Are Video Poker Machines Biased?

16 July 2022

By Jerry Stickman

I have good friends who firmly believe that casinos rig video poker machines. They feel the casinos cheat by not giving a random game. They cite some of the following observations in support of their beliefs.

• Have you ever noticed when you are dealt three-of-a-kind that you almost never get the fourth?
• What about when you are dealt four of a flush?
• You almost never complete it – do you?
• How about four of an open straight?

You might as well forget about completing it, right?

How many times have you saved four cards and redraw only to get the same rank as the card you discarded?

You discard the 3 of hearts and get the 3 of diamonds, discard the 8 of clubs and get the 8 of spades, discard a jack, get a jack, etc.

• Are the video poker machines rigged?


• Are they not random (or as random as a computer algorithm can make them)?


• Are the casinos cheating you?


• Let’s take a more detailed look.

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 every 23½ hands, on average, 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 is a rare occurrence, indeed.

You are dealt four cards of a flush.

There are 13 cards in each suit. Since four cards of one suit are already in the hand, there are 9 cards of the same suit in the remaining 47 cards that have not been dealt.

That means there is about a 1-in-5 chance of drawing a card that completes the flush.

While one in five doesn’t seem all that unlikely, two facts come into play.

The 1-in-5 times happens over the long run. It can be much longer in between. You may go five times before completing the flush, or you may go 10 times, or 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 each and every five times, but once in five times on average.

People tend to remember what they do not expect to happen. 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). We will remember the times it does not complete.

Over multiple thousands of hands, we will get close to the mathematical expectation, but we don’t remember it that way.

You are dealt four cards of an open straight.

Note: an open straight is a straight with no gaps that can be completed on either the upper or lower end.

Examples:
4-5-6-7
9-10-J-Q
2-3-4-5

• In the first example either a 3 or 8 will complete the straight.
• In the second example an 8 or K will complete it.
• In the final example an A or 6 will complete the straight.

When you are dealt four cards of an open 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 less often than once every six times.
• Just like 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 multiple thousands of hands, it will work out very close to what the math dictates.

You discard one card and it is replaced by a card of the same rank.

In this case there are three cards out of 47 that are the same rank. This is about one in 15 times. About once in 15 times the replacement will be the same rank.

Again, the human mind tends to remember things that are not the norm.

• It will remember the big wins and forget the smaller losses.
• It will remember the times that almost sure things do not happen.
• It will 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 is replaced be a card of the same rank, very little changes. We remember that because it is not the norm.

This is also true if the replacement is the same color as the discard.

None of the situations mentioned above are proof that video poker games are rigged. If we keep good records, we will see that after thousands to hundreds of thousands of hands, the results are very close to what the math says they will be.

No, the casinos aren’t cheating us by “rigging” the machine to not be random. We just remember it that way.

As always, may all your wins be swift and large, and your losses be slow and small.
Jerry “Stickman”

Jerry “Stickman” is an expert in craps, blackjack and video poker and advantage slot machine play. He is a regular contributor to top gaming magazines. He authored the video poker section of Everything Casino Poker: Get the Edge at Video Poker, Texas Hold'em, Omaha Hi-Lo, and Pai Gow Poker! You can contact Jerry “Stickman” at stickmanjerryg@gmail.com