Keno And The Law Of Large Numbers
There’s an old joke that the lottery is a tax on ‘people that don’t understand math’. It’s funny, but there’s a lot of truth to it. It’s also true about the casino game most analogous to the lottery–keno. As a group, it’s mind boggling how math illiterate most gamblers are. Considering that the entire world of gambling is circumscribed by mathematical concepts it’s downright absurd how adverse many people are to learning about even the most fundamental quantitative foundations of ‘their game’. These people are either oblivious to the reality of the math behind the various gambling disciplines or willfully ignorant, wanting to believe instead in ‘luck’ or ‘intuition’.
The corollary to this is that if you got all of the people that legitimately make money from gambling in the same room–poker players, sports handicappers, card counters, etc.–they’d have several things in common. First, none would be making a living from ‘negative EV’ games like slots, craps or keno. More importantly, they’d all have a better than average fluency in mathematical concepts and particularly those that influence ‘their game’.
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The Math Behind Keno
Most people understand the concept of the ‘house edge’. This is the mathematical advantage that the ‘house’ or casino has over the players in certain games. For example, most video poker machines return somewhere in the 97% to 98% range (though some offer higher returns). The 2% or 3% difference is the ‘house edge’. In the long term, the casino will take 3 cents out of every dollar put through the machine. Keno has one of the highest house edge’s in the casino–ranging from 20% to 35%. Video keno is a slightly better deal for the player, with a house edge ranging from 6% to 14%. These numbers are somewhat of an ‘apples and oranges’ comparison since video keno is a substantially ‘faster’ game than it’s ‘live’ counterpart. With game play in video keno 50% to 100% faster than its traditional counterpart the reality is that you’ll lose money faster on video keno despite the lower house edge.
That’s the house edge and there’s no strategy that can overcome it. The best you can do is play at a casino that offers the lowest edge available. The only input you have in the game is selecting the numbers and guess what? The numbers you select simply don’t matter. That’s why every system that is predicated on ‘tracking’ which numbers that come up so you can select ones that haven’t made an appearance in awhile is flawed. That’s called the ‘Gambler’s Fallacy’–it’s the mistaken belief that past random events bear some degree of influence on future random events. For example, if you flip a coin nine times and it comes up ‘heads’ every time guess what the odds are that it’ll come up ‘tails’ on flip number ten? Yep–50%, just like any other coin flip.
The Law Of Large Numbers
The mistaken belief that tracking keno numbers is effective is due to a misunderstanding of the law of large numbers. Advocates of number tracking in keno argue that it’s a matter of simple probability. If every number has an equal chance of coming up and one number hasn’t come up for awhile it *has* to come up sooner or later to make the averages work. That’s not the case and they’d know this if they understood the ‘gambler’s fallacy’ in conjunction with the ‘law of large numbers’. Simply put, the LOLN dictates that the probability of an event occurring will be closer to the expected value as more trials occur. In gambling , anything can happen in the short term. In the long term, however, the casino can count on the math working in their favor and in most cases the players can count on it working against them.
So back to the coin flip–it’s not unusual to flip 9 or 10 heads in a row. But the more you flip, the more the data you observe will reflect the expected value. Translated–over a few million flips you’ll be getting numbers closer to 50%. Probability theory operates on a very long continuum of events. The mistaken beliefs of gamblers don’t. There’s no theoretical basis for thinking that you’ll experience a short term reversal in fortune just to make the ‘averages’ work out. This is a huge mistake of many casual gamblers, including keno players.
