For casino goers

In My Humble Opinion
21

No, no, no, no! Probabilities are extremely counterintuitive and gambling is designed to make it even more so, but it still amazes me how many people don’t get it.

Even if every gambler left the casino as soon as they were up, the casinos would make a profit. In fact, they’d make the same profit as a percentage of dollars bet.

One of the things that makes gambling hard to understand mathematically is that people like to look at the conditions when they leave the casino, but they almost never define the condition that cause them to leave.

Let’s say that you will go into the casino with the plan that you will gamble until you either win ten dollars or go completely broke, at which time you will go home. If your net worth is $80,000, the odds are extremely good that you will win $10 before you go broke. You could go to the casino hundreds of times and place hundreds of thousands of bets and walk out every day ten dollars richer. You could easily go to the casino every day your entire life and leave ten dollars richer every time. A pretty good plan if you like to gamble and don’t need more than $10 a day, right?

No, because you only have to have one losing streak, and you’re out $80,000 (plus whatever you’ve won and not spent up to that point). The odds are strongly in your favor on any given day, but if you gamble every day for a million years, you’ll almost certainly have at least one day that is really, really bad, and if your plan is that every day you keep betting until you’re up $10 or completely broke, you’ll eventually go completely broke.

If you decide that to protect yourself from this, you gamble every day until you’re up $10 or down $500, you’ll still end almost every day $10 up. But not as many. All those days on the old plan where you down $600 or $1000 or $79,990 and then hit an amazing winning streak that ended with you being $10 up, under the new plan you’re out $500. So you lose less on the days you lose, but end more days on a loss. (On the old plan you were guaranteed to only have one day when you lost! Presumably you wouldn’t be able to go back the next day.)

You can structure your gambling so that you are almost guaranteed to walk out a winner, but if you do, you have to risk losing a lot more when you lose. You can structure it to where you never lose more than a dollar, but you’ll either have to win much less often or win much smaller amounts. What you cannot do is structure it so that you will come out ahead on average.

Most gambling statistics are put in terms of the “house edge.” This tells you the average amount you will lose to the house per dollar you bet. You could also calculate how much you will lose per round (if you know how much you like to bet at a time), or how much you lose per hour (if you know how much you like to bet at a time and how long it takes). Or you could calculate the chances that you’ll double your money before you lose half of it or that you’ll go broke before winning ten dollars, or any number of other things. You could look at volatility, or the degree to which your money will fluctuate unpredictably while still averaging out to a loss according to the house edge. (If every day you put one hundred silver dollars in a dollar slot machine with a 95% return and every day your sister puts 2000 nickels in a nickel slot with a 95% return, you’ll both lose five dollars a day on average, but you’ll have more days where you win big and more days when you lose big. Over enough days, it’ll work out the same, though. Dollar machines have higher volatility than nickel machines, even with the same house edge.)

Except for really extreme situations with very high-stakes gambles, the casino doesn’t care whether you bet slowly all day or gamble quickly for an hour, whether you tend to win small and often and lose big and seldom, or lose small and often and win big and seldom. Over time and over the large numbers of people it all works out the same for them. Over the long haul, they want you to put more money in overall, and they’ll make the house percentage over time no matter what.

22

BTW, this brings up a fallacy that I often see even among people who really know a lot about gambling and statistics. People will tell you that something (like, say, Keno) is a sucker bet. Well they’re all sucker bets if you’re planning a long term investment strategy, but different bets are good for different other things. As I said in the earlier post, the “house edge” tells you your average loss per dollar bet, but that’s not always what matters.

Almost any decent gambling site or book will tell you to always split 8s at blackjack. Some will explain why, since it seems counterintuitive, since you almost always lose on a pair of 8s whether you split or not, and splitting doubles your bet. Over the long term, the house edge is slightly better if you always split 8s than if you do anything else. That’s why splitting 8s is part of the “basic strategy” for blackjack. If you’re counting cards, you’re trying to push that house edge into the negative, and every tiny fraction of a percent is necessary. If you’re counting cards, you really are playing blackjack as an investment strategy, and your goal is the best return for your dollars.

