Video poker statistical analysis

As this is my first post, please, let me thank all active members who make this forum such a great resource.

Although I have searched the forum, I haven't found what I am looking for.
I want to analyze online video poker machines.

Especially, I am interested whether

• they are fair or biased
• there is any (statistically significant) difference, if you play for fun (points) or for cash
• ...

Is there special purpose software available that provides such statistical analysis?

Maybe someone can give me a jump start on

• how many hands I must collect at least (for JB and Joker's Wild)
• how I should 'encode' the hands such that they can be used for further analysis most effectively
• ...

What about the idea to map the dealt hands to unique hands such that it is easier (?) to find patterns regarding the first and second dealt, i.e., final hand.
Or does this transformation reduce or even bias the original data?

Any help and information regarding how to do statistical analysis the right way is highly appreciated.

1) Hi MoonRaker1, and welcome to the forums.

2) It's cheating to use Oddjob or MoonRaker... everyone knows that ;-).

3) A good place to start would be to look at the Wizard's Video Poker analyzer for your specific game (type / pay table).

https://wizardofodds.com/games/video-poker/analyzer/

After that you can take the resulting table with probabilities and build out an excel sheet (or something else more automatic if you know how to code), then just record hand by hand. It depends how in depth you want to get on whether or not you want to check individual hands. I think personally that would be a MASSIVE undertaking which would involve logging every single card from every single deal/draw. Basically you can record your "buckets" of results (such as are listed on the Wiz's return table):

(sorry for s&*t formatting, just doing this quickly):
Natural Royal Flush 4,000 49,677,654 0.000024 41,213.81 15.489727 0.019411
Five of a Kind 1,000 191,112,966 0.000093 10,713.06 3.696275 0.018669
Wild Royal Flush 500 213,025,399 0.000104 9,611.09 1.019627 0.010405
Straight Flush 250 1,177,014,059 0.000575 1,739.49 1.379925 0.028744
Four of a Kind 100 17,516,331,096 0.008555 116.89 3.086391 0.171108
Full House 35 32,101,452,702 0.015679 63.78 0.563232 0.109754
Flush 25 31,891,658,383 0.015577 64.20 0.248421 0.077883
Straight 15 33,976,555,727 0.016595 60.26 0.065951 0.049785
Three of a Kind 10 274,223,552,262 0.133937 7.47 0.132211 0.267874
Two Pair 5 227,002,401,450 0.110873 9.02 0.000005 0.110873
Kings or Better 5 290,645,557,531 0.141958 7.04 0.000006 0.141958
All Other 0 1,138,417,120,871 0.556029 1.80 0.563240 0.000000
Totals 2,047,405,460,100 1.000000 2.25 26.245010 1.006463

Basically log your hands in to a BLANK table like that and keep track of your total hands. Then after X hands (probably like 50k or 100k) you could check your results against the basic probabilities to see how they line up. For example, if you hit 1659 straights in your 100k hand trial, that would mean you hit on on average 1.6595% of the time, which would line up EXACTLY with expectation. Do that for all of your categories and see how well you fall in line with the probabilities. After X amount of hands (again something like 50k or 100k) you should have a large enough sampling size to know if you're well out of the realm of likely or not.

The PROBLEM is if online sites were SMART about cheating they would just shave each of the probabilities a bit so it wasn't too obvious and they could still jack up the house edge in reality by shaving each category just a little bit. So you could run 100k hands and due to variance find something that's 1SD down and that's still in the realm of 'normal' even though they might have programmed it to be 1SD worse than what it's supposed to be.

When it comes to online you need to either accept you're "gambling" with the sites reputation, or don't play online. The amount of time (and money) you're going to burn "checking" these online games, you could be putting that brain power to work beating real casino games and making money. Not worth it in my opinion, but I understand how people get locked in on ideas and want to solve the problem... Best of luck.

@Romes Thank you for your valuable information.

