Royal treatment

May 29, 2006 12:50 AM

A question I commonly hear is whether or not Expert Strategy maximizes the chance to hit a royal flush. Simply put, the answer is no.

Expert Strategy maximizes the overall payback of the game. In general, the royal flush is worth about 2% of the payback (on jacks or better or bonus machines).

While this is no small amount for a single hand, it is still a relatively small piece of the pie. Expert Strategy looks to maximize the size of the pie, not the size of any one slice.

If one were trying to maximize his chances of hitting a royal, he would play virtually every hand as if the only hand that mattered was the royal. So, even if dealt three 7s and a Jack of Diamonds, he would throw away the three of a kind to go for the royal.

Without even showing the math, I doubt there is anyone reading this who would even consider this play. But would you hold a lone Jack over only a pair of 7s?

What about a suited Jack-Queen over a low pair?

These questions get a little trickier, and quite frankly it depends on the specific paytable. When you’re playing a progressive game where there is a big prize for the royal, the hands that quickly move up the strategy table are the partial royal flushes.

But for today, I’m going to focus on full-pay jacks or better. If you’re lucky enough to be dealt a 4-card royal, there is little to decide. Unless it is a 9-through-king straight flush, you go for the royal. So, you will throw away a flush, a straight or a high pair in favor of the 4-card royal.

If you’re dealt a 3-card royal, it starts to get a little trickier. You’ll hold a high pair over a 3-card royal. You’ll also hold a 4-card straight flush or 4-card inside straight flush instead of the 3-card royal.

The same goes for a straight or a flush. You will, however, discard a fourth card of the same suit or a card that would make a 4-card straight, in favor of the 3-card royal.

One important note is that when you’re playing a progressive game, this hand can move ahead of a high pair as the jackpot grows. As the jackpot increases, the strategy slowly changes to increase the frequency of royals because hands such as a 3-card royals are played over a high pair.

Now, 2-card royals get much more complex. We need to categorize them by the specific card makeup. If the 2-card royal consists of only a J-Q-K (two of three), then it is categorizes as V3. If it contains an ace and a jack, queen or king, it is a V2. If it contains a 10 and a jack, queen or king, it is a V1. If it contains an ace and 10, it is a V0.

Each one of these variations of a 2-card royal has its own entry on our strategy table. They need to be categorized this way, because an ace is the high card on the straight and thus ”˜caps’ our chances of a straight. A ”˜10’ has less value because it is not a high card.

So, a 2-card royal V3 (RF2V3) ranks below ALL 3-card straight flushes. So, if you were dealt a suited 4-5-6 and a suited J-Q (different suit from 4-5-6), you would hold the suited 4-5-6. It also ranks below ALL 4-card straights and 4-card flushes, but ABOVE all 4-card Inside straights.

The 2-card royal V2 is not far behind the V3. The only hand sitting between the two is a 4-card inside straight with four high cards.

So, if dealt a J-Q-K-A where the ace and one other card is suited, you would still keep the 4-card inside straight. This hand, does, however, come ABOVE the HON3, which is a critical item to remember. A very common mistake made by players is to play three high cards when two of them are suited.

There is a significant difference in expected value between these hands (0.58 vs. 0.51), and can cost you a lot of your bankroll if not played properly.

Last but not least is the 2-card royal V1. This falls below a HON2, so if you have a 10-J-K where the 10-K is suited, you would still hold the J-K. The value of the high card outweighs the slight chance of hitting the royal.

The variation V1 is the last because variation V0 is NOT PLAYABLE in jacks or better. If you have a suited 10-A, you are better off playing only the ace. This is not the case for every version of video poker, but is the case in jacks or better.

Using expert strategy for a full-pay jacks or better machines will get you a royal flush on average, about once every 40,400 hands. Using expert strategy on a progressive machines where the jackpot has grown to double the normal payout (8000 coins for max-coin in) will increase the frequency to about once every 32,700 hands.

I’m sure someone could devise a strategy that would make it occur even more frequently. But the goal is not only to hit royals. It is to win as much or lose as little as possible, which increases your chance to walk away a winner. For expert strategy this means accounting for the large payout of the royal, but not exaggerating it.