Another Look at Leverage

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In a famous passage in “Super System”, Doyle Brunson writes:

“That has always been the key to no-limit play as far as I’m concerned. I want to put my opponent to a decision for all his chips. For example, if a guy’s got twenty thousand chips and you lead-off for six or seven thousand… you’re really betting him twenty thousand.”

Generations of poker players have found this advice intuitively compelling, but few of them have fully understood what Doyle is saying here. Why is the effect of the $7,000 bet larger to him than it is to you? Why wouldn’t a $4,000 or $5,000 bet be enough? In which situations does betting have this effect?

These questions are usually answered in terms of generalities about “aggression” or “pressure” or “putting someone to the test.” Better answers require more precision than this. Indeed, a truly adequate answer would require more analysis than I can give in a single article, because it would require a long study in game theory. If you want to tackle these questions intuitively and from first principles, you should study _Mathematics of Poker_. Rather than doing this, I’ll discuss Doyle’s example in some detail, and this will help us understand how leverage arises and what its effects are.

In Doyle’s example, the $7,000 bet “feels like” $20,000 because it threatens the opponent’s entire stack. What exactly does it mean to “threaten” a stack? First, let’s notice a few features of the example (some of which Doyle only implies):

(1)  There is a good chance of Doyle betting the last $13,000 if the opponent calls the first $7,000.

(2)  Doyle’s opponent is unlikely to get much information before that last $13,000 is bet.

(3)  Doyle’s opponent will often have a difficult decision if that bet arrives.

These features often explain the gap between the literal size of a bet and its real impact. They also help answer the question about why $7,000 threatens the stack but $4,000 or $5,000 does not, at least in hypothetical situations we construct from Doyle’s brief remarks. The $7,000 bet might cause future pot odds to be such that the opponent has a difficult choice if he faces a future all-in bet.

Let’s say the pot is $10,000 before the $7,000 bet. In that case, the opponent has to worry about a future bet on which he is calling $13,000 to win ($13,000 + 2 * $7,000 + $10,000); he’s getting almost 3:1 on that hypothetical future bet. Often, if he has enough of a hand to call that first $7,000, it will be hard for him later to be convinced that his hand doesn’t have 26% equity against Doyle’s range for betting that last $13,000. If we change the example so that Doyle bets $4,000 and leaves $16,000 behind, however, the opponent needs 32% equity on that future bet and is getting 7:2 on the first $4,000 bet. In this second scenario, it’s a lot easier to fold some of your range for calling the first bet to the second bet. Calling the first $4,000 and seeing what happens later is a much more attractive proposition; calling $7,000, however, is unlikely to leave you learning anything that will help you make the $13,000 decision, both because the odds on a future bet are better and because the immediate pot odds prevent you from having called the $7,000 too speculatively.

Fundamentally, these situations are about an asymmetry in the advantageousness in future betting. The last $13,000 bet favors Doyle, so Doyle wins by creating more situations where that $13,000 can be bet and where calling and folding both seem to be reasonable responses to that bet.

We should want to create these asymmetries and to keep our opponents from creating them. We can do this by understanding what generates those asymmetries. There are at least four factors to examine:

(A)  The number of streets of betting remaining.

The more streets of betting remaining, the greater a bet’s ability to threaten a stack. Doyle’s $7,000 bet might well have taken place on the turn; the remaining stacks if that bet were called would likely have been less than a pot-sized bet or even a half-pot-sized bet. On the flop, even a $3,000 bet would likely have been enough to set up a stack-threatening turn bet. Often, the earlier in the hand it is, the less you need to bet to “put stacks in play.”

(B)  The distribution of nut hands in each player’s range.

Future betting favors the player who has the most “nut-like” hands in his range; as the stacks get deeper, a hand needs to be better to count as “nut-like.” Part of proper poker is making sure to distribute your “good enough” hands over all the ranges that don’t involve folding. Sometimes this is as simple as occasionally slowplaying a flopped straight; other times it involves making sure you call with some nut flush draws and raise with others, so that your opponent can’t pressure you with impunity when the flush comes in.

Other times, the board simply elevates one player’s range over another. An early-position raiser has an advantage over a blind defender on a KJT board, especially at stack depths where sets should be played like the nuts. It is not an accident that the raiser can, in this situation, generate much more leverage by continuation-betting than the blind can by leading out. (It’s not always the stronger preflop range that gets this sort of boost, however.When small straight draws get there, for example, it often favors blind defenders and other players with wider preflop ranges.)

(C)  Position.

The ability to threaten an opponent’s stack more easily is another reason why it’s great to be in position. Sometimes the extra information you have in position is what lets you know that your range really is “more nutted” than your opponent’s; sometimes the fact that your opponent can’t put money in without making exponentially larger bets possible gives you lots of leverage. Where there are power asymmetries in poker, there are usually information asymmetries behind them; where there are information asymmetries, they usually benefit the player in position.

(D)  The chances of hand values changing.

All the above effects are stronger when the board is “dry” and the currently best hand is likely to stay best. (An exception to this is on early streets with deep stacks, when the distribution of possible future nut hands matters a lot even on dry boards.) Again, it is useful to think of the situation in terms of information: when the board has already given up all the information it’s likely ever to give, existing informational advantages are more secure, and whoever has that advantage can use it to create more leverage.

(E)  Differences in the marginal utility of chips.

In tournaments, the 13,000 left to be bet is tournament chips, not dollars, and sometimes they are worth more to one player than another, because the marginal utility of chips usually decreases as stacks increase. The deeper-stacked player will often be able to risk chips that are worth less to him than the calling chips are to his opponent. In a tournament, Doyle’s 7,000 chips might be worth $1,000, but his opponent’s 7,000 of calling chips might be worth $3,000 to him. Here Doyle would be risking perhaps $1,000 of chips to win a pot that is already worth $2,000 to him, whereas his opponent might have to call with $3,000 worth of chips to stay in a pot that is already worth perhaps $5,000.

Especially if some of the first four factors are also in play, the ability to threaten your opponents at a discount is often more important than the fact that what you stand to win is also discounted from your perspective. The fold equity that can be generated often gives the deeper-stacked player the advantage.

When you understand these principles, you can start to build strategies around them. Here are three ways to incorporate this knowledge into your game:

(i)  When the five factors above favor you, you can consider making bluffs that threaten your opponent’s stack.

(ii)   When those factors favor you and you really do have a great hand, you might consider slowplaying or making smaller bets if you fear you won’t get action. Of course, you should always keep in mind the reasons you often don’t want to slowplay. After all, getting your opponent’s stack is what you want when you have a very strong hand, and you can’t get a whole stack without threatening a whole stack. Sometimes, though, your fold equity is simply too high, and you’re better off manipulating the situation until some of the features no longer apply. This can take the form of waiting a street or of choosing a smaller bet size; in turn, waiting a street can be useful both because (say) a 1/4-pot bet doesn’t threaten stacks as much on the turn as it does on the flop and, if your hand is very strong, because the turn might figure to give your opponent some “good enough” hands against your range that are not good enough against the hand you hold this time.

(iii)  When those factors favor your opponent, you will sometimes be forced into passive play. This can mean checking a pretty good hand if the stacks are particularly deep and if other of the key features favor your opponent.

If you want to become a true expert in leverage, the next step is to put pen to paper and study the relevant game theory material in all its quantitative detail. You can do very well, however, without that kind of quantitative mastery–understanding these general principles will help you recognize when the screws are yours to turn and how to turn them effectively.