It’s Not Just About How Often You Win Your Bets
If you bet on a single number in roulette, the probability of winning that bet is obviously much lower—1/38, or 2.63%. There’s more to it than that, though. You also need to keep in mind the payout odds.
The House Edge Doesn’t Necessarily Change
You’ve probably heard or read the expression “house edge” before. It’s just a term used to describe the casino’s statistical advantage over the player. It’s expressed as a percentage.
On that bet on red, you’ll win WAY more often. On average 18 out of 38 spins. But when you win this bet, you’ll only win even money. Bet $100, and you’ll win $100 when you win. But if you play either way for 10,000 spins or so, you’ll eventually see the same results—a loss of about $5.26 every time you bet $100.
What About Other Casino Games Like Blackjack?
You actually have a lower probability of winning a hand of blackjack than you do of winning an even money roulette bet. The probability of winning a hand of blackjack is significantly lower than the probability of winning an even money roulette bet.
The difference has to do with the probability of getting the bonus payout for a “natural,” or “blackjack.” That’s a two-card hand that totals 21. The only way to get a blackjack is to get a two-card hand with a 10 and an ace in it.
So, you see, just because you’re more likely to win some bets, it doesn’t mean that you can generate a long-term profit from that strategy.
It’s Better to Find the Game With the Lowest House
In the long run, if your hope is to be profitable, your best chance is to stick with the game with the lowest house edge. You could get lucky and see a standard deviation early on that will make you a profitable player.
Casinos use a formula to estimate how much they’ll make from a casino game in the long run. Gamblers can use the same formula to decide how unprofitable such a game is for the player. The formula is simple:
House edge X hourly action = expected hourly loss
You need a second calculation to get your average hourly action, but it’s just another simple multiplication problem:
Average number of bets per hour X average size of bet = hourly action
Some Examples of Calculating Your Predicted Losses at Casino Games
Slot machines are some of the most expensive games in the casino. Let’s assume you’re playing Megabucks, which costs $3 per spin to play. Let’s also assume that the house edge on the game is 9%. (We don’t know what the real number is, but that’s probably not a bad guess.)
An average slot machine player might make 500 spins per hour. At $3 per spin, your hourly action is $1,500. With a house edge of 9%, your expected loss is $135.
Standard deviation might result in an hour or two of wins, but once you’ve put in about 20 hours of play, you should be coming pretty close to the expected loss per hour. In fact, by then, you should have lost about $2,700 on the game. That’s a sobering thought…
Let’s also assume you’re playing for $5 per hand. If you’re playing heads up with the dealer, you might be getting 200 hands per hour.
Your hourly action is $1,000. If you lose 0.5% of that on average, you’ll lose an average of $5 per hour. You have a couple of questions to ask yourself.
Would you rather lose $5 per hour gambling or $135 per hour gambling? Are you getting an additional $130 per hour of entertainment playing the slot machine game instead of the blackjack game?
If you’re a recreational gambler, you should change your mindset and start thinking about gambling as an entertainment activity. Then, you can analyze whether you’re getting your money’s worth from your entertainment dollars.
If You Want to Win, You Need to Get an Edge
Even though every game in the casino has a built-in house edge, you can still find ways to get an edge when gambling. If you repeatedly place bets with an edge, you’re considered an advantage gambler. And you can use the same formula as above for calculating those projected profits.
Here’s an example: Let’s say you learn how to count cards, and you estimate that you have a 1% edge over the casino when counting. Let’s also say that you ONLY play heads-up, and your average bet size is $20. (Since you’re raising and lowering the size of your bets based on the count, the average will almost always have to be higher than $5 per hand.)
So, you’re playing 200 hands per hour at $20 per hand, and you’re putting $4000 per hour into action. If you’re estimating that you’ll win 1% of that, you’re looking at hourly winnings of $40 on average.
The easiest way to increase your annual winnings is to increase your average bet size. To do that, though, you need to have a bigger bankroll.
The Importance of a Big Bankroll
Standard deviation is the expression that mathematicians use to describe the deviations from the expected results in a probability experiment. It means that in the short term, random events don’t usually hit the expectation, they’re usually higher or lower.
Here’s an example: You flip a coin 6 times in a row. The expectation is that you’ll get heads 3 times and tails 3 times. But it wouldn’t be unusual to get heads 2 times and tails 4 times.
It wouldn’t even be that crazy to see heads once and tails 5 times. It’s not unthinkable to get heads all 6 times, either. Those are all examples of deviations from the mean. The bigger the deviation, the bigger the multiple of the standard deviation is.
How does that apply to our hypothetical card counter at the blackjack table? It means that even when you’re playing with an edge over the house, you might go on a losing streak in the short run.
And if the losing streak is long enough, you can go broke before you ever reach the long run.
The possibility that this will happen is called the “risk of ruin.” It’s a probability, too.
If you really want to be profitable in the long run, you must have a big enough casino bankroll for the action to minimize your risk of ruin.
But you’re asking the wrong question. You’re probably more interested in getting a long-term edge over the casino.
Most gamblers just aren’t up for the dedication and work required to pull that off, but it can be done.
Counting cards is just one way to do it. Read my other blog posts for additional techniques for getting an edge and beating the casinos.