponent has been loose/aggressive to the point of recklessness. You believe you have a significant skill advantage in the match.
Action: You pick up 77 on the button, raise to 75, and your opponent shoves for 1200. You believe his shoving range here includes any ace, KTs+, KTo+, QJs, and any pair.
Should you call? I don't. Even though Pokerstove puts my 77 at 56.164% against this pushing range, I don't like the idea of flipping for stacks this early/deep against an opponent that I'm confident I can outplay, even if I'll be the one left with 600 remaining chips if I lose. It's only a matter of time before a reckless opponent like this will overplay their hand or simply bluff off their stack to me, and I'd prefer to wait for that to happen rather than call and hope I'm 2:1 against his ace-small.
There are many other considerations which can affect this decision, however. Let's make a partial list:
Opponent Skill Level/Perceived Edge - The other day I found myself in almost this exact situation against an aggressive/perceptive/skilled player in a $25 SNG. I raised 77 OTB and he came over the top for ~20 BBs; I snap-called, despite the fact that I figured his range to be more narrow than that outlined above. He showed AKs, and I won the race. I called here because, unlike the situation in Example A, I was not confident that I had a significant skill edge over my opponent, and was therefore satisfied with taking what small edge I might have in the hand.
Stack Size/Structure - Part of the reason I pass in Example A is because, after folding, I still have at least 38BBs behind with which to continue the fight; plenty to take advantage of whatever skill edge I have over my opponent, especially in a normal game. But what if the blinds are a bit higher? What if the match is a turbo, or a super-turbo? If I'm the shorter stack at 50/100, I've already brought myself down to 950 after making my 2.5BB raise, in which case I'm not folding to the wide range in Example A. And what if the blinds are 20/40, but will be 50/100 in 4 minutes (super-turbo style)? Part of the logic behind folding in example A is saving your ammunition for a better spot; if your ammo is more severely depleted, and you may not have time to wait, then that logic breaks down.
In an attempt to represent this with numbers, I calculated the EV of calling a 3bet-shove after a 2.5BB raise as a 55/45 favorite with effective stacks of 1200 at 3 blind levels: 15/30, 25/50, and 50/100. The resulting equations look like this:
At 15/30: .55(1275) + .45(-1125) = 701.25 - 506.25 = 195
At 25/50: .55(1325) + .45(-1075)= 728.75 - 483.75 = 245
At 50/100: .55(1450) + .45(-950) = 797.50 - 427.50 = 370
When you represent the EV of this call as a percentage of what your remaining stack would be if you folded to the shove, you get 17.3% at 15/30, 22.7% t 25.50, and a whopping 38.9% of your remaining stack at 50/100. These numbers make very clear that while a fold is reasonable early on, it is unconscionable in a high blind situation.
Metagame Considerations* - Are you likely to play more matches against this opponent in the future? On the site I play at primarily, there is a pool of regulars at the HU tables, and there are frequent random opponents who I see once or twice and never again. If you opponent is not a HU regular, and is just looking to double his buy-in "for a quick buck"*, not only is he probably playing rather poorly but will often stop playing altogether if he gets what he wants (and sometimes even if he doesn't). Against this type of player it is probably best to fold, and press your advantage in a better spot. But against a more regular HU player, metagame considerations come into play in marginal spots like this. What is your history with this opponent, and how does he perceive you? If you fold 77 to an all-in 3bet, you're obviously folding most of your raising range; over time, this may lead your opponent to (correctly) conclude that he can 3bet all-in very wide with a high probability of success. Or has he already concluded that, and adjusted accordingly? Indeed, against a less perceptive, LAG opponent, a fold/show of 77 might make a strong impression of you as weak-tight, which may profitably (for you) encourages him to widen his 3bet shoving range, and more generally to keep up the reckless aggression that you seek to exploit. On the other hand, even if you tighten up your opponent's range just a bit, and conclude that you are now on the losing side of a 55/45 flip, making the slightly EV- call might be worthwhile if you anticipate future/regular matches against the same person and believe that doing so will surprise/confuse/deceive your opponent, convey a particular image, provide you with information, or be otherwise significant for metagame reasons.
I'm going to leave this topic open, and encourage/hope for some comments & feedback. I don't have any definitive answer as to when a marginal fold becomes a call or vice versa (when are there ever definitive answers in poker, anyway...), but what I hoped to accomplish with this post was to illuminate a few of the factors that must be considered when you're faced with very slight EV+ gambles in HU. This post really just scratches the surface, so perhaps we can revisit this subject again in the future. For some more learned writing on the subject, check out the chapter 'You're Broke - You're Done' on page 19 of David Sklansky's Tournament Poker for Advanced Players. Comments!
* Thanks to Lorin Yelle for his insights on this topic.
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