How many of you remember ABC’s Wide World of Sports from a few decades ago? It has a famous opening that talked about the “thrill of victory and the agony of defeat.”
Who can forget that image of the skier wiping out on the slope? Some days it seems like they could’ve been talking about video poker with that tag line. In the past couple of weeks, I’ve had the opportunity to venture out and play some video poker.
Last week, I had a less than stellar outing. In the first 20 minutes I was handed numerous opportunities to crush the house. I was playing Double Double Bonus Poker and was dealt a plethora of Three of a Kinds right off the deal. What more can you ask for in this game that rewards so well for Quads?
I always promise myself I’ll keep detailed information about the frequencies of such phenomenon, but alas, I never do. I’m forced to approximate what took place and undoubtedly fall into the common trap of remembering things a bit differently than they actually took place. But, for illustrative purposes, we’ll go with my best recollections and take them with a grain of salt.
I would say in those first minutes I was dealt about 10 Three of a Kinds in the first 100 to 150 hands. The odds of being dealt Three of a Kind are just over 2%. But, being dealt 10 in 150 hands seemed like a lot (this is closer to 6.7%). I calculated the odds of this and it is about 1 in 959.
Certainly not a common occurrence, but hardly earth shattering. To add to my intrigue (and my less than successful evening), none of these 10 Trips resulted in a Four of a Kind. This seemed almost as bizarre. But, when I performed the calculation to determine the probability of this, I found that hitting zero Quads should happen about 67% of the time.
This is not for a single Trips, but for all 10 resulting in zero Four of a Kinds. That’s right, it is nearly twice as likely to get no Four of a Kinds as it is to get one or more. Only about 1 in 23 Trips will turn into Quads. What I thought was an unlucky streak in that I didn’t get any Four of a Kinds was probably actually a lucky streak that I got this many Three of a Kinds.
Unfortunately, by the end of the night, I seemed to struggle to get any Four of a Kinds, and eventually the Three of a Kinds dried up a bit too, and well, it just wasn’t pretty. You can be a skilled video poker player and still have bad nights if the cards just are not in your favor.
Fast forward to this week. I decided to play a less volatile version of video poker and went for Bonus Poker. This invariably leads me to hitting Four Aces almost every time I play. Why should it hit on the version that pays considerably more, when it can torture me by hitting it on a non-Double Double machine?
That night was no exception, and to add to the insult, I hit it with a Deuce kicker. But that’s not really the point of the story.
I initially was playing off some of my comp money from the casino. This is one of the reasons I was playing Bonus Poker. When playing comp money, I aim for high payback, low volatility games that tend to result in a higher likelihood I will wind up with a larger portion of my comp money in cash.
After having played about half of the comp, I had only had about an 80% return on my money – which is absolutely awful for a full-pay machine. I seemed to be getting a fair amount of Pairs through these hands, but noticed none had turned into Trips. This is a far worse fate than having Trips not turn into Quads as most Pair hands are losers. I would say about 20 of these happened in a row.
Back to my calculator I went. What is the likelihood 20 straight Pairs will not turn into Trips or Quads. It turns out the probability is about 8.2%. The probability of having any single hand turn into Trips or Quads is just over 11%. I was running cold, but we’re not exactly talking frigid. Then, as often is the case with video poker, things began to turn around.
Finally a Pair drew into a Trip. Then it happened again and again. I hit two or three in a row. Then a Pair picked up the other pair and I hit a Four of a Kind. Finally, I was dealt Three Aces and drew the fourth Ace plus the two. No, it didn’t pay the big bonus like in Double Double, but I gladly took my win.
By the time I was done playing my comp money, I had a return of 125%, which is, to say the least, not too shabby. If I look at only the second half of my mini-session, I actually had a return of nearly 200%. It is amazing how the agony of defeat can be turned into the thrill of victory when the machine starts to heat up.
While sitting there, did I think for a moment that maybe the machine was running particularly cold because I was using comp money. Yeah, I probably did. Then sanity came back to me and I realized video poker is a streaky game.
There will be cold and hot spells. Stick with the program and eventually it all evens out to where it is supposed to be.
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].