# Dealt three of the kind might be the most frustrating hand

June 27, 2017 3:00 AM
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Of all the relatively common hands in video poker, I find Three of a Kind at the top of the list of frustrating ones. This might seem a little odd.

It is a guaranteed winner, paying three in most variations on the game. So, why do I feel this way about the hand? There are only three outcomes possible when dealt a Three of a Kind. It finishes as a Three of a Kind, you draw a Pair for a Full House or you pick up the fourth for Quads.

Both of those non-Trip hands pay considerably more than Trips. Quads will pay 25, 50 or more if you are playing Double Double Bonus. This is where the problem comes in. You want those Three of a Kind deals, but you also wish to hit your fair share of Quads, maybe even more than your fair share. This can clearly be the difference in winning or losing.

There are 1,081 possible outcomes when drawing two cards. Only 46 will result in Four of a Kind. This is 4.25% or 1 in 23.5. You will be dealt Three of a Kind about 1 in 47 hands. Thus, you should be dealt Three of a Kind and in turn draw Quads, once in about 1,100 hands.

But, these are all averages and certainly not hard numbers. We’ve all been dealt Trips on two hands in a row, perhaps even three. These hands are so critical to having a winning session. If the Trips are the bonus trips in a Bonus video poker game, they become even more important.

But, these averages mean that in a two hour period you’ll be dealt about 20 Trips, and roughly one will turn into Quads. But, the math I mentioned above also tells us it is very possible you can go well past 23 consecutive times of having Three of a Kind without hitting Quads.

This may not be as obvious while playing a single-line game. If you play for about two hours, you may or may not hit one, and not hitting one will not seem so out of the ordinary. But, if you play a multi-play with three or five lines, the resulting hands play out 3x to 5x faster. All of a sudden, in an hour you could easily realize you had 50 resulting draws without hitting the Quads.

When I get a bit frustrated at how my session is going, I have a tendency to track this number. I have frequently hit 50-70 hands without hitting Quads. These are rarely winning sessions. If I hit 1 in 10, it’s usually been a good day.

I guess the issue with this hand is it is such an “all or nothing” type, yet it is so common. Obviously, one could look at a 4-Card Royal in the same way. You have a 2% chance to hit the Royal, another 2% chance to get a Straight Flush. But, you also have a 15%-plus chance at a Flush, another 15%-plus chance at a Straight and countless opportunities for High Pairs. Also, a 4-Card Royal is a rare hand, not one that happens every 5-10 minutes on average.

There’s a huge difference between hitting Three of a Kind and Four of a Kind. A series of Trips can help build your bankroll, but it will take a lot of them to do it. Hitting those Quads, especially bonus ones with a kicker, can frequently mark the end of a session. It is a hand that significantly lifts your bankroll to the point it becomes a good place to stop. And you get teased with it constantly when playing.

So, I guess when I say it is a frustrating hand, I mean when it doesn’t turn into Quads. I’ll happily take Three of a Kind on every hand!