How to play a small straight

Mar 19, 2007 10:55 PM

When video poker first hit the casino floor, all I could do was play by common sense along with everyone else. It was only after my father, Lenny Frome, developed his analysis that I was able to follow along according to expert strategy.

I was young and impatient and I didn’t have time to really sit and study his strategy, so instead, he would give me the basics verbally. One of these lessons included one of the key rules to playing full-pay jacks or better, because the hands are so common. If you have a low pair and a 4-Card flush, play the flush. If you have a low pair and a 4-Card straight, play the low pair. (There is, of course, one exception to this latter rule, but in an attempt to get me to improve my play, he kept it simple.)

I’ll admit that the common sense player in me, and not the budding mathematician, was finding this hard to believe. I have nine ways to complete the flush and eight ways to complete the straight and this so dramatically changes my play? The answer is ”˜yes’ and ”˜no’ to this one, as this does not fully address the issue.

As always, the decision is ruled by the expected value. The expected value is calculated by multiplying the payout of the hand by the number of possible ways that hand can be the final result and dividing this total by the total number of possible hands.

When holding four cards, there are 47 outcomes. In full-pay jacks or better, a flush pays 6 and a straight pays 4. So, the expected value for the 4-Card flush is 9 ways times 6 coins for 54 divided by 47 or just below 1.2.

The 4-Card straight on the other hand is calculated as 8 ways times 4 coins for a total of 32 divided by 47 or just a smidge under 0.67. If the 4-Card straight has any High Cards, we can add 3 more coins to the total for each High Card for the possibility of a Jacks or Better. In the end, it will never approach the expected value of the flush or even get close, and it is possible for the flush to contain some High Cards as well, which was not considered earlier.

The difference between the expected values is more impacted by the payout of the hand than the number of ways the hand may occur. It is this difference that creates the rule in the first place.

To further prove this point, let’s consider the game of All American Video Poker.

This game, which is now nearly impossible to find in its full-pay version (probably because of its 100.7% payback), pays 8 on a Full House, flush OR straight, while paying 1 on Two Pair and 40 on Four of a Kind.

These are the hands in play for the scenario we are discussing. The impact of the Full House payout and Four of a Kind payout will make a minor impact to our Low Pair. The impact of paying 8 on the flush and straight, however, make an even greater impact on the 4-Card hands. The net result is that a 4-Card flush is now played over ALL Pairs, not just Low Pairs. The 4-Card straight rule has been turned upside down.

All 4-Card straights are played over Low Pairs. They are even played over a High Pair! In this version of the game, the payout on the straight being raised to 8, even causes 4-Card INSIDE straights to be not only playable, but played over Low Pairs, EXCEPT when the 4-Card Inside straight contains ZERO High Cards.

There are two important lessons to be learned from all this. The first is that the expected value is a product of both the likelihood of a particular final hand AND its payout. The second is that because of this, every change to the paytable may cause significant changes to the strategies that must be used in order to maximize the payback of that paytable.

A one size fits all approach is not a good one where video poker is concerned. Perhaps our strategy table would be simpler if we could just get paid for a ”˜small’ straight, as if we were playing Yahtzee.