Testing for Fair Play

Hello,

I will soon have 10,000 hands of virtual blackjack recorded. I'm wondering if it's possible to use this data to conduct a variety of 'fair play' tests. I recall Wizard discredited the Casino Bar software by observing an unnaturally low frequency of dealer busts on the 3rd card over a 332 hand sample. I'm curious what other scenarios are relevant to test? Dealer bust frequency? Card distribution? Which are most relevant? How would I run these tests? What numbers to look out for? Basically, how can I best use this data to test the fairness of blackjack game providers. Thanks.

How detailed is the data? Does it have every card and every play decision? Does it have the bet amounts?

Here are some checks I would run given an extensive data set:
1) The distribution of player hand starting total versus dealer up cards
2) Frequency of player blackjacks
3) Frequency of player bust, controlling for total
4) Frequency of dealer final total/bust, controlling for upcard
5) Do any of these first tests results seem to vary based on bet amount (given bet size was varied)

Quote: roznez

Hello,

I will soon have 10,000 hands of virtual blackjack recorded. I'm wondering if it's possible to use this data to conduct a variety of 'fair play' tests. I recall Wizard discredited the Casino Bar software by observing an unnaturally low frequency of dealer busts on the 3rd card over a 332 hand sample. I'm curious what other scenarios are relevant to test? Dealer bust frequency? Card distribution? Which are most relevant? How would I run these tests? What numbers to look out for? Basically, how can I best use this data to test the fairness of blackjack game providers. Thanks.

If you are flat betting small amounts I would toss the data in the trash, unless you find something totally outrageous.

If the casinos are going to cheat you its going to probably be on big bets. Everyone wants to test using table min. No reason for the casinos to cheat min bettors, the math takes care of them just fine. Once they gain your confidence its all over for you once you start with the big bets.

Thanks for the responses

@Mike: Yes it has every card and play decision.

Fwiw it's flat $20 bets.

I'd skip the blackjack game results altogether and just test individual card probabilities. The odds of each card appearing in each individual position (player's 1st, player's 2nd, dealer's up, dealer's hole) should be (a) equal and (b) uncorrelated with any other card position or previous event. That should be a sufficient test at first, and if the game passes that, all the game-level tests will also pass.

Quote: MathExtremist

I'd skip the blackjack game results altogether and just test individual card probabilities. The odds of each card appearing in each individual position (player's 1st, player's 2nd, dealer's up, dealer's hole) should be (a) equal and (b) uncorrelated with any other card position or previous event. That should be a sufficient test at first, and if the game passes that, all the game-level tests will also pass.

I agree with this, but also, add dealer's fist hit to that list (because dealing seconds to avoid dealer busts is a simple cheating method that has been used before)

Quote: roznez

Thanks for the responses

@Mike: Yes it has every card and play decision.

Fwiw it's flat $20 bets.

sounds Interesting......... What was the table min and what was the max?


Is this a casino hand history type thing, recording or did you just write down the details?

If you just wrote down the details yourself. It wont fly. You must have solid proof of anything good or bad. Most people wont take your word for it.

Do you mind telling us what casino and results you had?

the chi-square goodness of fit test might be of interest to you.

watch out for selection bias. Rule of thumb is throw any data out unless you were 100% set to collect the data before you started. Otherwise only data that grabs your interest will be selected, hence only people who got screwed would test for fairness.

Quote: roznez

I will soon have 10,000 hands of virtual blackjack recorded. I'm wondering if it's possible to use this data to conduct a variety of 'fair play' tests.

Well, if you would like to conduct a statistical test, you would need to collect your samples *after* you defined all your tests and significant sample sizes.

It is very likely that you are significantly down after 10k hands (say 3 standard deviations), and become somewhat suspicious that the game isn't fair. But any statistical test you do on your past collected data is more likely to show up unfair results - simply because you would have not tested the game if it went more benefitial to you.

Edit: Neutrino (as expected^^) was faster raising this point.

Quote: Neutrino

watch out for selection bias. Rule of thumb is throw any data out unless you were 100% set to collect the data before you started. Otherwise only data that grabs your interest will be selected, hence only people who got screwed would test for fairness.

With such a small sample, this is your most important factor. You have to have gathered the information randomly or it is completely meaningless. In addition, it must show exceptional deviation from normal to be of any significance.