Dispelling Notions of Rigged Video Poker Machines
By Jerry “Stickman” Stich
I have friends who firmly believe that casinos “fix” their video poker machines. They feel the casinos are cheating by not giving a random game, and in support of their beliefs, they cite some of the following observations:
- Have you ever noticed when you’re dealt three of a kind, you almost never get the fourth?
- What about when you’re dealt four of a flush—you almost never complete it.
- How about four of an open straight? You might as well forget about completing it, right?
And how many times have you saved four cards, and redraw only to get the same rank as the card you discarded? You discard the three of hearts and get the three of diamonds, discard the 8 of clubs and get the 8 of spades, discard a jack, get a jack, etc.
So are the machines rigged? Are they not really random? Are the casinos cheating you? Let’s take a more detailed look at these phenomena, and get to the truth.
You are dealt three of a kind. What are the odds of drawing to four of a kind? Five cards of the 52-card deck have been dealt. Three of those five are your three of a kind, so there is one card in the 47 remaining that will complete your four of a kind.
However, you have two cards to draw. The actual odds of completing a four of a kind when you already have three of them is 1 in 23.5. Only once in nearly 24 attempts will you complete the four of a kind. Combine this with the fact that you are dealt three of a kind only once every 424 hands, and it’s a rare occurrence, indeed.
Now let’s look at when you’re dealt four of a flush. There are 13 cards in each suit. Since four cards of one suit are already in the hand, there are nine cards of the same suit in the remaining 47 cards that have not been dealt. That means you’ve got about a one in five chance of drawing a card that completes the flush. While one in five doesn’t seem all that unlikely, another factor comes into play: one in five happens over the long run, and people tend to remember what they don’t expect to happen.
You may go five times before completing the flush, or you may go 10 times, 15 times, or 20 times or more. Then you might complete the flush two, three or four times in a row. The fact is, it will not be once every five times, but once in five times on average. When we see a hand having four of a flush, we expect to complete it. The human mind, being what it is, will tend to forget the times the flushes complete frequently (because it is expected) and remember the times it does not complete. Over thousands of hands we’ll get close to the mathematical expectation, but we don’t remember it that way.
The same situation exists when being dealt four of an open straight. (This is a straight with no gaps that can be completed on either the low or high end.)
In the first example, either a three or eight will complete the straight. In the second example, an eight or king will complete it, and in the final example an ace or six will complete the straight.
There are eight cards in the remaining 47 that will complete the hand when dealt four of an open straight: four on the low end, and four on the high end. Eight out of 47 cards will complete the hand, or just a little more than once every six times. As with four of a flush, we expect to complete this hand. When we do, we tend to forget about it. When we don’t, we tend to remember it. Over thousands of hands it will work out as the math dictates.
What about the situation where you discard one card and it’s replaced with the same rank? In this case, there are three cards out of 47 that will work—or about one in 15 times. Again, the human mind tends to remember things that are not the norm. We remember the big wins and forget the smaller losses; when almost sure things fail to happen, that sticks in our brains. And, we remember when things that shouldn’t happen do happen.
This might be particularly true for cards of the same rank. When the draw button is hit, we expect the discard to change. When it’s replaced by a card of the same rank, very little changes. We remember that because it’s not the norm. This is especially true if the replacement is the same color as the discard. However, if you keep good records, you’ll find that after thousands of hands you get the results the math dictates.
No, the casinos aren’t cheating us by “rigging” the machine to not be random. We just seem to remember it that way.