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The GameMaster's Secrets
Is This Game Rigged?

It's only human nature to think a game is "rigged" if we lose and we might think that a game is "honest" because we won. However, winning and losing are only a part of the puzzle, so what I want to do here is show you some of the ways we check Blackjack games at Internet casinos to see if they are offering a "fair" game. While this is the place where I tell a lot of my secrets, I'm not going to reveal all of our tricks for catching cheaters at Blackjack, because I obviously don't want to help someone who has larceny in his or her heart.

Let me just set the scene for those of you who aren't big Blackjack players. First of all, keep in mind that 99.9% of all Blackjack games have rules that give the casinos an edge over any player, amateur and pro alike, so don't be surprised when you lose because you're destined to lose, even if the casino is totally honest. What we're talking about here are those few casinos who have allowed greed to be a part of their business plan, so instead of offering a game where they have a small edge, they go for a much bigger advantage.

It is very easy to "rig" a game of Blackjack where the casino has a larger-than-normal advantage over the players, but fortunately, it's also easy to catch someone who is doing that. Blackjack is a game of pure mathematics, at least from an analysis point of view. For example, while a player may change his or her strategy and/or bet size, the dealer must always play by one set of rules and, of course, the bet size doesn't matter for the dealer. Also, a deck of cards has only 52 different cards in it so, even when six or eight decks are used in the game, the combinations of hands that can result are easily categorized. For example, a dealer can end the hand in only one of several ways: First, the player may bust, so the dealer does nothing. Or, in some games, the player may surrender and the dealer does nothing. Otherwise, the dealer will end with a hand totaling 17-21, will bust or will get a "blackjack".

The Dealer's Hand

The dealer's 'ending' hand is the first thing we track. When the player has not busted, surrendered nor received a "blackjack", we record the dealer's final result and we also track how many "blackjacks" the dealer gets. For example, a dealer will end with 20 about 7.4% of the time. So, if we collect data from 1000 hands of play, the dealer's hand should have ended with a total of 20 about 74 times. Standard statistical analysis gives us an indication if the game is honest or not. Let's say the dealer ended with 20 for 95 of the hands, instead of the expected 74, does this mean the game is "rigged"? Not really. Just as we don't expect to see heads come up exactly 50 times in every 100 flips of a coin, we understand that there can be some variance from the expected, even in an 'honest' game. The magnitude of that variance is what matters and we can measure it in terms of probability. In the example above, the dealer ending with a 20 in 9.5% of the hands is pushing the limits of acceptability, but it can still happen in a fair game. To carry this out to its natural conclusion, had the dealer ended with 20 for 108 or more of the 1000 hands, we would probably conclude that this is a "rigged" game, especially if it happened in a followup trial of another 1000 hands. Here are the percentages we expect to see in a game where the dealer stands on A-6:

Dealer's Ending Hand	% Probability
17	14.6%
18	13.8%
19	13.5%
20	17.6%
21	7.4%
BJ	4.8%
Bust	28.4%

The Card Summary

Another important element in our analysis is the number of times each card in the deck appears. A very easy way to cheat is to remove from the deck(s) certain cards that benefit the player, mainly the 10s and Aces. We track each card that appears as the hands are played and, as you might expect, we verify that they are all showing in a proper proportion. Ignoring suits for the moment, there are 13 different cards in an honest deck and, within certain parameters, they should all show an equal number of times. Whether or not the casino suffles after every hand has no bearing in this, because the proportions should remain the same. Here is the raw data from a game we recently checked by playing about 7500 hands:

Card Value	Number Seen
Ace	3345
2	3222
3	3257
4	3215
5	3340
6	3243
7	3270
8	3312
9	3317
10	13330

First of all, you will notice that we track all 10s (10, Jack, Queen and King) as one card. It's only if we see an anomaly that we separate each one out in a follow-up trial. The total of all these cards is 42,851 and, since each card should show up one-thirteenth of the time, the "expectation" is 3296 (13,184 for the 10s). Right away, the Aces and the 5s pop out as being above what's expected, but is that a sign of cheating? Probably not. What we have here is normal variance that will likely diminish (in terms of percentage) as the size of the sample grows. Using these numbers, we can expect the appearance of each card to vary, plus or minus, by 57. The Aces are 49 (1.486%) over the expectation and that is within acceptable parameters. The number of 2s that were played is below expectation by 76 and the 4s are below by 81, which is troubling, but not a clear indication that something is wrong. Perhaps someone who is more skilled than me in statistical analysis can figure out if this casino is cheating, because I just don't see it.

The Player's and Dealer's Blackjacks

One very easy hand to track is the number of "blackjacks" the player and dealer get. It seems reasonable to assume that a cheater could try to manipulate this, so it's worth recording. These are counted only if they occur on the first two cards and, since the probabilities are well known, it's a good test. Here are the probabilities of a 'natural' in various games:

1 Deck:	4.8265%
2 Decks:	4.7797%
4 Decks:	4.7566%
6 Decks:	4.7489%
8 Decks:	4.7451%

So, if you play, as an example, 1000 hands and the dealer received 55 naturals and you got only 45, is the casino cheating? Here's how to find out: First, figure the "expectation" (0.048 x 1000) and that's 48 for this example (remember, you can't get a fraction of a blackjack). Compute the square root of 48 and you'll get 6.92, but let's call it 7. This is the standard deviation. The dealer's 55 naturals is 7 over "expectation" and that's equal to one standard deviation which is quite normal. Your 45 is just half a standard deviation below expectation and that, too, is quite normal. What's not normal? About 3 SD is pushing things and 4 SD is a big warning flag. So, for our 1000-hand example, if the dealer had received 75 naturals, I would at least suspect cheating. If a similar number showed up in a follow-up sample, that would confirm my suspicions. Is it absolute proof of cheating? No, but it would tell me to stay away and, I promise, I would tell you.

Wins, Losses and Pushes

This is probably the only means of measurement that most players use, but it's also the least reliable. While we can precisely calculate just how many hands we should win, lose or push, you need to remember that how well you play the game can effect these numbers, especially in relatively small samples. If someone is always hitting 17, then they are simply going to lose more hands than someone who always stands on 17. But, in a small sample, either of them could win more hands. See the problems this creates? That's why we don't put a lot of stock in it, yet ironically it's the whole reason why we do all this measuring: wins. losses and pushes are all that really matter in the game of Blackjack. It's just that they aren't good measuring devices. Nonetheless, we track the numbers and what we expect to see is 43.2% win, 47.9% lose and 8.9% push.

Using This Information

I think that about 95% of the people who play Blackjack at Internet casinos think they're being cheated when, most likely, only a small fraction are. Blackjack is a weird game and if you play it long enough, you'll see some amazing things. But don't operate off emotion. Record the data, such as the dealer's ending hands and the number of naturals you both get and you'll start to see that most games are honest. If the dealer "always" gets a BJ when you get one, start recording all the BJs in the game and you'll see that it isn't really "always". Taking the emotion out of playing will make the game more fun and,perhaps, more profitable.

Next time we'll cover Video Poker.
See you then.