Applications and Limitations of the Alpha Value

The alpha value is one of the most important numbers in a discussion of poker because it gives you a lot of information with a simple calculation. However, it’s often applied incorrectly because of a lack of understanding of what it can and should be used for. Our goal here is to gain a better understanding of when the alpha value should and should not be used.

The Alpha Value Defined

Most people who have been around poker discussion here on the forums will have seen the calculation bet/(bet+pot) at least once. For example, if a player was betting $4 into a pot of $6, then the alpha value would be 4/10 = 0.40 or 40 percent. Many players use the alpha value to find profitable bluffing spots or to determine if a call is profitable. There are very strict limitations on when the alpha value works as a guide in any type of situation, and those limitations are the focus of our discussion here.

Using the Alpha Value When Calling

If you are calling to close the action (ie: calling on the river or calling an all-in), then you can use the alpha value as a guide to determine if your call is profitable. For example, suppose that after your opponent goes all-in that the pot is $20 and you have to call $9. In this situation, the alpha value would be 9/29 = 0.31, so you would need to have at least 31 percent equity to have a +EV call before taking into account the rake. The main limitation on using the alpha value with calling is that it has to be a call that closes the action on the hand completely. Here are some examples of when the alpha value does not apply when making a call:

There are players left to act on the current betting street.
There will be betting on a future betting street.
Calling will result in a side pot because of multi-way play.

Suppose that there is a 3x raise pre-flop by a player in middle position in a 100bb no-limit hold’em cash game, and you call from the button with T9s. The blinds fold, and the flop comes AK9 rainbow. Your opponent makes a continuation bet of two-thirds the size of the pot. I have seen players try to use the alpha value to justify calling (or folding) in this type of situation. This is absurd because the alpha value is completely irrelevant!

The Relationship Between Bluffing and the Alpha Value

If you are making a pure bluff with absolutely no chance to win unless your opponents fold, then you need to take the pot down at least the alpha value percentage of the time for your bluff to be profitable. For example, if you were to bet $5 into a pot of $10 in a heads-up pot with no pair and no draw, then you would need your opponent to fold at least 5/15 = 33.3 percent of the time for your bluff to be profitable.

One of the most common mistakes that players make when it comes to using the alpha value to determine the profitability of bluffs occurs in multi-way pots. If we were making the same bet of $5 into a pot of $10 in a three-way pot, then we would need both of our opponents to fold a combined 5/15 = 33.3 of the time. Players often take this to mean that each player has to fold 33.3 percent of his or her range individually, but that’s a big mistake. If both players fold 57.4 percent of the time each, then we will take down this pot just 33.3 percent of the time.

Another big mistake is using the alpha value to determine the profitability of a bluff whenever there are future streets of betting left. The implied odds, reverse implied odds and chances for future bluffs all drastically change the expected value of bluffing on an early street, so the alpha value becomes of little use. You often see this when players make a continuation bet with a weak draw or when they make a 3-bet pre-flop. By trying to take a shortcut with the alpha value, they inadvertently avoid looking into the real factors that influence the profitability of their plays, and this hurts their overall ability to learn what really makes these types of situations tick.

Avoiding Exploitation With the Alpha Value

If you’re closing the action on the river, the alpha value can give you what percentage of your total range that you have to call with to avoid being exploited by bluffs. As is the case with a lot of the situations that we have discussed here, a lot of people try to apply this to earlier streets without the best of results.

Here’s a common example. Suppose that Hero raises pre-flop to $3 and Villain 3-bets to $10 from the big blind in a $0.50/1 game. Because alpha is 9/13.5 = 66.7 percent from the point of view of Villain, some people would try to say that we have to fold 66.7 percent or less to avoid being exploited by bluffs. The problem with this logic is that there is future betting that drastically changes the calculation. If we’re winning a lot with the times that we continue, then it isn’t going to matter that we’re folding more than two-thirds of the time. Along similar lines, if we’re spewing chips when we continue, then it’s not going to help us much that we’re folding less than two-thirds of the time.

The Common Theme

The common theme with all of these examples of the alpha value being applied incorrectly is that implied odds, reverse implied odds and future bluffing opportunities usually change our total expected value a lot more than what’s happening on the present betting street. Because the alpha value is only a shortcut for basic, single-street situations under specific limitations, it cannot be applied as anything more than an extremely rough and borderline-useless guideline in the majority of other situations.

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