FYI, the last 67K Joker's Wild (play for fun) hands logged:

No problem... I thought I put this in my original post, but re-reading apparently I did not... Another thing to note is that while you could take 100 hours of your life and dedicate it to figuring out if one site and one game is fair or not you could learn another entirely more useful skill. Hell, you could even learn to be exceedingly proficient with card counting, or perfect your strategy for ANY kind of VP game, or learn about other AP opportunities through research and study. Basically, while I understand the "itch" and need to know if the game is fair or not, why not just dump online and put your time in to something more useful/profitable? Maybe not even in AP but in your career, relationships, etc, etc?

I appreciate your life coaching.
You may rest assured that I have a good work/life balance; I do not gamble at all.

Quote: MoonRaker1

I appreciate your life coaching.
You may rest assured that I have a good work/life balance; I do not gamble at all.

To my understanding, that sounds like NO life. :-)

Anyway, I would first search reviews of specific software providers. Some online software, you KNOW they are rigged. Count on it. Some others, very reputable. Might save you some time.

LOL

Anyone interested in the collected data?

I'm not really interested in seeing the data, maybe others are... But one question... Wouldn't it be easier to determine a game is fair based on the frequency each card comes up than it would be to analyse the frequency each hand is made? Seems like if each card appears within X standard deviations from the mean, you have a fair game.

Could it be that easy?

I assumed that it may be possible to have an overall sound card frequency distibution while the hands made could significantly deviate.
Sorry, if these are basic questions for the wizzes amongst you but I am terrible lost in this kind of reasoning.

Quote: MoonRaker1

Could it be that easy?

I assumed that it may be possible to have an overall sound card frequency distibution while the hands made could significantly deviate.
Sorry, if these are basic questions for the wizzes amongst you but I am terrible lost in this kind of reasoning.

I would like to meet the person who can make all the cards appear in the correct frequency but still rig the game. I would also like to be friends with this person especially if they work for Powerball.

I try and limit myself to 2 good ideas a day. This may or may not be one.

In VP there are dependent draws. Doesn't this make a difference?

Here is some data.

This is the game:


149976 games logged.

Frequency distribution of returns:


Frequency distribution of cards dealt:

Quote: prozema

Wouldn't it be easier to determine a game is fair based on the frequency each card comes up than it would be to analyse the frequency each hand is made? Seems like if each card appears within X standard deviations from the mean, you have a fair game.

No, absolutely not. Mathematically and analytically this is a really wrong-headed idea.

Simple-minded example: you are playing texas hold-em. Om two consecutive pre-flop hands you are dealt these 4 cards: 2 kings and 2 sevens. Clearly, being dealt KK and 77 on those two hands is better than being dealt K7 and K7.

Quote: gordonm888

No, absolutely not. Mathematically and analytically this is a really wrong-headed idea.

Simple-minded example: you are playing texas hold-em. Om two consecutive pre-flop hands you are dealt these 4 cards: 2 kings and 2 sevens. Clearly, being dealt KK and 77 on those two hands is better than being dealt K7 and K7.

I'm fairly convinced that VP is not rigged at B&M casinos. I've had too much experiences and too many wins and losses to feel otherwise. I've thought about ways to test for fairness and sometimes all I look at is the distribution of the important cards on the deal, such as 2s in DW or Aces in a DB or TDB game. But really, to get to anything statistically relevant you have to look at many, many hands.

Quote: gordonm888

No, absolutely not. Mathematically and analytically this is a really wrong-headed idea.

Simple-minded example: you are playing texas hold-em. Om two consecutive pre-flop hands you are dealt these 4 cards: 2 kings and 2 sevens. Clearly, being dealt KK and 77 on those two hands is better than being dealt K7 and K7.

That makes sense. If I imagine a game that only had Kings and 7 in the deck and I got the right number of each card over enough two card draws, but never got a pair that would definitely cause suspicion.

Thanks for correcting me.