Strategy of holding high cards

Jul 31, 2006 3:26 AM

When my father, Lenny Frome, completed his first video poker analysis, one of the biggest surprises that came out of that process was that keeping three high cards was not necessarily preferable to keeping two high cards.

While it may seem intuitive that the best play would be to keep a J-Q-A instead of just two out of the three, it turns out this is not the case. The very strange part about this is that the proper play is to discard the ace, unless it is a suit match to one (or both) of the other two cards.

While an ace can be a very powerful card in a regular poker game, it really has no more value than any other high card in video poker, and in fact, can actually be worth less as it is harder to make a straight while holding that Ace. I’ll leave the specifics of this to another column.

First, let’s review the strategies for these types of hands. The ONLY time you keep three high cards is if ALL three are suited (a 3-card royal) or if all three are unsuited and they are a J-Q-K. If you have any other three high cards and two of them are of the same suit, then you keep those two, even if it they are a J-A combination. If all three are unsuited, and one of them is an ace, discard the ace and keep the J-Q, J-K or Q-K.

The strategy brings up two key questions. The first is, why should we keep two suited cards high cards, instead of three unsuited high cards (where three of them are suited)?

The obvious answer is because the expected value of the 2-card royal is far greater than that of the three high cards. In the case of a J-A suited plus a Q, the expected value of the three high cards is only 0.46 while the 2-card royal (J-A) is 0.58.

The real question is why is the expected value so much higher for the 2-card royal? Well, this is because by holding on to the 2-card royal, we give ourselves the ONLY opportunity to hit a royal.

But, this accounts for only about 0.05% of the difference between the two. The rest is because we also have the opportunity to hit a flush.

Once you hold an off-suit card, a flush is out of the question. At the same time, we greatly hurt our chances at hitting a straight. However, this is offset by a greater number of quads, full house, trips and two pairs. The net result is that the 2-card royal is clearly the proper play.

The second question is if the three cards were unsuited, why would we drop the ace if we were dealt J-Q-A? This is a closer call than the previous situation, but again, it comes down to the expected values.

The J-Q has an expected value of about 0.50, while the three high cards still has an expected value of 0.46. While holding only two cards reduces our chances of hitting the straight, it is not nearly as pronounced as if it were a J-Q-K (which is why would we KEEP an unsuited J-Q-K). With a J-Q-A, we only have one way of completing the Straight (with a 10-K).

With the J-Q, even though we need the three cards, we have many more ways to complete it, so the impact is minimized. At the same time, we give ourselves a chance to draw a four of a kind, or a full house, which is not possible with the J-Q-A.

We also greatly increase our chances to draw three of a kind. When all of this is combined, the expected value of the two high cards slightly exceeds that of the three high cards (where one is an ace), and thus, the right play is to drop the ace.

It is my belief that it was hands just like these that caused the creators of video poker to create games with near or above 100% paybacks.

Without a complete and proper analysis, almost any player would play these hands according to the intuitive approach and not the proper mathematical approach. These hands are very common hands, and making repeated mistakes will add up to a significant percent of your payback that you will never be able to claim. Sometimes, two IS better than three.