Is Video Poker Fair? Followup.

28 July 2024

By Jerry Stickman

From Joe K.

Hi Stickman,

I just read your July 6th article titled “Is Video Poker Unfair.”

(Note: Here is a link to the referenced article - Is Video Poker Unfair? (casinocitytimes.com) )

Excellent answer – up to a point. Can you share some of your data/statistics concerning the original hands in question (Flush, Straight Flush and Full House)?
Joe K.

Hi Joe K.,

I purposely left out data and statistical details for a reason – and that is, most readers do not really care about the details and tend to stop reading at that point. But since you asked, here goes.

I had to be able to gather all the information needed without taking too much time to gather it. I carried an 8-1/2 by 11 sheet of paper folded into quarters giving eight surfaces that measured 4-1/4 by 5-1/2.

When I first sat down to play in a new casino I would document the following at the top of a page:
Location (e.g. Las Vegas)
Casino (e.g. Red Rock)
Date

When I started play, I would note the following information:
Machine number
Game (e.g. 9/6 JoB)
Denomination (e.g. $1)
Dollars per player’s club point
Start time
Starting Player’s Club points
I would then label several lines –
4FL
Made
4SF-O
Made
4SF-I
FH’s
4RF
Made
4K

While playing I would document the following information:
Each time money was fed into the game and the amount (e.g. $100).
I made hash marks in the proper line for four-of-a-flush, made four-of-a-flush, four-of-a-straight-flush (open or inside), made four-of-a-straight-flush (open or inside), full houses.
For four-of-a-royal I would note the suit and which card was missing and if it was made.

Whenever a four-of-a-kind, straight flush or royal flush occurred the following was documented:
Time
Rank (for four-of-a-kind)
Cards in the straight / royal flush – before and after the draw

When I was done playing a game, the following was documented:
Stop time
Ending Player’s Club points
Amount cashed out

This information provided everything I needed to calculate frequency of hands as well as return and all IRS required information. Number of hands played are calculated by subtracting the ending player’s club points from the starting points giving the points earned in the session. This is multiplied by the dollars per point giving the dollars played. Dividing the dollars played by the amount bet per hand gives the number of hands played.

The statistics for various years are as follows:

Heading meanings:
Yr = Year code
Hands = Total Hands
Hnds/Hr = Hands per Hour
4-Ryl = Four of a royal flush
FH/Freq = Full Houses / Hands played per flush
4K/Freq = Four-of-a-kinds / Hands played per four-of-a-kind
SF = Straight Flushes
RF = Royal Flushes
4-FL / Made / % = Four of a flush, number made, percentage

Yr Hands Hnds/Hr 4-Ryl FH/Freq 4K/Freq SF RF 4-FL/Made/%
A 31,354 753 55 355/88 75/418 0 1 1,143/222/19.42
B 83,893 812 98 1,329/63 171/491 7 0 3,000/580/19.34
C 52,126 789 -- -------- 109/479 7 0 1,810/364/19.99
D 50,909 778 -- -------- 107/476 4 1 1,735/322/18.56
E 78,128 782 -- -------- 170/460 7 2 2,743/544/19.83

Notes:
Originally the only statistic for determining whether the games were “fair” was the number of four of a flush hands that became flushes. Notice that this number tracks very closely to the statistical value.
Full houses should appear about once every 87 hands. Four-of-a-kinds should occur about once every 430-480 hands depending on the game. Four of a flush hands should fill about 19.15 percent of the time.
The observed frequencies of each of the above hands, based on a somewhat limited but reasonable sample, are very close to the mathematically determined values.
Four of a royal and full house information was not kept for years C, D, and E.

The observed results of nearly 300,000 hands are very close to the calculated values. This was proof enough for me that video poker games played are at least close enough to “fair” to be considered fair.

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 and 888casino.com. 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