Mathematics of Gambling Lesson 2: Never Parlay

Posted: August 31, 2011 in Gambling Lessons
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I like to call the parlay the amateur’s bet. Although I must admit that even though I am well aware it makes no sense mathematically to ever parlay, I too get sucked in sometimes. To understand why you should never parlay, let’s first recall some of the math from lesson one. First, let’s find the expected value of a straight bet with the typical (-110) price. To keep this lesson simple, let’s assume a 50% chance of winning. The expected value is equal to:

50% x (-$110) + 50% x $100 = (-$5)

In other words, you are expected to lose $5 for every $110 bet you make with a 50% chance of winning. A $5 loss on a $110 bet yields a return on investment (ROI) of:

(-$5)/$110 = (-4.54%)

That means the house has a 4.54% advantage anytime you make a straight bet assuming a 50% chance of winning. Many gamblers who fail to consider the math at play incorrectly assume the house has a 10% advantage ($110 is 10% higher than $100). As my math just demonstrated, they are selling themselves short.

Now onto parlays. First, we will consider a two-team parlay, each game at (-110) with a 50% chance of winning each. Most of you know that a two-team parlay, both at (-110) pays 2.6:1 (or +260). However, most of you don’t realize that your true chances of winning this parlay are determined first by multiplying the chances of winning each independent game:

50% x 50% = 25%

In other words, you actually have a 25% chance of winning the parlay, and a 75% chance of losing. That being said, let’s determine the expected value and return on investment of a two-team parlay. A win on a $100 bet would yield $260.

EV = 25% x $260 + 75% x (-$100) = (-$10)

ROI = (-$10)/$100 = (-10%)

In this case, the house now has a 10% advantage instead of a 4.54% advantage over you! If you think that is bad, let’s do one more just to get the point across. Without showing the math, I will tell you now a three-team parlay has an ROI of (-12.5%). Let’s check out a four-team parlay. A four team parlay pays out 10:1 (or +1000). Seems tempting right? Wrong! The actual chances of winning a four-team parlay are 50% x 50% x 50% x 50% = 6.25%. A win on a $100 bet would yield $1,000, but you have a 93.75% chance of losing $100!

EV = 6.25% x $1,000 + 93.75% x (-$100) = (-$31.25)

ROI = (-$31.25)/$100 = (-31.25%)

You just gave the house a 31.25% advantage over you! Every team you add to your parlay, you only increase the house advantage! There is a reason why Vegas exists and flourishes! They have an advantage over you! There is no reason to add to their advantage! If you have trouble understanding the math here, I suggest reading it over a few times or maybe buying a book on statistics. You will never be a successful gambler over the long run without understanding expected value and return on investment.

  1. […] this, the move from -110 to -115 gives the house an even greater advantage. If you think back to my mathematics of gambling lessons, the house has a 4.54% advantage at -110 assuming you are an average gambler with a 50/50 chance of […]

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