The Mathematics of Breaking Even

Author: Mark Pilarski

Dear Mark: Now that the football season is over, I ended up pretty much breaking even for the whole season. I’ve read that the house edge is 4.55% on sporting bets. How is that figured, and would that mean I lost just under 5% of my bets? Dave D.

Actually, Dave, you lost less than that percentage-wise, 52.273% to be exact, but that figure presupposes that all of your bet amounts were identical, always wagering $11 to win $10, for example.

I’ll get to that 52.273% in a moment, Dave, but, for an appetizer, let’s break down a typical $11 wager. For those who dabble on individual games, the sportsbook, bookie, or even Uncle Leo is going to make the bettor risk $11, or $10 plus 10%. When you win, you get back your $11 wager, and $10 in winnings. If you lose, you get back, as legendary Las Vegas sports bettor Billy Walters says, “feathers, no chicken.”

Your cost – the house edge – on any sporting bet where you wager $11 to win $10 is 4.55%. Note though, Dave, that extra $1 is NOT a percentage edge, but a commission or “vigorish” (a.k.a. vig), taken by the house as compensation for allowing you to have action on the game while you suck down beers and eat chicken wings.

Here’s the barnyard math, Dave, to get to that 4.55%. Let’s say that both you and I are betting on the Detroit/Chicago football game. You favor the Bears, while I’m on the Lions. We each bet $11, which gives the sportsbook a total cash inflow of $22. So if the Bears win, you turn in your winning ticket and get back $21 –– your original $11 challenge plus $10 in winnings.

While the house pays you the winner $21 –— the $11 wager plus $10 in winnings from my losing bet, the house pockets my remaining dollar. Divide the dollar profit for the house by the $22 wagered between us, and you get .0455. Now multiply .0455 by 100 to convert it to a percentage, and you get the 4.55% the house has on each of our wagers.

But that, Dave, is the edge on both of our wagers. The percentage of sports bets you need to win to break even is at least 52.273% of any wager you make. So, Dave, if you bet on 100 games, you would need to win 53 bets to be ahead of the house. Here’s how we get to that figure.

If you make 100 $11 wagers, you risk $1,100. If you win 53, you would get back $1,113 and show a $13 profit. Win 52 bets and lose 48, you get back $1,092, $8 shy of breaking even.

Now armed with some arithmetic, what you shouldn’t do, Dave, is quit your day job and move to Las Vegas on the assumption that you can easily win 53 plus percent of the time. You’ll find out mighty quick ‘taint easy.

Dear Mark: I recently hit a $5,000 jackpot and after my payoff, the slot person turned a key in the machine before I could play again. What were they doing to the machine? Susan M.

Anytime you hit a jackpot where the IRS wants a part of the booty, which in the case of a slot machine payout is $1,200, the machine automatically locks up. After you sign the required tax form, the slot attendant unlocks the machine so you can start feeding it your winnings.

Gambling Wisdom of the Week: “There is enough energy wasted in poker to make a hundred thousand successful men every year.” —Arthur Brisbane, The Book of Today

Gambling City

We are Cash Back

The Mathematics of Breaking Even

Cookie Policy