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I played on a mobile app of Texas holdem poker called pokerrrr 2. I suspect the game deals non-random hands.

How can I prove the deals are not random?

I prefer a test that can get an answer using just few hundreds of samples since that game engine does not offer the option to export the hands (another red light). Thus I would have to manually record each hand. The deals are really absurd, thus I hope I can prove it with few hundreds of samples.

I thought about a test that only examine either the 5 community cards / only my hands / the winning hand strength (I can record a game with friends where we see each river in order to not miss information).

Another thing that increase my suspicion are the reviews on the app-store, for example:

The odds and hands they deal are total fraud. It is 100% obvious that they keep hands close between 2-4 players each hand, with flush, straight, boat, and quad chances ALWAYS present.

mdewey
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Cohensius
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    It would be good practice to decide before collecting the data precisely what counts as an *absurd* deal and then calculate how likely they are to actually appear – Henry Apr 06 '20 at 09:16
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    Implausible results could be made to come about in several different ways. One could stack the deck, arranging cards so that individuals receive pre-chosen hands. But the computer would have to predict the action (stay in, fold) of each player. One could limit the variety of cards that appear--reducing variability would increase the likelihood of straights, trips and so forth, but no flushes necessarily. But it sounds like you suspect that choice of card is dependent on the cards in play. – Ed Rigdon Apr 06 '20 at 12:07
  • I am not sure what in the deal is not random, like you say, it could be in many ways. From what I observe, the ratio of Huge hands is amateurishly ridicules. currently it is just the opinions of some people. I want to prove it statistically. – Cohensius Apr 06 '20 at 12:30

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(Speculating.)

As Henry says, you need to first decide what are the implausible events that you want to track. I recommend flushes, because the components of a flush are visually striking and easy to track. To have five cards in suit, with a max of seven cards "in play" for each player, you must either have two cards suited in hand and three cards suited in the community or else four or five cards suited in the community. The latter events are quite striking. The odds of any of these events are easy to compute.

Implausible results could be made to come about in several different ways. One could stack the deck, arranging cards so that individuals receive pre-chosen hands. That is easy in Texas hold'em, since everyone receives two cards, before any decisions are made. Alternatively, one could limit the variety of cards that appear--reducing variability would increase the likelihood of straights, trips and so forth, but not flushes necessarily. A third option, and perhaps the one that you suspect, is that card appearance is dependent on the cards in play.

If you suspect that the deck is stacked for flushes, then you just need to count the frequency of the enabling events and compare it to the odds with a fair deck. But if you think the app is choosing cards in response to player holdings, you might go further and more effectively, by randomizing the decision to stay or fold when suited hands appear. If the app is responding to cards in play, then staying in should increase the odds of cards in that player's suit appearing in the community, while dropping out should reduce the odds (assuming that different players staying in have cards in other suits).

If flushes are unusually common, this should not take long, and if you fail to find evidence, then you can refine your hypothesis.

Ed Rigdon
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  • O.k, I like your direction, lets assume a a player that see all 7 cards, will get a flush 3.03% of the hands (source: Wikipedia). What is the test that I need to do in order to prove this dealer deals more flushes than the randoms distribution? https://en.wikipedia.org/wiki/Poker_probability – Cohensius Apr 06 '20 at 12:55
  • @Cohensius that sounds like a proportion test of $H_0: p=0.0303$ vs $H_a: p>0.0303$. – Dave Apr 06 '20 at 14:06
  • @Henry comment: "good practice to decide before collecting the data precisely what counts as an absurd deal". How that translate to the test? Assume I take 100 samples, how many flashes will prove H_a? – Cohensius Apr 07 '20 at 06:41