Another Gambling Riddle About Wins and Losses

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In this post, I am providing hypothetical situation to test your perspective on casino gambling. And I’m going to ask you what the better situation is for a gambler.

You should think about your answer to the question first before I give a thorough explanation. Whether you think about your answer, write it down on a piece of paper or your phone, it’s best to make note of why you came upon that conclusion.

Then, figure out what you can learn from this riddle by reading my explanation.

The Hypothetical Gambling Situation

My friends Patrick and Lee are the two gamblers in question. Patrick takes three trips to the casino. He loses $100 on his first trip and $200 on his second trip.

But on his third trip to the casino, he wins $300.

After the three trips to the casino and winning the $300, he breaks even. Patrick hasn’t profited, but he doesn’t have a net loss either.

Lee, on the other hand, is playing for higher stakes. On his first of three trips to the casino, he loses $1,000. And on his second trip, he loses $2,000.

On his third trip to the casino, Lee wins $3,000.

Lee, too, has broken even after three trips to the casino. No net win, but no net loss either.

Now, here’s the question:

Which one is in the better gambling situation?

A Couple of Assumptions About the Two Gamblers

First, let’s assume that both Patrick and Lee are professional gamblers. They only place bets when they have an edge over the casino. Both of them would rather eat liver with onions than place a negative expectation bet.

Second, let’s assume that both of them are bankrolled well enough that their risk or ruin is appropriately low—less than 1%.

Casino Games

If you assume these two things, how do you decide which of the two gamblers is in the better situation?

Who’s doing it right?

The Effect of Psychology in Gambling

Some people might prefer Patrick’s situation. Even though he broke even, he was never down more than $300. Some people are just more comfortable dealing with lower stakes. These people might not make it as pros even if they’re sticking with positive expectation bets. After all, if you’re not putting enough money into action, your edge won’t translate into enough dollars and cents to earn a living.

As horrifying as being down $3,000 might sound to some people, Lee’s results after the first two trips to the casino won’t bother him at all. He’s confident that he’s making the right decisions all the time. And he’s also comfortable that he won’t go broke; he has a big enough bankroll to handle the swings.

Here’s who’s doing it right, though, assuming they both have the same size bankroll:

Lee.

The way an edge works in real money gambling is that you multiply it by the amount of action you bring to determine your expected win or loss amount.

If you only put $600 into action over three trips to the casino, you’re only going to win an average of $6 if you have an edge of 1%. Of course, Patrick probably put more money than that into action; he did win SOME of his bets on each trip after all.

So, let’s assume he put $60,000 into action to generate those results. His expected win was $600.

And even though he broke even on these three trips, if he keeps gambling this way, his results will eventually look like the expected results. The Law of Large Numbers will eventually kick in.

Lee probably put 10x as much money into action, so his expected winnings are $6,000. The Law of Large Numbers will eventually kick in for Lee, too.

But there’s more to the discussion than just theoretical wins in the long run.

Casinos Reward Bigger Players

When you’re losing big money at the casinos, the casino management is going to treat you like a rock star. They’re not going to be impressed with the $300 in losses that you sustained on your first two trips to the casino. So, they’re probably not going to give you much in the form of comps. Patrick will be lucky to get a few free drinks.

Lee, on the other hand, has lost $3,000 in his first two trips, and that kind of action doesn’t go unnoticed by the casino. They’re probably going to offer him some free meals and a free room with those kinds of losses.

And yes, the casino will notice that they won on the third trip.
But as long as neither Patrick nor Lee do anything to clue the casino in that they’re advantage players, the casino won’t mind. If you win $300, the casino figures you’ll come back tomorrow and lose $600.

And if you win $3,000 today, the casino figures that you’ll be back tomorrow to lose $6,000.

They’re going to do whatever they can to encourage you to come back and keep gambling.

Money

For the advantage gambler, though, all these perks are just gravy on top of their expected winnings.

How much value can you expect to get back from a casino based on your losses?

Someone like Patrick, who lost only $300 on his first two trips, might not get anything free. If he’s lucky, he’ll get a comped meal at the coffee shop.

But someone like Lee is probably going to see something like 10% of his losses come back in the form of comps. Since he lost $3,000, he’s probably going to get $300 in freebies of some kind. That might just be a nice meal in the steakhouse, but that’s on top of his eventual expected wins, too.

Here’s Another Hypothetical Situation

You don’t have much control over this, but if you win on trip #1 and lose on trips #2 and #3, you won’t see the same kind of red carpet treatment from the casino.

Let’s suppose that Lee won $3,000 on his first trip to the casino, but then he lost $2,000 on his second trip to the casino.

Lee would hope that the casino would give him some comps based on his $2,000 loss, but you should think about it from the casino’s perspective.

Since he won $3,000 on his first trip, he’s just losing some of what he’s already won back to the casino. As far as casino management is concerned, Lee’s playing with house money.

You and I both know the folly as a player of thinking that you’re playing with house money. Any money that belongs to you actually belongs to you. It doesn’t matter if you won it from the casino or dug a ditch to earn the money.

It’s your money.

But the casino has different ideas.

C’est la vie.

But after trip #3, where you’re finally back to even again, the casino MIGHT offer you some comps based on the losses from those trips even though you’ve broken even. They might not, though. They might want to see more action from you before rolling out the red carpet again.

Conclusion

Another variation of this riddle is presented in Million Dollar Video Poker by Bob Dancer, although I’ve covered some ideas that he missed in his book.

Learning HOW to think about these situations is critical if you’re serious about gambling for a living, though. Even if you’re a recreational gambler, you should understand the math and thought process well enough to get the most for your money.

Michael Stevens

Michael Stevens has been researching and writing topics involving the gambling industry for well over a decade now and is considered an expert on all things casino and sports betting. Michael has been writing for GamblingSites.org since early 2016. ...

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