But if your goal is to play 25 rounds, splitting 8s is a bad strategy, because you’re betting twice as much in a round you’re likely to lose. If you’re playing for 90 minutes and then done, it’s also a bad move, assuming that it takes less time for the dealer to split your 8s that to deal an entire round (which it should.) OTOH, if you’re playing until you’ve placed exactly $200 in bets, then splitting 8s is absolutely correct.

Remember Keno? It’s the classic sucker bet because it has the highest house edge in the casino by far. But lets say you need $10,000 to pay your coke dealer or he kills you, and you only have five bucks. You’re almost certainly dead no matter what, but your odds of living are probably better if you play Keno than blackjack. Remember, it doesn’t matter if you win $9,999, you’re still dead. You could put that five dollars in a savings account and be guaranteed a positive return (the equivalent of a negative house edge and zero volatility), but you’re also guaranteed not to make $10,000 overnight that way. I forget the technical term for the measurement, but although you’re much, much more likely to lose your $5 at Keno than blackjack, and also likely to lose much, much more per dollar on average, you’re also more likely to get to $10,000. (I think. I haven’t done the math on this, but I recall that it works out that way.)

23

I’ve also got my own pet theory on the lottery (the powerball/megamillions/super jumbo pot sized ones).

Here’s the accepted rule: they’re almost always negative expectation. What that means in any gambling situation is that if you put money in, you should expect to lose money on that particular bet over the long haul. Odds of winning a Powerball are usually in the range of 145 million to one against you. And even when the pot is larger than 145 million you still have to account for taxes and other things which will knock out your winnings. And even when THAT is above 145 million, you still have to account for the (increasingly likely) odds that someone else splits the pot with you because that large of a pot lures more and more people into playing.

The bottom line from any expert in the field is that playing the lottery is a sucker’s bet, almost regardless of pot size.

But here’s the thing. if you win, despite how terrible the odds are against you…you’ll win more than you possibly could have spent on the lottery in your entire life even playing twice a week. Yes, overall, the game has a negative expectation. But when you’re dealing with a pot size in the millions, it really makes no difference just how bad the bet is or how negative your expectation is. One win will make it all up and then some.

So my feeling is, if you can afford it, and understand the risks…go ahead and play the lottery, negative expectation be damned. Here’s hoping you win!

24

Never. After a couple of disastrous college poker games, I adopted the technique of putting my betting money in one pile and my winnings in another. When the betting money was gone, I quit and cashed out. There may have been moments in the process where the winnings pile was more than the amount of money I had put in to that point, but by the end of the night, I have never come home with as much money as I started out with.

The closest I ever came was losing a net total of 25 cents over the course of an evening.

25

Nope, they still win in the math. “Usually ahead by a little at some point” doesn’t beat “behind by a lot the other times”.

Using the same example of a 49%/51% biased coin flip game, say your strategy is “Play until you are ahead OR until 200 flips have been played.” It’s true that you’ll end up ahead in 92.3% of the sessions, but you’ll only be ahead by one bet’s worth. When you’re down after 200 flips, you’re down by much more than one bet’s worth. This strategy, in fact, yields you a profit of -0.51 betting units per session. So, if you are playing a $5-bet game, you’ll lose, on average, about $2.55 per session, even though you will be ahead in 92.3% of sessions.

If you could predict which sessions would be among the losing 7.7% of them, you could skip those. But you can’t.

This holds for all casino table games. You can’t win in the long run, even with a strict ending strategy.

26

When I go because I want to and only play poker: 3/4 times.
When I go with other people to casinos that don’t have poker and am forced to play slots or do nothing 0/ however many times I’ve gone (4?)

27

You’re right – I screwed it up. That would change my vote from 0-25% to 50-75%.

28

The only time I ever went to a casino was as part of a conference event. They gave us each a roll of five dollars in quarters. I put it in my pocket, and walked out the door, $5.00 to the good!