Video poker is a game that allows players to calculate the return of the game – if it is a “fair” game. Fair, in this case means random.

Many video poker players have doubts about the randomness (fairness) of the games they play. This article explores video poker “fairness” and how to prove it.

1. Why players feel the games are not fair

Every casino game has streaks – both winning and losing. This is true for slot machines, video poker, and table games.

Slot machine players do not know the house edge is for games they play. In general, slot machine players expect to lose. There is nothing they can do that will influence the outcome.

Video poker is different. The pay table and knowledge of how often the winning hands will occur allows players to calculate the house edge.

The player also has a choice. That choice will impact the outcome of each hand. 

The knowledge of the house edge and the ability to affect the outcome of each hand causes some video poker players to have an expectation of how frequently the winning hands should occur.

When those expectations are not met (usually during a long losing streak), often players accuse the game of being unfair (not random).

2. How randomness manifests itself

Many video poker players expect each winning hand to appear close to the average frequency. For example, in a random game a full house has a mathematical probability of appearing once approximately every 85 hands. Players expect them to occur once every 85 hands or so.

According to Wikipedia: “randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable”.

Results cannot be predicted. A particular winning hand could occur two, three, or more times in a row, or not occur for two, three, or more times its mathematical cycle.

A full house that mathematically should occur once every 85 hands might not occur for 200, 500, or even 1,000 hands – or it might occur five times in 20 hands.

The mathematically derived frequency is an average. It is based on an infinite number of hands.

Video Poker

3. Frequencies of winning hands for selected games

Listed below are mathematical frequencies for winning hands for two games.

Frequencies of Winning Hands

Hand Jacks/Better 9/6 Double Bonus 9/6/5
Royal Flush 40,390 40,864
Straight Flush 9,148 9.205
Four of a Kind 423 -
Four Aces - 4,462
Four 2s, 3s, or 4s - 1,906
Four 5s thru Kings - 617
Full House 86 92
Flush 90 90
Straight 89 64
Three of a Kind 13 13
Two Pairs 7 8
Pair-Jacks or Better 4 4

4. The proper way to determine whether a game is fair

The human mind is an amazing thing. However, it can easily be fooled. Players remember long periods without any winning hands. They tend to forget those times when winning hands appear more frequently than normal.

We cannot rely on our memories to determine if a game is fair. We must record actual data. 

The number of hands played and the number of winning hands are required. This is a lot of work and probably not worth all the effort. But it is necessary to prove fairness (randomness).

Recording the number of hands played and only one or two infrequent winners (such as full houses) is more manageable.

Rather than try to count each hand played, take advantage of the players card bonus point count. Almost all players clubs give points based on dollars per point. To calculate the hands played follow either option A or B.

  1. If you know the dollars per point:
    • Calculate the number of hands played by subtracting the starting points from the ending points giving the number of points earned this session.
    • Multiply this by the number of dollars per point. This gives the dollars played this session. 
    • Divide that number by the amount of each bet – for example, $1.25 for a quarter game or $5 for a dollar game. This gives the total hands played.
  2. To calculate the dollars per point:
    • Make a note of the starting players club points.
    • Play 20 to 50 hands (the more the better). Keep track by making a hash mark when each hand is bet.
    • Remove your players card and then reinsert it to update the point count.
    • Subtract the new count from the starting count to get the points earned.
    • Multiply the number of hands played by the cost per hand to get the total dollars played.
    • Divide the dollars played by the points earned to get the dollars per point.
    • Go to A.

While playing, keep track of the number of full houses. This can be done by making hash marks. Add up several sessions totaling at least 20,000 hands. The more hands, the closer the results will be to the average frequency.

It is a whole lot of work. However, if the effort is taken, I am virtually certain the results will confirm a fair game in major gaming venues. Remember, the more hands captured, the closer to the mathematical frequency you should be.

Video Poker

5. Summary

Video poker players sometimes feel games are rigged (unfair).
A player’s memory is unreliable as it remembers long periods without hitting winning hands, but forgets winning hands that are more frequent than normal.
Based on the game and pay table, the frequency of winning hands can be calculated.
Determining the fairness of the game requires a lot of work and will almost certainly prove the games in major markets are fair.

Jerry “Stickman” has been involved in casino gambling for nearly 30 years. He is an expert in blackjack, craps, video poker and advantage slot machine play. He started playing blackjack in the late ‘80s, learned several card counting systems and used these skills to become an advantage blackjack player and overall winner of this game. He also acquired the skills necessary to become an overall winner in the game of craps, accomplishing this by a combination of throwing skill and proper betting techniques. Stich is also an overall winner playing video poker.