Interesting data (post about variance)

[Winnergambling]

I have played a lot in a certain casino for over a year, which uses semipopular casino software, so not one of the biggest software providers but a medium sized one. Some experienced players might guess the casino in question, but it is not important here in this post.

Here is the data from my game play, which I got from support without asking while solving one problem. My bet amount per hand has been in between $4-$10 during this sample 90%+ of the time.



What we can see from these stats are the payout percentages I have received from these games. Sample sizes are somewhat large so it is interesting to do some analysis.

Mulligan Poker: I have wagered $116,540 in that game and return has been $112,510. This gives return percentage of 96.54% and therefore a house edge of 3.46%. Real HA for Mulligan Poker per unit wagered with optimal strategy is 2.17%, so my return has been somewhat below expected return.

Let It Ride: Wagered $122,254 and return has been $114,532. This gives payout percentage of 93.68% and house edge of 6.32%. The real HA for this game per unit wagered is 2.85% so I have been running WAY below expectation.

Pai Gow Poker: Wagered $264,540 with payout amount of $257,498. This leads to a payout percentage of 97.34% and house edge of 2.66%. The real house edge for this game is 2.73% so I have been running slightly above expectation on this.

Caribbean Stud Poker: Wagered $193,000 and return has been $189,520. This gives payout percentage of 98.20% and therefore house edge of 1.80%. House edge for this game per unit wagered on this software is 2.47%, so I have been running somewhat above expectation.


What implications can we make from this data then? Well, first of all - we can see how big factor variance really is short-mid term. Only in very low variance game - Pai Gow Poker (lower variance than in BJ) I am within 0.1% from the real house edge with over $250,000 in wagered.

When we move from these really low variance games to medium variance games like Let It Ride, Mulligan Poker etc. - then $100,000-$200,000 wagered (which sound like a big number) with relatively small bet size is a very small sample size to determine long term results. Difference between independent player results can be very far from the real house edge of the game.


Keep this in mind when you next time wager something like ~$5,000 in a casino and you run bad, then start to shout that casino must be rigged or something. It is not. It is just that thing we call variance.

[JarnoV]

This is useful information, but I think this thing called variance needs more explanations for people who aren't familiar with the concept. I am familiar, but most people aren't and I think the fear of losing money is what might be holding back some people from starting this thing. So, in a sense this casino grinding is a sure way to win money, but on the other hand, it does have a high variance. Not everyone understands this completely. Though I'm not sure how to explain the concept in layman's terms.