Saturday, October 5, 2013

Give and Receive: The Other Side of Implied Odds

When most books and experts explain implied odds (IO), they focus on what odds you are receiving with speculative hands, and whether you should proceed in the hand or not. You're dealt 5-5 in LP and a nitty EP player opens for a standard raise UTG. You go through REDi, and put the opp on a big hand that could pay you off if you hit a set. Effective stacks are relatively deep, you're getting greater than 10:1 implied odds, the villain is the type that has trouble letting go of TPTK-type hands, etc. So you make the call, with the intention of folding if you miss the flop...yada, yada, yada. Every modern poker book discusses this exact IO scenario. If you don't understand this--or aren't implementing it in your game--you need to go back to school. This is Poker 101, folks. Basic set-mining is a bread-and-butter play for winning cash game players...

...okay, fine. I now want to talk about Poker 202. What if you're on the other side of the implied odds equation? I.e., let's imagine that you're the one holding A-A or K-K preflop, and you believe your opponent has a hand like  pocket fives and is set mining. What are you to do?

Answer: Give them the wrong implied odds to proceed, that's what.

For example, let's say we're playing in a live $1/$2 game. We're in the big blind with A-A. Effective stacks are 100BB and the table is filled with so-so and beginning-level ABC players who know the rudimentary basics of immediate pot odds, position, and so on. They also know the Negreanu adage that small pairs and other speculative hands are "bust'em" hands that can stack-off big hands like Aces. They've seen Kid Poker play like this on TV, taking raises with 2-2 and 8-7o, hitting the flop, and then getting paid off. These players are also smart enough to know that their post-flop skills aren't as good as Negreanu's, so they don't continue in the hand if they don't hit the flop; they're playing fit-or-fold poker. They'll gladly call a raise (or even reraise) preflop with a small pocket pairs because they believe they'll stack you if they hit their set. Said another way, they're focused on hitting their hand, and not really paying attention to the exact IOs they're being offered.

Okay, back to our example. The first few players fold, and then a mid-position player open limps. The rest of the table folds, and the action is on us in the big blind. Our rockets are well disguised, so we momentarily think of slow playing them. Ah, but we know better than this, right? We put this ABC player on a hand exactly like a weak pair, and we don't want to give them the right odds to set mine. Said another way, we know we should raise, but how much?

Well, basic poker probability tells us that the villain will hit his set one out of eight times (i.e., 7:1 against). This means that if you give your opponent worse odds than this and he calls, you have made money.

Let's repeat that for clarity: If you give your opponent the wrong odds to continue in the hand, and he or she does so anyway, you have made money. Period

This is the very definition of what a +EV play is. Make the right decision, let your opponent make the wrong one, and you win. Poker is a long-term EV (i.e, Decision) game, and if you give a set mining opponent the wrong odds to set mine and they call--regardless of whether they hit their set and win this particular hand or not--you will make money in the long run.

We know that one out of eight times our opponent will hit. Let's ignore the small amount of existing money already in the pot (i.e., the blinds and the villain's limp) as it just makes the math a little messier, and only has a small effect. If we know our opponent will call a preflop bet that is at least 12.5% of the effective stack (i.e., 1/8), and then we shove all-in on any flop, we profit. This is true even if we tell our opponent what hand we have so that he can fold on the flop when he misses.

Yes, this is true. Seriously. Yes, I really mean it! You could actually tell your opponent that you have Aces, shove, and profit. Hell, you could literally show them your cards and you would still make money.*

For example, let's say we bet an amount well over 12.5% of the effective stack size. Call it 25%, or $25, for argument sake. Our opponent calls, hoping to hit a set. He's obviously made a mistake by doing this, but to illustrate let's make this example really absurd; i.e., we're going to shove any flop, knowing full well that our opp will fold if he misses and only continue if he hits.** This is still profitable for us; they'll hit the flop one out of eight times, or 12.5%, and we'll still be ahead 87.5% of the time on any flop. In other words, when we're considering this preflop action, 87.5% of the time we're going to win the $25 our opponent puts in the pot, and 12.5% of the time we're going to lose our entire stack ($25 preflop + $75 shove on the flop). Here's our expected value of this play:

EV = (87.5% x $25) - (12.5% x ($75+$25))
EV = +$9.38

Said another way, we're making well over nine dollars every single time we make this play, and our opponent is losing this same amount. That's called printing money.

Now, is this the best way to play poker? No, of course not (because it doesn't maximize our EV; e.g., we want our opponent to continue in the hand, making further mistakes when he misses and therefore shoveling more money into the pot). That said, this example does illustrate pretty clearly the concept of profiting in poker purely by giving your opponent the wrong odds to continue in a hand when you know he's drawing. Slow playing big hands is generally a terrible idea in hold'em, and this example illustrates why. When you're ahead in poker, you should bet for value (which is also known in this particular situation as "betting for protection.") 

The bottom line is you need to bet an amount that is more than the equivalent odds your opponent needs to make his or her hand. The more you can bet the better, but you also want your opponent to call, so you have to be judicious. Obviously, if you can just shove preflop and get called, you're maximizing your EV. But even truly bad players usually won't call off their entire stack preflop with 5-5. A good rule of thumb is to bet at least 20% of the effective stack preflop when you know your opponent is drawing; this way you're giving the opp the wrong odds to call, but you're still realizing an immediate EV profit.

All-in for now...
*Of course it would be dumb to do this, as you're helping your opponent make a better decision, but the point still holds-- you've already profited preflop in an EV sense, which is what matters in this example.
**Again, this isn't optimal poker by any stretch of the imagination, but it's still profitable.

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