‘Expert’ play isn’t always ‘perfect’

Jan 18, 2005 5:54 AM

By Elliot Frome

When my father, Lenny, decided to name his strategy, he called it Expert Strategy, not Perfect Strategy. Depending on the game, these terms are not always interchangeable.

Perfect strategy means exactly that. Every hand is played according to what the math dictates. Computers can help determine the perfect strategy, but my dad quickly realized that translating this into something that a -human could apply might not always work.

In a game like Three Card Poker, for instance, perfect strategy and expert strategy are the same. It takes a simple rule like "fold if you don’t have at least a Q-6-4" to achieve perfect strategy, so there is no need to simplify it for human use.

Video poker is not nearly as simple. Most versions of video poker require about 30 or more rules to remember. A strategy table lists each of the playable hands in order of their expected values, which are decimal rankings of the chances of hitting a winning hand (1 represents a 100 percent chance of catching a winning hand).

Generally speaking, we don’t concern ourselves with "penalty card" situations. These situations deal with the times when one of the cards we discard can actually help create a winning hand, but we discard it anyway in hopes of making an even better hand.

So, if we have a three-card straight flush with no high cards, but also have an unsuited jack, we will discard the jack (and the fifth card). Discarding the jack reduces somewhat the chance of ending up with a high pair. Thus, the jack is a penalty card. In this case, it may make no difference how we will play the hand, but in some cases it might.

The goal of this particular article is not to focus on the merits of expert strategy versus perfect strategy, but on what it takes to play expertly.

We’ve already pointed out that expert strategy is not perfect strategy, which means we recognize that humans cannot play 100 percent accurately all the time, the way computers can. The question becomes, just how accurate should we expect ourselves to play, and what is the cost of our mistakes?

These kinds of mistakes happen because we are tired, we rushed our play or we had a distraction.

So, what is the cost of these mistakes? We can create a close approximation by making a few reasonable estimates. The first is how often a mistake is made, and the second is how big the mistake . To do this, we categorize the hands based on the complexity of the decision needed to play them.

About 75 percent of all plays require little or no thought. For instance, if you’re dealt a four-card flush with no pairs or a four-card straight with no pairs, there is little room for debate.

But we’ve all thrown away a low pair and wound up drawing five new cards, but this is rare. For this example, let’s say we make a mistake on these hands about once in 1,000 hands. We’ll say that the mistake was of the magnitude of throwing away a low pair (expected value of 0.82) and drawing five cards (expected value of 0.36), which is about as bad as it gets.

About half of the remaining hands require some decision-making. We learn to hold a high pair over a four-card flush or a four-card straight, and a four-card flush over a low pair. We’ll estimate that we make a mistake twice in 1,000 hands. We’ll assume the size of the error to be as if we had thrown a high pair (1.54) in favor of a four-card straight with a high card (0.74), which again is about as bad as it gets.

The most common mistake occurs when we have a hand that has a mix of three-card straight flushes, four-card inside straights and two-card royals. In our haste, we’re going to misplay a few of these. We’ll say we’ll misplay 10 out of a 1,000 hands, or 1 percent. Of course, the magnitude of these errors isn’t as bad because most of these hands have an expected value ranging between 0.75 and 0.50. To be fair, we’ll assume that these errors cost us on average about 0.20 each.

So, we multiply the frequency of the error times the magnitude of the error. When we do this, we find that the cost of these mistakes is a measly 0.08 percent!

This assumes making slightly more than one mistake an hour, and that each mistake is a relatively large mistake. Playing 600 hands per hour on a quarter machine will cost about 60 cents an hour more because you’re human.

It seems like a small price to pay to be an "expert."