I’ve been playing PaiGow a few days, and got suspicious that the dice machine (the part that selects which players get which hands) was fixed. So, last night, I recorded 20 dealer hands and at home, dealt 28 hands myself to compare results.
Home results:
33.7% of all hands (28 deals X 7 hands, 196 samples) were 2 pair or better.
43.9% had an Ace or higher as the 2 card hand.
15.8% had paigow, or Ace high or worse.
Casino results, 20 total hands over an hour, only recorded dealer hands:
40% of hands were two pair or better. 75% of hands had ace or higher as the 2 card hand.
10% of hands had paigow.
Obviously, I need to collect more samples of dealer hands, but if this trend holds true, is the casino definitely cheating at paigow? Who would I report it to?
The sample size is too small to prove anything. When you have a few thousand hands let us know what it shows. There is no reason for the Casino to cheat since the house usually has an advantage.
Now, I firmly believe that this trend will not hold true, because the casino isn’t cheating. I have a hard time understanding exactly how the casino is going to cheat, they would have to know the exact position of each card in the deck before fixing the dice roll. That’s two types of cheating just to gain an edge in a game where they have an explicitly defined edge over the players.
One more thing. The size of the progressive pot is not incentive for the casino to cheat. It is self funding and shows up as both an asset and a liability on the casinos books.
In addition to what others have said, which I agree with to the extent that I understand it (I’m not familar with the game), saying the casino is definitely cheating is a pretty damn hard thing to prove without other non chance-based evidence. A perfectly honest flipped coin will come up heads 10 times in a row around one in 1024 times (fairly certain that is correct; if I am wrong it is either 512 or 2048).
If the casino has had many thousands of Pai Gow games (I would assume so if it is a popular game) then I would expect to find weird runs somewhere in those thousands of games; they would argue that you just happened to hit one.
That doesn’t hold water, and your last statement shows why. If you run the probability, you already account for the likelihood of “just happened to hit.” If the probability is so low, it’s beyond credibility, then the casino is cheating, by definition.
You can’t say “there are many thousands of Pai Gow games” without actually showing the data for those thousands of games. If they show a counter-balancing, non-cheating distribution, then case closed. If they show a lot of players getting screwed, then your defense is rejected and we’re back to “this casino cheats!”
Um, yes. It’s random sampling. Enough random samples should represent the entire sample, if done truly randomly.
I collected more data and it seems like the initial data I collected is holding true for the casino hands. The second day, dealer hands with an A+ top dropped to about 53%. The third day was even lower.
However, another issue popped up that probably I will be unable to prove statistically. Regardless of what the dealer has, the dealer never has the worst hand on the table (I would need to see all 6 player hands to determine the overall placement of the dealer hand, and I am unable to see them consistently.) For example:
Dealer hand: KT top, A9 bottom: 1 loss, 2 pushes, 3 wins.
66 top, 88 bottom: 1 push, 5 wins.
J9 top, 22 bottom: 2 losses, 4 pushes.
In each of the cases above, the dealer had below average (almost bottom 10% of hands actually) yet did not lose half the hands. In the hands I have been able to see (about 2-3 player hands on average) I always see the dealer hand being the 2nd or 3rd best hand on the table no matter what they have.
Agreed - if this is like most progressive pots I am aware of - the casino takes a small part of each round of betting and keeps adding it to a progressive jackpot. They might start it at some minimum (and I think I haven’t seen it without one).
So if anything - it is better for the casino to pay out huge jackpots - as the % of money that they kicked in is much smaller.
The OP doesn’t mentioned where the casino is - and you certainly can complain to that states Casino Control board or whatever. However - unless you have some facts or detailed analysis to provide - they almost are certainly going to dismiss you as crazy - as they get tons of these a year I am sure.
I am not aware of any recent case where a modern casino I. The US has been caught cheating. There was cases such as a video poker machine that I believe paid out 50% less often on the royal flush - and a certain betting pattern could be initiated to trigger such a payout. This wasn’t the casino cheating - it was a programmer who snuck this in and was cheating himself.
Casinos really have no reason to cheat. Slot machines are a perfect example of a Skinner box. The more often you “win” - the more often you bet. There is a curve which maximizes the casinos profit - and in the case of a slot machine - it is almost certain in the long run a slot machine that pays back 95% on average will make more money for the casino than one that pays 5%.
In order to cheat at Pai Gow - they would almost certainly have to involve the dealer. Who doesn’t get paid much - and a certain percentage of them would get disgruntled and turn in their bosses.
Casinos don’t need to cheat - players are willingly putting themselves in a position where they will on average lose money. They are often billion dollar corporations who have no need to jeopardize their casino license to attempt something that will probably be less profitable for them in the long run anyway.
But my point is that the OP isn’t showing whether or not there is a counter-balancing distribubution. He is saying that for those games he has sampled he is seeing a very unusual distribution. I probably shouldn’t have said “if the casino has run many thousands of games” since that is irrelevant to whether the particular sample indicates cheating; my point in saying that was simply that there will have been many other weird “coincidences” that haven’t been noticed if enough games have been played.