Can a casino game with a fixed return-to-player (RTP) have any strategy?
It sounds like a strange question. By definition, if the RTP is fixed, nothing the player can do can change that. Every bet will lose the same amount on average.
However, to say that such a game has no strategy assumes that the player only cares about their average net winnings and losses. That’s not true for most gamblers. If it was, we wouldn’t gamble at all, or care about all the lessons like this one in our Bonus Casino School.
A casino player will lose money on average; that’s just the way the math works. But if you’re gambling to have fun, you need to factor that in when evaluating the outcomes.
It’s pretty easy to see that net winnings and losses aren’t the full story when it comes to how much fun you have. Consider two gamblers who each lost $100:
- John walks into the casino, plays a single $100 hand of blackjack, loses, and goes home.
- Jane puts $100 into the slots and starts playing $1 spins. After losing half her money, she hits a $250 minor jackpot. She then moves over to a $5 machine to try to run it up, but her luck turns, and she goes home a couple of hours later after losing her winnings and her original $100 stake.
Maybe Jane wishes she walked away when she was up. Nonetheless, there’s no doubt she had a more exciting time than John. That’s partly because she played longer but also because there were some ups and downs on the way.
From that, it should be evident that even games with “no strategy” that could change the RTP do have a strategy for having fun.
An Exceptionally Short Introduction to Game Theory
The economist John Nash (pictured right) developed game theory to analyze human behavior. It tells you the correct strategy for playing a game, but the idea is that you can also apply it to anything people do, treating life as a game of sorts.
(You might know of Nash from the movie A Beautiful Mind.)
To a game theorist, a “game” is any series of decisions that ultimately leads to a numerical “payout,” which can be a positive or negative number. The theory assumes that everyone will make the decisions they believe will maximize their average payout based on the available information.
Because game theory was developed for economics and money is easy to quantify, it’s common to start with dollars as the way of measuring payouts. But there’s a problem with that: it’s easy to find examples of people not maximizing their money.
For instance, giving money to a stranger in need makes no sense if you’re only thinking about dollars. But it might if you consider the benefactor’s desire to feel like a good person when calculating the payouts of the “game” they’re playing.
Gambling is a little bit like that, except that the gambler is chasing excitement rather than a sense of virtue.
Of course, that leaves economists—and us—with a different sort of problem: how to assign a number to things as abstract as happiness, self-esteem, or excitement.
Often, that means economists work game theory in reverse. They start with behavior and try to understand the set of incentives that would make that behavior rational.
You can do the same thing while gambling. Pay attention to how you bet and what you’re trying to achieve. That emotional intelligence will help you develop new strategies for an even better experience.
Common Motivations in Gambling
Gambling psychology is extremely complicated and not well understood, even by scientists. However, if you pay attention to your gambling, you’ll probably notice at least three desires you have in common with almost every gambler:
- You don’t want to lose all your money too quickly,
- You want some chance of winning an amount of money that feels meaningful,
- And failing that, you’d rather end the session in the black if possible.
The relative importance of those things varies from person to person. But almost no one is pursuing one to the exclusion of the others. Let’s look at them individually.
Ultimately, gambling is an entertainment expense. Duration isn’t the only thing that factors into whether such an expense is “worth it,” but it definitely matters.
You might be reluctant to pay full price to watch a movie that’s only 30 minutes long. By the same token, most gamblers want to find ways to make their budget last a while, even if they’re not getting lucky.
If you were only concerned with spending as long as possible at the table, the right strategy would be to find the game with the lowest volatility and bet the minimum each time. However, no one does that unless they’re killing time until the cocktail server comes around because it’s not fun in other ways.
A Meaningful Win
The exciting part of gambling is getting to hope for a big win. Not many people would play if the only possibilities were breaking even or losing. So, everyone gambling has some number in mind, if only unconsciously.
For one person, that might be winning enough to pay for dinner. Someone else might be dreaming of a new car or a bigger house.
Probably more than anything else, the size of the aspirations determines the volatility a player is looking for. Placing $10 outside bets at roulette is never going to win you a car, but the progressive jackpot from a slot machine might do the trick.
Those chasing really huge wins to the exclusion of all else don’t play casino games. That’s what national draw lotteries like Powerball are for. But even those offer some time value because the draws happen infrequently. The anticipation between the ticket purchase and the draw is where the entertainment value comes from.
