The REAL House Advantage

Or “What the Casinos REALLY Don’t want you to know.”

A friend of mine just popped into my office to let me know he was headed to Vegas for the weekend. He flashed that standard rueful “I’m going to Vegas” smile, while I tried share his enjoyment and keep my sigh internal. Most of you who know me are probably already aware that I am not all that excited about gambling in general. I would even go so far as to say that I am pretty solidly against both commercial and government-sponsored gambling.

The reason is simple. I just happen to know enough math to understand that the way these systems are set up is a loosing proposition for the gambler. Big time. My major beef is that whoever is running the game has a very strong incentive to make sure that the customers understand as little as possible about their real chances, and all of the marketing, lighting, sounds with victory and silence for defeat, air conditioning with piped-in oxygen, readily available alcohol, lack of clocks or windows, EVERY little detail of these establishments is set up to purposefully mislead the innumerate into unwise continued gambling until they have lost all their money. And as private companies, they never are in a position where they must disclose exactly how much money they are making and thereby expose their deceit.

And they are making a LOT of money. If I were to ask, “well, exactly how much money do you think they are making,” most people who thought about it for a bit would likely head for a discussion around the odds of each specific game, and the small house advantage, such as 5.26% in roulette, and how with the right systems, or counting techniques, you can get pretty close to evening the odds. If that were all there was to it, I might even head for the tables more often. Sadly, though, there is another detail you need to know.

I am here to tell you that the REAL house advantage is MUCH bigger than that. Besides the numerical advantage of slightly stacked odds, the casinos have an even bigger lever. They have effectively infinitely deep pockets compared to any individual gambler, and this turns out to be an staggering advantage. If you combine the relative purse sizes with the fact that those house odds apply PER BET, rather than in comparison to your purse size, the story starts to look a lot bleaker for the gambler.

Any discussion of making or loosing money based on the house odds would only really be valid if you gambled for an infinite amount of time. Remember that a fair game is random; you will be up some of the time, and down some of the time in a random walk, trending in the long-run of many many trials towards whatever the house odds happen to be.

But with a finite pocketbook, there is one condition that forces you to stop (when you run out of cash or credit) even when you might otherwise recover later were you able to continue. So with random walk excursion upwards, you can keep playing, but with any excursion downward which exceeds your purse, you are forced to stop, and at that point, the casino keeps ALL OF YOUR MONEY, not just 5.26%. Unsurprisingly, most players keep betting while they have money, and stop when they run out. Some players, of course, manage to walk away while they are ahead, but they are the exception, not the rule.

A simple thought experiment, that I first saw articulated in the book “Statistics Hacks,” involving 1,000 gamblers (to make the math easy) is revealing.

Let’s assume that each of 1,000 gamblers starts with a $100 purse and plans to spend 4 hours gambling in an evening. If we assume the house edge is 5.26% as with roulette, and we track a conservative bunch of gamblers that on average place $100 worth of bets per hour:

At those odds, about 100 people will run out of money per hour and be forced to stop. After four hours, about 600 people would still be playing and have an average purse of about $78.96 each, which would total $47,376. The casino will have accumulated $52,624, which amounts to about a 52.62% take. That’s a bit steeper than the published house odds, eh? And for those 400 people who lost, they didn’t loose 5.26% of their stake, they lost ALL OF IT. And somehow, I have yet to see any casino really articulate this effect.

Now how many people do you suppose would gamble to begin with if they knew the odds were REALLY stacked against them by 41% when you account for limited purse size, or perhaps walk by a posted warning that “52% of you people entering this casino should expect to loose all your money and the rest of you will likely loose about 20% on average?”

It is exactly this willful deceit that pits me against the gambling establishment. And while one might certainly make the argument that it is a personal responsibility to be aware of the risks of gambling and temper spending, most people in the US have never taken a statistics course. And with a strongly vested interest in maintaining and even promoting the ignorance and encouraging irresponsible behavior, casinos and even state governments that run the lotteries, have demonstrably failed to guard the public interest in this regard for quite some time. While you ponder the morality of this issue, reflect on the personal responsibility issues surrounding the health effects of smoking, and how an entire industry mislead their largely biologically uneducated market to ensure continued profits. It doesn’t seem all that different to me.

If you doubt this sort of analysis, try and make a Monte-Carlo simulator which follows these more realistic, finite rules. And if you aren’t all that inclined to go to that effort, all you really need to do is take a closer look at how many big and lavish casinos have become models of ostentation. That’s your money they are using. If you want to have any real chance of preserving winnings, your best bet is to just pick a time that you will stop gambling whether you are up or down, and stick to it. That way over time, you might at least begin to approach the house odds and take a while to loose all your money.

Good luck!

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Filed under Humor, Math

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