Gambling Math

by Frank Scoblete

Gambling Math can tell us quite clearly what our average expected loss (or win) will be at each and every game by plugging our betting levels into a very simple formula: Average Bet x Speed of Game (or Number of decisions per hour) x Hours Played x House Edge = Expected Win/Loss.

So if you wanted to play blackjack for one hour at $10 a hand playing perfect Basic Strategy at a one-half percent disadvantage, you could expect to lose on average four dollars ($10 average bet x 80 decisions per hour x 1 hour x .005 house edge = $4).
You can plug in any game and find this average amount. Unfortunately, owing to the streaky, freaky nature of chance, the above formula really wouldn’t tell you if you were going to lose all, some, most, or none of your money in that hour or the next -- or whether you would win a bundle, or a single bet, because averages are, well, averages.

Therefore, winning and losing at casino games rarely match the average expectation on a given evening because wild, weird, and wonderful things can happen, as the following true-life examples demonstrate:
 
1. At the Maxim Casino in Las Vegas in July of 1995, a $5 player won 23 straight hands -- some with doubles, splits, and splits with doubles -- in blackjack playing heads up against a dealer in a six-deck game. At the fourth hand, he started to escalate his bets and he won several thousand dollars in that run. I saw this.
 
2. At Caesars Palace on July 14, 2000, gaming writer Barney Vinson witnessed the number 7 come up at roulette six times in a row -- a billion to one shot!
 
3. At the Desert Inn in February 1998, slot Expert John Robison went 93 spins on a slot machine without one hit.
 
4. In August of 2000, Joan Cartwright played Let It Ride at Bally’s in Atlantic City and lost $300 at $10 per hand -- without winning a single hand!
 
5. In roulette, Morris Guttermann lost 11 times in a row on red when black came up 12 times in a row at the Imperial Palace in Las Vegas in August of 1994. Somewhere in that awful run, Morris decided to start increasing his bet figuring that red had to come up sooner or later -- as indeed it did. After he lost all his money!
 
Outlandish wins, or horrendous losses, and a given evening sees your bankroll skyrocketing to the heavens, or skidding down the storm drain. To protect yourself against the latter happening, here is a simple formula to help you determine what you need to bring to the casino for one hour of play at your favorite game to insure that you will not go broke: Ps = (q/p)a - (q/p)s / (q/p)a - 1 x Pi x e=mc2.
Just kidding.

Just bring enough to last one hour under the assumption that you’re going to lose every single bet! It doesn’t get simpler than that.

The gambling math you have to figure out is how many decisions the game you are playing has in a given hour and multiply that by your betting unit ($5, $10, $15, $25 or more) and you will arrive at the absolute foolproof way to assure that you can last for one hour if the goddess of chance decides to treat you the way the pigeons treat the statues in the park.
Bring half that much if you figure you can handle it if the worst possible scenario occurs and you lose it all, as half of the suggested bankroll will, for all intents and purposes, be very difficult (but not impossible) to lose in one hour’s time. 

Gambling Math: Blackjack
A crowded table at blackjack will have about 60 decisions an hour. So bring 70 units. Why 70? Because on some hands you’ll have to split and/or double down.
A $5 player should have $350; a $25 player should have $1,750. Bring this much and you’ll probably be delighted to discover that as a Basic Strategy Player you can probably play two or three hours (not just one) without any serious threat of going belly up.

Gambling Math: Craps
How much you need to guarantee that you’ll not be wiped out is tricky as craps has many different kinds of bets. If you make the Crazy Crapper bets with high house edges and low hit frequencies (for example, the 12), then you would need a LOT of money as craps can have 120 or more rolls per hour.
However, if you play a very conservative game -- in other words a smart game -- of Pass/Come with odds, place the six and/or eight, then you should bring 10 times the amount of your spread when you are up on the total number of numbers you want to be up on.  

Here’s an example: If you want to bet $5 on the Pass Line and back it with $10 in odds and then go up on two Come numbers $5/$10 and $5/$10, you’d need $450 as $45 is your spread. If you just wanted to go with one Pass or Come number, then you would need $150 as $15 was your spread. 

Gambling Math: Roulette
On the outside even-money bets (Red/Black, Odd/Even, High/Low); you’d need 40 times your unit bet to assure that you can’t possibly go broke. Roulette will have approximately 40 decisions per hour so a $5 player would need $200. However, a more realistic figure would be 23 times your bet. Why 23? Because that is the most any outside bet ever came up in a row (if memory serves me well, it was black) and I doubt if the next time you play roulette you’ll see such a record broken.
So $5 bettors could be reasonably assured that they could last one hour with $115. The inside bets are another thing entirely as 38 numbers make it hard to guarantee that you’ll win even one bet in an hour of play. In fact, it is not unusual for someone to lose 40 decisions in a row betting one inside number.
So here you’d have to go with 40 units and pray that the dealer doesn’t spin any more decisions than that! 

Gambling Math: Let It Ride
Here’s a game with a low house edge that can be wonderful or awful depending on how your luck is running. Generally, it is awful until it becomes wonderful. Here’s why: The win frequency is approximately 25 percent. That’s right -- you win only one in four decisions, and you can gallop a long, long, long time on the losing end of this pony.
So how much is enough? About 60 times your minimum bet.
Since Let It Ride allows you to take down two of your three initial bets, you tend to lose only on the third bet -- the “$” bet -- when you lose. With some exceptions, you will not let that first bet (“1”) or the second bet (“2”) ride unless you are assured a winner (10s or better). So if you play for $5 bring $300 with you and you shouldn’t have any fear of being stampeded.

Gambling Math: Caribbean Stud
This game can be fast or slow or in-between depending on how fast the dealer deals and how fast (or slow) the players make their decisions. On average 40-50 decisions an hour are common so bring 50 times your minimum bet and you should be able to last one hour if a hurricane of bad fortune slams your way. 

Gambling Math: Baccarat and Mini-Baccarat
Baccarat is a slow game and mini-baccarat is a fast game.
The former will have 30-50 decisions an hour at a full table, the latter will have upwards of a 150 decisions an hour. If you can afford it, play baccarat (even if you have to play for slightly more money) as the speed of mini-baccarat. can really rip through a bankroll. 

Gambling Math: Three Card Poker
This is a very fast game so bring about 80 times your bet and you should have no fear of being wiped out. Learn the correct strategy so you keep the house edge as low as possible.

Recall that the purpose of these articles was not necessarily to tell you the best ways to play the above games, or which games to play and which to avoid. It just explained what you need to bring to assure yourself of not being wiped out if Lady Luck wipes her feet on you.

Remember this too. Learn from my mistake. I know what it’s like to come home with no gambling math or empty pockets. It’s one of the worst feelings in the world.

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