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The GameMaster's Secrets
Is This Game Rigged? Part 2

As I said in Part 1 of this series, a lot of gamblers use their monetary results to determine if a game is honest or not. If they win, they're inclined to think it's an honest game, but if they lose, they're inclined to think the game is "rigged". In reality, it could be just the opposite, so what we do is test the game from a strictly mathematical point of view, since wins and losses - at least from a short-term point of view - are not a reliable indicator of anything in a game like Video Poker.

The problem is that Video Poker games require literally millions of hands of play for the expected statistics to be realized. For example, if a Royal Flush is expected to occur once every 40,000 hands on average, it's obvious that a sample of even 100,000 hands is too small to confirm that the game is honest. But we can at least confirm the game's fairness with a high degree of confidence by checking the frequency of more common hands like Flushes and Full Houses.

In a game like 9/6 Jacks or Better, a player who uses the proper playing strategy may expect to receive a Full House about once every 87 hands. (That calculation varies from game to game according to the pay schedule, but software such as "Bob Dancer Presents WinPoker" will give you the probabilities of all hands for almost any game.) It naturally follows that in a sample of 1000 hands, the player should see eleven Full Houses but we have statistical variation to deal with. In other words, not every series of 1000 hands will produce exactly eleven, but whatever the result, it is measurable.

Let's say that we play 1000 hands at a Jacks or Better game and receive only eight Full Houses. Is this a "rigged" game? Probably not. The math is actually pretty simple for this situation. Since 1 in 87 is a probability of 0.0119 (1 divided by 87), we calculate the square root of that, which is 0.1072, multiply it by the square root of the number of hands played (the square root of 1000 is 31.62) and we get 3.239. That number is the standard deviation for this equation. Since 95% of all the results of trials like this will fall within the 2 SD level (assuming an honest game, of course), we would expect to see a minimum of 4 Full Houses in a trial of 1000 hands. So, the eight that we got is well within acceptable parameters. A quick way to do this calculation is to figure the square root of the expectation (11.5 to be precise, so it's 3.4) and use that as one standard deviation. Then figure out how far you're under "expected value" and if it's much more than 2 SD, I'd be worried. If it's beyond 3 SD, I'd be very scared of the game.

We check a variety of hands, like Two-Pair, Flushes, etc. in this way and that's a good indicator of a game's fairness, but it's not all we check. Much like we do in Blackjack games, we also keep track of all the cards that are played. For example, in a Joker Poker game, one expects to see the Joker, on average, once every 53 cards. Even in an honest game that can of course vary, but the deviation from expectation is measurable. If either the ending hands or the frequency of each card fall beyond the 2 SD level, we run another 1000 hand trial to verify the data. Oftentimes this second sample brings things back to normal so, while we cannot be completely sure the game is fair, it raises our confidence level.

I know what you're thinking. If a casino is going to cheat, they are likely to do it by "rigging" the Royal Flush and I have to agree. I have heard of "jackpot switches" that can be turned on or off, thus preventing the game from issuing a Royal. Do they really exist? I don't know but I will tell you that it's all but impossible for us to find out. To identify such a situation would take about 250,000 hands of play and we don't have either the time nor the $$$ to do it. But from a practical point of view, I doubt that there are a lot of casinos out there who are cheating at Video Poker, simply because 99.9% of the available games have a built-in casino edge that even the most skillful player cannot overcome. So why cheat? To get an even bigger edge? Perhaps, but you need to remember that most casinos enjoy an even bigger edge than is indicated by the pay schedule, due to players' mistakes. Brick-and-mortar casinos have offered games with 100+% returns for years and many are still available for you to play. I know a lot of good VP players, but I don't know any that play every hand perfectly, myself included. It's a different matter at Internet casinos, however, because a player can, through the use of software like "Bob Dancer Presents WinPoker" and "robot" players achieve 100% accuracy. The demise of almost all of the 100+% return games on the 'Net tells me that the casinos would rather remove the games than cheat and I understand their position.

Since getting involved in this business, I've seen us go from "killing" the casinos who offered 100+% games to now being skeptical if a casino offers one. There is no doubt in my mind that "rigged" VP games have been used at some Internet casinos in the past, but they are far and few in between these days. I'm not here to champion the cause of the casinos, but just as I said in the Blackjack portion of this series, cheating is not an easy thing to do if one expects to remain undetected. We all hear stories about players who are absolutely convinced that some casino's VP game is rigged, but unless you do your homework and do it very carefully, it's very hard to prove.

If you're suspicious of a game, you need to collect data from at least 1000 hands of play. Keep track, by type (high pair, trips, etc.), of every hand you end with that pays something. From that, we can calculate the "non-pay" hands and can get an idea of what's going on with the Full House and lower hands. While 1000 hands isn't sufficient to draw any rock-solid conclusions, it can give you some idea of the fairness of the game. With all the choices of casinos available today, there is no reason whatsoever to play at a casino where your suspicions have been aroused. If you want my opinion, I think that the vast majority of Video Poker games available at Internet casinos are fair, yet we maintain an attitude of "trust, but verify".

See you here next time.