Playing Draws Against Habitual Underbetters

Just a decade ago, it was hard to find an affordable, live big-bet hold'em game. The only way for most players to practice poker's most dynamic form in public games was in tournaments. Although you could find the occasional pot-limit Omaha game if you had a big enough bankroll, there was little chance of finding enough players to start even a $1-$2 blinds pot-limit game in most cardrooms. Now, thanks to the popularization of no-limit hold'em on television, many casinos spread small no-limit games, often with blinds in the single digits and minimum buy-ins of as little as $100.



The prevailing wisdom about big-bet poker is that big cards rule, and drawing hands are the fastest way to end up on the rail. But due to a phenomenon I like to call "rampant underbetting," there may be more opportunities to play drawing hands than many players think, especially in smaller no-limit games. And, of course, this includes hands that have high-card value but might turn into drawing hands on the flop (notably, A-K suited).



How do you know your draw might be worth pursuing? As always, it comes down to a question of value. If you're faced with a $20 bet, is the value of your hand after making the call more or less than $20? Of course, making this calculation reliably is not easy, and probably impossible at the table. It's only mildly arithmetically involved, but the really hard parts have more to do with psychology; if your opponent is highly likely to blow off a huge stack in the event you hit your flush, drawing might be a better idea than if your opponent is already all in. And you have to figure things like that out for yourself. But the numbers are still useful in creating some points of reference to which you can anchor your judgments at the table. I've always advocated running through some numbers away from the table to help feed your intuition while you play, and I'm convinced it's still true in no-limit, where the numbers may tell only a small part of the story.



Let's look at a simple but common scenario that crops up in small no-limit hold'em games. You have the nut-flush draw with one overcard. Your opponent has underbet the pot, and you both have enough chips left for more action. You've decided not to raise, so the only question is whether or not it's worth a call. (You may, after doing all the calculations, also check the numbers for a raise, but not today.)



The main reason it's difficult to do this kind of analysis is that there are too many distinct possibilities for what can happen after you make your decision, many more than in limit poker. And estimating the probability of each depends not just on the probability of seeing different cards, but also on your assessment of your opponent's likely future behavior. What's worse, it's not as easy to ignore unlikely events as it would be in limit poker. In limit poker, if there's only a miniscule chance of hitting your flush and losing, you can often ignore the probability and still get almost the right answer. In no-limit, conceivably that's the one scenario in which you would blow your entire stack, and it would be a mistake to ignore it, even if it happens only infrequently.



When you approach this kind of analysis, you can decide as you go how detailed your approximation needs to be, and how you want to estimate the different unknowns that go into the calculations. Imagine that the pot is $100 on the flop, your opponent bets $35, and you're trying to decide if it's worth calling. If you're so inclined, you could just guesstimate that after calling the bet, you'll have $50 in pot equity. That guesstimate might be pulled out of thin air, but since at some level you will have to rely on guesswork, you may as well start at the top. Paying $35 for $50 in equity is a good deal, so if that's your best guess, you should at the very least call.



Pure guesswork is fine in a pinch, but since we have a little more time, we can refine our guess by breaking the problem down into pieces and trying to come up with better estimates for each piece. Perhaps some parts we can calculate more exactly, some we can guesstimate with more confidence, and others we can choose to ignore for now. Let's suppose we start by dividing our equity on the turn into two cases: hitting the flush and missing the flush. If our opponent is certain to price us out of the pot on the turn, none of our equity comes from the case in which we miss. The case in which we hit occurs about 19 percent of the time. If we assume that we always win when we hit, but get no further action, our equity is 19 percent of $170, or about $32.50. That's less than the $35 we paid, and probably not a great deal anymore. So, it's a fold. In fact, with a little math, we can see that the break-even point comes out to about $31.



Perhaps now would be a good time to consider the possibility that our opponent, spooked by our bold call on the flop, will let us have the river card for free – and that again, a flush card will give us the pot while a non-flush card will give us nothing, with no further action. If there's only a 10 percent chance of the free card, that $35 call flips over to marginally profitable. And if it's 20 percent, we can even call $40 profitably. So, if we really believe there's a substantial chance of a free card, we can do a lot better than $0 for estimating our equity from the miss-on-the-turn case.



Are we done? Of course not, we're not even close. I've carefully avoided having to factor in stack sizes. We haven't considered the ways you can hit the flush and lose. We haven't considered potential wins and losses when you hit your overcard. And, most importantly, we haven't considered the impact of future action from your opponent. Every extra dollar your opponent will pay off (on average) when you do make your flush contributes to the value of your hand, and therefore to the amount you should be willing to call.



Given the enormous number of potential scenarios, it's possible that if you try to calculate the exact break-even point for a call on the flop, you'll forget a few situations and end up with an incorrect analysis. In limit poker, these analyses tend to be dominated by the few most likely outcomes; as long as you don't miss any of the big pieces, you'll tend to get close to the right answer. In big-bet poker, unlikely outcomes can have a large effect on your calculations if they involve big wins or losses. A hand that has a tiny chance of materializing might be an important consideration if it will wipe out your entire (large) stack when it does. So, when I gloss over the possibility of your hitting the flush and losing, I do so with an implicit warning that it could be a serious error.



Although there's no insurance against gaps in your reasoning, I'd still suggest using your favorite spreadsheet program to try out different numbers for whatever situation interests you most. As your thinking develops, you can break the hand down into smaller and smaller pieces, which lets you decide what to focus on and what to gloss over, and helps you develop a stronger sense for what's most important. If I get enough e-mail about it, I'll try to put a sample up on my web site, so at least you can work out when to pursue that flush draw.

Daniel Kimberg is the author of "Serious Poker" and maintains a web site for serious poker players at http://www.seriouspoker.com/. You can contact him at [email protected].