Four Of A Kind Is Pretty Fair Consolation In Video Poker

Aug 28, 2012 3:00 AM

For those who read my column regularly, you are probably now well aware that a full-pay Jacks or Better video poker machine pays 99.5%. Many people are still confused, however as to what this means. 

It does not mean that if I start with $100 I will walk away with 99.5% or $99.50. It means that in the long run, you could take the total amount you wager (not your bankroll) and multiply it by 0.5% (the “loss” rate or 100% minus the payback). This should be the amount you have lost over time.

So, if you play 10,000 hands over the course of a year (or a month or a decade) plus max-coin $1 machines, you would have wagered $50,000 and can expect to lose about $250. 

In video poker, however, 10,000 hands isn’t really the long run. Don’t get me wrong, it is certainly approaching the long run. But, given that a Royal Flush should occur about every 40,000+ hands, it would be hard to declare 10,000 to be the long run. 

If you’ve hit at least one Royal, you would be ahead of the game. If you haven’t, it would be totally fair to say you are behind because you still have 30,000+ hands to go. Royal Flushes account for about 2% of our payback. So, if you were to never hit one, you’d theoretically be playing only a 97.5% game.

With a hand frequency of 1 in 40,000+, Royals sort of march to their own drummer. You might hit 2 or 3 in 40,000 hands or you might go 100,000 hands without hitting one. When you hit one, you’re going to have a very good month and when you don’t, well, it will be harder to even break even.

Four of a Kinds, on the other hand, should occur about 1 in about 420 hands. With the average player playing hundreds of hands per hour and perhaps thousands in a session, this hand becomes critical to our chances of success over a session or two. It accounts for 6% of our overall payback. 

Relative to the other hands, this is not necessarily large, but it is a hand that is frequent enough that you expect to hit it over a session, but not frequent enough to be sure you’ll hit your fair share over a few nights. 

If you were to play 10,000 hands, you’d probably find that the frequency of high pairs, trips and straights are very close to what they should be. Royals will by very definition have to be either more frequent or less frequent than expected, but Quads can be just about anywhere over that period of time. 

In theory, you should hit about 24 over that time. The math says you very likely could hit only 12 or as many as 36. If you hit 12, you’re about 3% short in payback. Assuming you haven’t hit a Royal and you’re now 5% short. The odds of coming up a winner over that span is very unlikely as you’ll be playing at 94.5% and hoping the other hands come up big - which simply isn’t very likely.

Conversely, if you’ve hit 36, you’ll be at 100.5% even if you haven’t hit a Royal. A winning session is not guaranteed but certainly more likely. Over time, the frequency of the Quads will slowly head towards that 24 per 10,000 hands, but your results in the short or medium run is heavily dependent on hitting your Four of a Kind.

As with anything video poker, the number of Four of a Kinds you get is at least partially attributed to luck. We’ve all played for hours and been dealt dozens of Three of a Kinds to watch none turn into Quads. We’ve also all sat there and drawn 3 Kings to a single King. Nothing that happens is truly out of the ordinary. However, you can increase your chances by playing the right strategy. 

If holding a 4-Card Straight over a Low Pair, you are going to greatly reduce your chances of Quads. If you hold 3 High Cards instead of just the 2 that are suited, you will lower your chances for getting Quads. The reason why we hold only the 2 suited cards is both to give us a chance to hit the Royal and to increase the chances of Quads. 

Both of these hands are reduced to zero chance if you hold 3 off-suit High Cards!

Of course, if you choose to hold a Low Pair over a 4-Card Flush you may increase the frequencies of Four of a Kinds, but you’ll do so at your own peril. Quads are important, but not so important that you should be throwing the proper strategy out the window.

Elliot Frome, a second generation gaming analyst and author, can be reached at www.gambatria.com His math credits include Ultimate Texas Hold’em, Mississippi Stud and many other games.

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