There’s a natural tendency to fixate on the amount of money you started with. Being up $5 might not count as a meaningful win, but it feels significantly better than being down $5. More importantly, that difference feels a lot bigger than, for instance, the difference between being down $50 and down $55.
Because of that, many gamblers tend to try to finish their session above where they started. While a natural emotional reflex, this is more dangerous than the other motivations. Taken to an extreme, it can lead to chasing losses, a significant risk factor for problem gambling.
Any casino bet you make will lose more money on average than it wins, so chasing losses to get back to even is a slippery slope.
That said, some strategies produce more winning sessions than others. So, if ending up no worse than where you started adds to your enjoyment, there’s no harm in factoring that into your plan, so long as you’re still committed to your budget and time limit.
Roulette: a Case Study in Recreational Gambling Strategy
Roulette is a great example to study the impact of different gambling strategies. The RTP is the same for all bets, so there’s no better or worse strategy in dollar terms. But there are many betting options with different levels of volatility. We even have an article explaining the math of volatility using roulette as an example.
There’s a lot you can do in roulette involving varying the size of your bet or combining inside and outside bets. However, to keep things simple for this article, we will look at three players with differing motivations and three simple strategies they can choose from.
All three players show up at the casino with the same basic plan for their session:
- They’re going to play roulette, placing a single $10 bet on each spin.
- They’re going to play for a maximum of 80 spins (about two hours at a retail casino, depending on the dealer’s pace).
- They have a budget of $200 and will quit early if they lose that much.
- Finishing up $400 counts as a “big win,” emotionally speaking. All the players will quit while they’re ahead if they’re up $400 or more.
- They’re either going to bet on colors (even money on red/black), corners (8-1 bets on four numbers), or numbers (35-1 bets on a single number).
Economists talk about “utility” to mean how favorably a person rates a given outcome. But we’re going to use 😀 to denote units of happiness.
All our characters treat $1 as one 😀, but get different amounts of 😀 from the length of their session, from doing better than break-even, and from hitting the “big win” target.
The Cast of Characters
Social Sam: Sam’s just there for the experience. Breaking even would be nice, but mostly, she doesn’t want to have to leave early.
Sam gets +3 😀 per spin, +100 😀 for a break-even or better session, +100 😀 for a big win.
Moderate Matt: Matt’s money-minded. He’d like the chance to win big, but coming out ahead is the most important thing for him.
Matt gets +1 😀 per spin, +400 😀 for a break-even or better session, +200 😀 for a big win.
YOLO Yolanda: Yolanda is focused on the big win. She’d like to prolong her session because it means more chances to chase the prize, but she’s not too worried about coming out behind and isn’t excited by smaller wins.
Yolanda gets +2 😀 per spin, +75 😀 for a break-even or better session, +600 😀 for a big win.
Bonus ran a simulated game of American (double-zero) roulette using each of the three simple strategies: betting colors, betting corners, or betting numbers. We stopped each session after the player won $400, lost $200, or had played 80 spins.
Here are the average results after repeating the experiment 10 million times:
|Strategy||Avg. Loss||Avg. Spins||Win or Break Even %||Big Win %||Sam Happiness||Matt Happiness||Yolanda Happiness|
|Colors||-$41.50||78.9||35.9%||0.0%||231 😀||181 😀||143 😀|
|Corners||-$31.03||59.1||40.8%||8.6%||196 😀||208 😀||169 😀|
|Numbers||-$15.52||29.5||23.7%||25.0%||122 😀||159 😀||211 😀|
Here are some things to note:
- Low volatility means longer sessions. That makes betting colors a good option for a social player like Sam.
- High volatility means shorter sessions. By the same token, it actually reduces average losses when the player has committed to both a loss limit and a winnings target because more sessions hit one limit or the other and get cut short.
- High volatility also means more big wins. Naturally, this is the preferred option for a player like Yolanda.
- Sometimes, the mid-volatility option gives the best chance of a winning session. Players like Matt might prefer to bet corners because they need some volatility (and luck) to come out ahead. On the other hand, too much volatility means the chance of going broke quickly and not having the opportunity to make a comeback. Remember, the more volatility, the more spread out the results; if there was no volatility at all, every session would be a loss.
Casino School: Strategy
This has been Strategy Lesson 4 of our four-part series. Go back through the other lessons in case you missed them, or visit our Casino School to learn more ways to play smarter.