Keep a ‘straight’ face!

Feb 8, 2005 1:30 PM

If you’re playing five-card poker at home, drawing to a four-card straight may be a good play.

Basically, you’ve got an eight-in-47-chance of drawing that straight, and 12 additional chances to draw a pair, so if it’s a high-ranking straight you’re trying for, the hand looks relatively playable.

Of course, real poker relies on bluffing and tells. So, when you draw one card, the table begins to wonder if you’re bluffing or trying to make a straight or a flush. Maybe you’ve got two pair and you’re going for the boat. How you bet and how good of a poker face you’ve got can determine whether you’ll win the hand almost as much as which card you actually draw.

Video poker lacks these human elements — bluffing, tells and raising. You can’t give the machine a dirty look and hope that even if you don’t draw the straight it might decide to fold and pay out anyway. This is why expert strategy is based purely on mathematics. There are no hunches. There is no trying to beat the guy across the table who never bluffs or maybe only whistles when he bluffs. All that matters is the final result of your hand and the paytable that the machine is using.

So, while a four-card straight may not be a bad pre-draw hand when playing with your friends, how does it rate when you’re playing video poker? Quite frankly, if you were dealt a steady stream of four-card straights, you’d go broke pretty quickly. In full-pay jacks or better, the best possible 4-card straight is one with three high cards. With this hand, there are eight ways to complete the straight and nine ways to pick up a high pair. Since the straight pays four and the high pair pays one, we calculate the expected value by summing up the expected wins (eight straights times four plus nine high pairs times one equals 41). And, 41 divided by 48 is 0.87 and this is the expected value for a four-card straight with three high cards. Keep in mind that J-Q-K-A is defined as an INSIDE straight as there is only one way to complete the straight, not two.

As we subtract one high card from the straight, the expected wins decrease by three units, which reduces the expected value by just a little more than 0.63. Thus, the expected value for a 4-card straight with two high cards is 0.81, with one high card it is 0.74 and with 0 high cards, 0.68. Why do we bother counting the number of high cards? Why don’t we just lump them all together as four-card straights and average out the expected values? Not doing so, would cause us to miss many important plays.

A four-card straight with three high cards is the ONLY straight that ranks over a low pair. Admittedly, here is only one way this hand can occur (10-10-J-Q-K), but it’s just indicative of why we break out the four-card straights by the number of high cards. A low pair outranks ALL other four-card straights. While playing regular poker, you might decide to throw a low pair in favor of a four-card straight, using an all-or-nothing type of approach. In Video Poker, this could cost you a great deal. Low pairs have an expected value of 0.82, which is considerably higher than all the other four-card straights, and we haven’t even brought inside straights into the discussion yet. When playing video poker, it’s not necessarily the smart move to use an all or nothing approach. Playing the low pair, hoping to catch the trips, even though a straight outranks it is still the proper play.

So far, I’ve discussed outside straights that can be filled in two different ways. Inside straights that can only be filled one way have far lower expected values. The highest-ranking one (J-Q-K-A) has an expected value of only 0.59.

So, despite having four high cards, the ability to make the straight with only four cards (instead of eight with an outside straight) lowers the expected value greatly. As a result, in full-pay jacks or better, we find that if the four-card inside straight doesn’t have at least three high cards, we’d be better off playing just the high cards, or even throw all five cards if the four-card inside straight doesn’t have a high card.

Additionally, many three-card straight flushes will outrank these four-card straights making them very rare plays. As always, I strongly recommend you study the strategy table before putting your hard-earned cash at risk in a casino.