Yesterday I was playing low stakes online poker. No limit Hold’em to be more precise.
In this noteworthy hand, I had A9o in the big blind. A player in middle position limped in, and everyone else folded. Effective stacks were 83 big blinds (BBs). I checked my option, not wanting to bloat the pot out-of-position and there not being enough money in the pot to make it worth fighting for. Yet.
The flop was K99. Trips for me with top kicker. I had noticed this villain bluffing when checked to earlier, and there aren’t many hands he can have that would call a bet here. I checked. He checked back.
The turn was an Ace, giving me a full house. Maybe he’ll see that as a good bluffing card. Maybe he has an Ace-X suited – a popular limping hand at low stakes – and will be for value. I checked again. He checked back again.
The river was a J. Now the board reads K99-A-J and I have A9. While not the absolute nuts, the only hands that can beat me are AA, KK and JJ. All of these would have raised pre-flop, and combined represent only 7 combinations. Let’s just say I have the effective nuts… there is 2.5 BBs in the pot and the villain has 82 BBs behind, which I cover. What should I do?
Well, what would Sklansky do?
One of my earliest poker mentors, at least in terms of books that helped me learn many important fundamentals, was David Sklansky. One of his books, co-authored with Ed Miller, is No Limit Hold’em Theory and Practice. Although many excellent poker books have pushed the envelope of poker thinking since this was first published in 2006, it’s still hard to beat for certain fundamentals.
Sklansky was one of the pioneers of thinking in terms of expectation, or Expected Value (EV). Simply put, imagine your are heads-up on the river and have the nuts. The EV of your bet is the probability it will get called multiplied by the size of the bet. Early in the book, Sklansky provides an example, where a $50 bet will get called 80% of the time, a $150 bet will get called less often at 40% of the time as the villain narrows his calling range in response to the larger bet, and a very large bet of $450 will only get called 20% of the time, representing the very top of the villain’s range.
$50 * 80% = $40
$150 * 40% = $60
$450 * 20% = $90
In this example, the most profitable play – the bet with the highest EV – comes from the largest bet.
(Of course, there’s a whole lot that goes into coming up with these percentages, including what we know about the villain’s tendencies and the action in the hand up to this point. All of which is beyond the scope of this blog post.)
Later in the book, Sklansky notes that an all-in bet with the nuts on the river is “very likely to be the best play in some circumstances.” These circumstances include spots where the villain is likely to be weak, but could be sandbagging and may be just as likely to call an all-in bet as any other medium-to-large sized bet.
Back to yesterday’s hand.
With only 2.5 BBs in the pot and a villain showing no sign of life, I expected a fold to almost any bet, even for the bare minimum. But if he has a 9 and has been lying in wait for me to bet first, or has QT – a plausible limping hand – and just completed a backdoor straight, maybe he will make a massive mistake.
So I go all-in.
And he snap calls, so fast my heart skips a beat.
It turns out he had K9o, flopped a full house, and slow-played me while I was slow-playing him. Try to imagine what that must have felt like…