# Are there too many times three of the same suit are dealt on the board in Replay Poker?

Thank you for your input. We need to look at the big picture.

Chet

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Your 100 hand sample doesnât stray from the expected mean as much as my sample in the original post does. The probability of three of the same suit appearing on the flop is 0.05177. Therefore the variance of any sample measuring how often this happens is 0.05177 * (1 â 0.05177) ~= 0.049. The standard deviation for a sample size of 100 is sqrt(100 * 0.049) = 2.21. The expected mean for how many flops contain three of the same suit for a sample of 100 is 100 * 0.05177 = 5.177. Your sample contained 4.82 (rounding to hundredths) more than the expected mean. This is 2.18 standard deviations outside of the expected mean with a p value of 0.985. Even your data, for which you furnished no evidence, is not as deviant as my sample for which the data is accessible.

The statistical power of my sample is stronger. The standard deviations from the expected mean in my sample of 118 hands is 2.64 which has a p-value of 0.996 (rounding to thousandths). This means that if you were to take 1,000 similar samples you should expect only 4 out of 1,000 to deviate as much from the expected mean. This one sample, with an accessible data set, is sufficient in and of itself to suspect that something is amiss. This is one peculiar âclusterâ indeed.

There is a problem, but the problem is not with the amount of times three or more of the same suit is dealt to a board consisting of five cards on Replay. The problem according to Brian Alspachâs calculations, and my affirmation that his calculation is valid and accurate, is that the probability of a five card board consisting of three or more of the same suit is 0.371 and not 0.23589 as listed on Card Playerâs website. When substituting Brian Alspachâs probability for Card Playerâs my sample falls within one standard deviation of the expected mean and is actually slightly lower than the expected mean.

Referenced Materials:

Brian Alspachâs probability http://people.math.sfu.ca/~alspach/art4.pdf

Card Playerâs probability https://www.cardplayer.com/poker-tools/odds-and-outs
(found at the bottom of the webpage)

My confirmation of Brian Alspachâs calculation can be found in the comment section of this post. Alspach calculated the amount of combinations where three or more of a same suit appear out of all possible five card combinations, and I calculated the amount of combinations where three or more of the same suit do not appear out of all possible five card combinations. The sum of both our calculations equals the amount of total five card combinations so the probability that Alspach propounded in his writing seems valid to me.

It changed he said when he got to the 500 hand mark.

My point is that even his initial 100 hand sample which he thought to be somewhat suspect is not as deviant from the expected mean as my sample in the original post. Moreover, his subsequent sampling must have deviated from the expected mean in the opposite direction to produce the 500 hand results at which he purportedly arrived.

The higher the sample the more the deviation is what we are saying.

Not sure what exactly you are getting at, but I think we agree - the number of 3 suited cards on the flop - when a large enough sample is examined - gets right down to about where it should be.

The only reason I pointed out the first 100 hands was to point out that such a sample can lead people to believe something is amiss. That kind of thing happens on here all the time - People saying âI know what I seeâ without providing anything other than anecdotal evidence to back it up (âHereâs 10 hands - see!!! I was right!!!â).

All.
The.
Time.

(you did not do this - you were working with apparently flawed information from Card Player, and thatâs not your fault)

âMoreover, his subsequent sampling must have deviated from the expected mean in the opposite direction to produce the 500 hand results at which he purportedly arrived.â

Well, yeah - thatâs how this kind of thing works - itâs not a smooth line to 5% - it has plenty of ups and downs over short term samples - but a large enough sample is going to show where the truth lies.

And honestly, my âmore than 500 or soâ sample could have easily shown 7%, or 6%, or whatever percent. 500 just isnât that much either in the grand scheme of things. I had a real strong âthree on the flopâ run those first hundred hands - but I hit some real droughts of it on the subsequent hands. I just got tired of logging information when I felt like I could clearly see where it was heading.

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But, it shouldnât. If you take a 100 hand sample that is 2.18 standard deviations above the expected mean then take another sample of the same size that is 2.18 standard deviations below the expected mean the mean of the two samples will be exactly the expected mean. However, less than five percent of samples are supposed to be two or more standard deviations away from the expected mean. So, there can be an issue with the random distribution even if the mean of all samples is identical to the expected mean.

An extreme example of my point is illustrated if we imagine that 100,000 samples of 100 hands each is drawn. Imagine that 5,177 of those hundred hand samples contain 100 out of 100 flops with three of the same suit. Also imagine that 94,823 of those 100 hand samples contain zero flops with three of the same suit. In this hypothetical the mean of all 10,000,000 hands matches the expected mean exactly, but one could hardly conclude that the cards are randomly distributed.

If you sampled 100 hands with a mean that is 2.18 standard deviations above the expected mean then the next sample of 100 hands was 2.18 standard deviations below the expected mean this still raises red flags when spotting patterns that are not random. This is so because less than 5% of samples should have a mean that is 2 or more standard deviations away from the expected mean.

Thatâs all I was trying to say. I really donât want to get any further into the weeds on this matter because the original issue I raised is resolved to my satisfaction, and I havenât the inclination to question and then confirm or reject the accuracy of your sampling procedures.

Donât need need calculus to know that the way the cards fall at this site is like a cartoon caricature of actual poker odds. All the programs on line are developed to promote betting and increase rake.

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I unfortunately am forced to agree with you. It is better than no poker surely but a strong stomach is needed if one knows what true random dealing looks like. You get that experience in casino poker rooms -if you can still find one- but that isnât free folks !

Would you be so kind as to provide a modicum of evidence to support your allegations. Also, please study the link provided below

@mikepsg, you may be right that integral and differential calculus is not necessary but data and calculation is absolutely required.

Your homework is to calculate the required sample size required to determine whether the dealing is random or not to 6 sigma probability. Having done that, you are expected to collected the appropriate amount of data and and make the appropriate calculations.

Just like any other person who is truly interested in obtaining the truth, I expect that you would be willing to share your data and a discussion of the methods that you used so that others can verify your work.

Alternatively, you can look at the site certificate for the algorithm used and accept the word of highly paid professionals.

Regards,

TA
Slava Ukraini

This site has computer generate better hands for more action and the 5% rakeâŚI played MANY years in cessions, online cash games etc. and my 1 year here have seen WAY more great hands then anywhere lol.

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You are 100005 right

1000000000000000% right lol