CardSharp

In this series I discuss how bets and raises are classified, and the thinking behind determining if a given bet or raise is correct.

Part 1

As you’ll recall from last article, there is a well defined system for classifying calls as correct or incorrect using odds math. That math essentially analyzes three relevant facts:

1. How much money you win if your call works (ie. you hit your draw, or have the best hand already) ($win)
2. How much you lose if your call doesn’t work ($lose)
3. How likely your call is to work (P(win))

At that point the expectation for the call is easy to calculate:

Expectation = $win * P(win) – $lose * (1-P(win))

The important thing to recognize here is that this formula is essentially

expectation = reward – risk

That’s all there is to it. The nice thing with a call is that you often have exact numerical values for all three pieces of information. That allows you to do a simple pot odds calculation and decide if a bet is correct or not. It’s nice, neat, and self contained. That’s why every poker book ever written talks about getting the right odds on your calls – it’s simple and easy to talk about.

Now, to the big point of this article:

Deciding whether a bet or raise is correct is no different than deciding on a call. You figure your reward and your risk and see which is bigger. However, unlike with a call you usually don’t have solid numerical values for the relevant facts when betting or raising. But the process is exactly the same.

Understanding Reward – How You Make Money

So what, precisely, is your reward when you bet? We already have part of the answer from the discussion of play on the end:

If you get a worse hand to call, you profit

If you get a better hand to fold, you profit

And if we’re talking about a betting round before the river

If you get a worse hand to fold, are rewarded with his share of equity in the pot

It’s important to notice that these rewards are not necessarily the same size. When you get a worse hand to call, you win a fraction of the size of your bet based on your relative equity in the pot. When you get a better hand to fold, you win whatever his equity in the pot was, which is often a substantial amount since he was best. When you get a worse hand to fold, you likewise win his equity in the pot.

So what should we learn from this?

1. On early streets, the rewards for value betting and bluffing are reduced. In the value bet case, villain may still draw out on you. In the bluff case, you might still have drawn out on him.
2. There is a third way to profit from a bet on early streets by folding out worse hands. This way can also serve as a “consolation prize” for a value bet or bluff. If you think you’re bluffing, but in fact your opponent has an even worse hand than you do and folds, you still get something of value.
3. In limit games, when bets are small relative to the pot, the biggest gains often occur when you get an opponent to fold whether or not you were currently ahead of them.
4. In NL games, the various rewards may be close to the same size, since bets/raises are often close to pot sized.

Understanding Risk – How Bets Go Wrong

The most common way to lose money from a bet/raise is to have insufficient equity in the pot when you make the bet – in practice this means you bet when you were behind. You can also lose money on a bet by subsequently being bluffed out of the pot. There are the well understood ways a bet can go bad. There is, however, a third more insidious way you can lose money on a bet. When you cause a worse hand to fold, you lose the opportunity that he might subsequently bet at the pot either thinking he held the best hand, or on a bluff. This opportunity isn’t a particularly valuable one in a limit game, but at NL where the bluff might be a sizable portion of the pot this can be a very substantial loss. This third way a bet can go wrong is rarely discussed, because it’s an opportunity cost rather than an obvious visible cost.

Likelihood Of A Good Result

Estimating the liklihood that a bet will produce good results is rather complicated. However, it helps to think of your opponent being on a range of hands with a dividing line. If you bet and he holds a hand below that line, he will fold. If he holds a hand above that line, he will call or raise for value. A picture something like this is helpful:

hands he will fold | Hands he will call or raise with
<--------------------------------------------------------->
worst---------------Opponent Range------------------best

Now, your first task is to estimate where that dividing line is. This in essence comes down to a measure of the perceived strength of your opponent’s hand. If he’s played his hand very strongly, there are likely fewer hands in his range that he will fold to a bet or raise. If he’s shown no strength whatsoever, the opposite is true. It’s often valuable to make a guess of exactly what the dividing line hand is. For example, if you make making a strong leveraged bet on the turn in NL holdem you might estimate that villain will fold anything weaker than top pair, top kicker and call/raise with anything stronger. Then you can estimate what portion of his range falls on which side of the line – say half the time you think he has better than TPTK, and half the time he has worse.

The next task, and this part is easy, is to note where the hand you’re considering betting falls relative to the dividing line. Now you have a strong method of estimating the chances that a bet will be successful:

When you hold a hand close to your opponent’s dividing line, the risks of a bet are increased and the rewards decreased. When you hold a hand far away from his dividing line, the risks are decreased and the rewards increased.

This should be obvious when you think about it for a bit. Imagine for a second you held the exact hand you think is his dividing line, and you bet. There is little reward – you don’t think a better hand will fold. You don’t think a worse hand will call. You may fold out a worse hand, which does have some value if there are cards to come. In other words, you’re getting minimum benefit. However, you believe you’re taking maximum risk – you think all the hands that beat you will call and you’re incurring the maximum opportunity cost of folding out all the hands worse than you that might bet in the future.

It should be obvious that such a bet, with maximum risk and minimum reward, is not usually a good idea.

Now consider how the situation changes if the hand you hold moves away from the dividing line. If you’re well below the dividing line, you now have the opportunity to fold out many hands better than you. That increases the reward. And the chances of folding out a hand worse than you are radically decreased because there aren’t many hands worse than you. So your reward has gone up, and your risk has gone down.

Similarly, if you bet a very strong hand that’s well above the dividing line then your reward is increased and your risk decreased. You can now get worse hands to call, which ups the reward. And there are fewer hands that beat you, so your risk drops.

The fundamental thing to take away here is that you should usually avoid betting hands that are close to your estimate of  your opponent’s dividing line.