Play like an expert

Dec 11, 2006 11:48 PM

Last week I explained the importance of the first leg of Expert Strategy, which is knowing the right games to play. If you pick a game with a low payback, no amount of strategy is going to turn it into a game with a high payback. Of course, picking a game with a high payback only has benefits, if you bother to learn the right strategy.

For video poker, determining the right strategy is relatively simple. There are 2,598,960 ways five cards can be dealt from a 52-card deck. For each of these ways, there are 32 different possible ways to draw, ranging from drawing 0 cards to drawing all 5 cards.

From a mathematical perspective, in order to maximize the payback of the game, you should pick the one of these 32 ways that maximizes the expected value of the hand. The expected value is determined by adding up the results all the possible outcomes of the draws and dividing by the number of possible outcomes.

So, if you draw to a 4-card straight, you will wind up with a straight eight times out of 47. A straight pays 4 credits (in full-pay jacks or better), so the expected value is 32 divided by 47, or 0.68. This assumes that the player did not have any high cards (Jacks or Better), which would provide an opportunity to wind up with a high pair.

Using this method for determining the best play requires the admission that you may sometimes sacrifice the short run for the long run. The critics of Expert Strategy try to make you believe that the short run is a few hundred hands and the long run is a few million hands. Thus, they try and make you believe that you are sacrificing one session of play in order to win over many lifetimes, which is a goal no one person achieves.

This is simply not true. The short run can frequently be a single hand. The long run, while longer than a single session, can frequently just be a year or two of play, and does not requires you to play 40 hours a week for 50 weeks out of the year.

The reality is that using Expert Strategy is simply about playing the odds. It looks at all the possible outcomes and the paybacks of those outcomes and picks the one that is likely to return the most to the player over time.

On any ONE hand, anything can happen. The more that particular hand comes up, the more likely the outcomes will begin to look like the ones that the probabilities say they should. The critics like to point to a single hand that didn’t turn out for the best and use it against the strategy. In the end, following these critics is what will cost you some significant cash.

For example, let’s assume you are dealt the following hand:

8¨ 9¨ 10¨ J¨ Jª

There are essentially two possible plays for this hand. You can hold the high pair or you can hold the 4-card straight flush. The expected value of the 4-card straight flush is about 3.5, while the high pair has an expected value of only 1.54.

From an expert strategy point of view, there is little to decide. You definitely hold the 4-card straight flush. But is it still the right play if you are dealt this 3 or 4 times and you wind up drawing absolutely NOTHING? The answer is an unequivocal YES.

Over time, the results of this hand will begin to approximate the expected probabilities. That is, you will wind up with a straight flush about two out of 47 times. You will get a flush about seven in 47 times. A straight will occur six out of 47 times. It will not take a lifetime for this to occur. It probably won’t happen in a single night either. It might take a couple of years, depending on how rare the hand is. But, after that time, you will wind up much better off by playing the 4-card straight flush instead of the high pair.

The inevitable question is "Is there ever a time in which you want to take the sure hand with the lower expected value, instead of the non-sure hand with the higher expected value?" The answer to that question is not so straightforward. There are times in a tournament, you may want to take your guaranteed payout, but I’ll ignore that situation for the moment.

From a purely mathematical perspective, the answer is no. You should always play the hand in the way that maximizes the expected value. From a more practical perspective, you have to make a reasonable decision. Would I ever play the high pair over a 4-card straight flush in the situation I described above? With an expected value difference of nearly 2, the answer is no.

There are times when the expected values get much closer. Especially in the Bonus games, where a full house with three aces can have an expected value that is very close to the three aces by themselves. In this case, would I ever consider just taking the full house?

The answer, quite frankly is yes. It will depend on just how close the expected values are, and a variety of other factors (how late it is, how much more I wish to play, how close I am to reaching my win target for the evening, etc”¦).

If I do choose to keep the full house, I do it with the knowledge that I have actually sacrificed some long-term potential for a short-term gain. In the long run, I will wind up winning a little less. However, I make the conscious choice to do this, without trying to fool myself into somehow thinking I have beaten the math, which is simply NOT possible.