Are Casinos Rigging Your Video Poker Machine?

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 eight of clubs and get the eight 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.

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Originally Published at Casino Center