Drawing for Scare Cards

It's hard to know what's going on in another poker player's mind, especially if you're not in the game. You'd think lipstick cameras would help, but sometimes seeing the cards during a televised poker tournament only makes the play more mystifying. "I have no idea what he could be thinking," you'll often hear from baffled commentators. I don't claim to have any better psychic abilities than most poker commentators on TV. But, in my never-ending search for rational excuses for all forms of bad play, I thought it would be worth examining one strategic possibility that I think is often overlooked.

Scare cards – cards that look like they might have made someone a strong hand – can provide some of your best bluffing opportunities. Taking advantage of scare cards is an important tool in any player's strategic arsenal, and especially against easily frightened opponents, they can basically be counted as extra outs (albeit outs that are not guaranteed to win). Scare cards are more valuable against some players than others. At the extreme lie what I like to think of as "scare players," players who can talk themselves into fear of just about any card. Against these players, bluffing is clearly a critical weapon, and the main issue becomes adopting a bluffing frequency that maximizes your profit without setting off alarms. But there are many more moderately timid players, players who are so focused on solid play that they can often be pushed off a legitimate hand with a well-timed bet – not always, but often enough. And if the opportunity to make such a bet is looming, it would be foolish to exit the hand early, no matter what you have. Against such a player, it occasionally might be correct to play a hand with no real outs whatsoever, as long as you have enough scare-card outs.

A typical example might come when holding a weak hand in the big blind. Holding 9-4 offsuit, you might see a flop of A-Q-J in two suits, along with the small blind and two other players who just called the blinds. If a conservative player bets and the other players fold, you could hardly be faulted for mucking your garbage hand and seeing the next hand. But if your opponent is playing a style that could be called, for lack of a better term, overly solid, a call might be worth it on the off chance the opportunity to buy the pot will present itself.

Just to see how this could play out, let's run some numbers. First, to keep things simple, imagine that it's a limit hold'em game with five small bets in the pot and it's your turn to act. Ignore raising for the moment, and let's be content to assume you have no chance of winning a showdown. In fact, let's assume that you will have exactly one chance to win the pot, and that's with a lead-bet bluff when the turn brings something scary. Finally, let's assume that all scare cards are equally scary.

What's your expected return on calling that small bet? You should call only if your equity in the pot after the call will be greater than the small bet you're investing. And all of your equity derives from the possibility of your opponent folding to your turn bet. So, there are three possibilities: You check the turn and lose, you bet the turn and lose, and you bet the turn and win. When you check the turn, you lose just your one small bet. When you bet and lose, you lose three small bets. When you bet and win, you win five small bets.

So, the question becomes: How nervous does your opponent have to be to make this a profitable bet? If all the scare cards are equally scary, we can calculate how many scare cards need to be out there for the bet to be profitable. This means that the number of times you'll hit a scare card, bet, and get your opponent to fold will outweigh the times you hit a scare card and waste two small bets. And the difference has to be great enough to overcome the small bet you've invested just to see the turn.

Before going too much further, one useful point of reference is 38 percent. That's the minimum required folding percentage for this play to make a profit. If your opponent will fold less than 38 percent of the time (that is, call more than 62 percent of the time) no matter what comes on the turn, you can't possibly make a profit with this play.

The following chart shows how many cards you need to count as scare-card outs in order to make the call profitable, as a function of your opponent's probability of folding. If your opponent will fold 50 percent of the time, you need to count 32 scare-card outs. But, if your opponent will fold 80 percent of the time, you need only 14 scare-card outs. Note that these are the minimum numbers; your call will be only marginally profitable in these situations, even if all of the assumptions are met.

Clearly, it takes a fairly unusual situation to make the flop call worth it for just this reason. But it's not hard to imagine a player who would be sufficiently wary of a range of flush cards, overcards, and possible straights. One shortcoming of this kind of table is that it assumes all cards are equally scary. What happens if we have a mixture of 80% cards and 50% cards? The following shows a few combinations of 50% cards and 80% cards that make up a just barely profitable mixture:

So, while ordinarily you'd need 11 80% cards to make the flop call correct, you can make up the difference with a handful of 50% cards. If you're counting nine flush cards in the 80% group, you need just four 50% cards to make up the difference.

The requirements for a call on the flop are fairly stringent, and it shouldn't be surprising if it turns out that a flat call with absolute garbage is generally the wrong play. It's also not a play you want to abuse. The more often you act like you've hit the turn, the less likely your opponents are to believe you. At the same time, there are compensating factors that make the play liable to come up more often than you'd think, especially against your more paranoid opponents. One of the nice things about scare cards is that they're much easier to come by than genuine outs. With a board of 10-9-2, any 6, 7, 8, jack, queen, or king (24 cards) could make a straight. An additional nine cards pair the board, and if the board is two-suited, there are four additional flush scare cards. Even if two of these are already dead in your hand, 35 of the 47 outstanding cards offer something for your opponent to think about. Not all of them will seem equally intimidating to even the most jittery opponent; a 7 on the turn might not be your most favorable opportunity to steal. And some of the scare cards you're counting will certainly help your opponent. But an unexpected bet on the turn can give players with overactive imaginations the motivation they need to cook up a worst-case scenario. Even with that board of 10-9-2 and a 7 on the turn, there are players who will convince themselves that with two straights and some odd two-pair combinations, it would be better not to pay off two big bets to find out.

You may have noticed that I started off this column talking about tournament poker on television (almost all of which is no-limit hold'em), and somehow ended up analyzing a limit hold'em situation. As usual, I've done this to keep things simple, and the broad variety of no-limit situations makes it somewhat difficult to cook up a "typical" example. That doesn't mean you can't do it on your own, and I'll make my spreadsheet available to anyone who's interested. However, it's worth making a few points relevant to the difficulty in considering the variety of possible no-limit situations. First, if you make that first call in a no-limit situation, you are likely making a much larger call in relation to the pot size than you would be in a limit game. Second, when your relative stack sizes cooperate, you may be able to exert more control over your opponent's probability of folding by manipulating your bet size. That said, bluffing is generally a more important tool in no-limit than in limit play, and working out a few examples for no-limit might be a worthwhile exercise.

Clearly, whatever the situation, you need a pretty good read on your opponent to draw for scare cards. If you figure your opponent is 80 percent likely to fold to a flush card every time the percentage is really 25 percent, you will eventually lose all of your chips with this clever play. But if you're reasonably confident in your reads, it's a play you might consider every now and then, especially if you can put your opponent on middle pair or some other vulnerable hand. If the board already offers enough for your opponent to worry about before the turn card even shows up, you can consider anything that comes on the turn a scare card. And don't worry about those lipstick cameras. We'll understand.

Daniel Kimberg is the author of "Serious Poker" and maintains a web site for serious poker players at www.seriouspoker.com.