King Yao is the author of Weighing the Odds in Hold‘em Poker, and Weighing the Odds in Sports Betting. He uses his experience from making millions in financial derivative markets and translates it into gambling. Since he left his trading position, he has been playing poker and betting on sports. He travels to Las Vegas frequently, especially during football season.

All sports bettors should possess the information presented herein. Other types of casino advantage players, including blackjack players of all skill sets, including card counters, should have good working knowledge of Expected Value as well.

You should not be betting online or anywhere else without this fundamental knowledge.


In sports betting, a middle is a combination of two bets that are closely related, but not exactly mirror images of each other. The combination of the two bets still has risk remaining, but usually is less risky than having just one side naked. Middles are riskier than scalps, but the potential rewards are higher. Typically a middle provides a big win if the event lands on a perfect number or a few perfect numbers, depending on the size of the middle. The risk is that if the game does not land on a perfect number, then you lose a small amount.

Example of a middle

The Jets are playing at the Raiders.

Bet 1: Jets -2.5 -110, risking $110 to win $100.

Bet 2: Raiders +3.5 -120, risking $120 to win $100

You believe the correct line is Jets -3 -100. You also believe there is a 10% chance that the Jets will win by exactly 3 points. Therefore, you believe the Jets have a 45% chance of winning by more than 3, and the Raiders have a 45% chance of covering +2.5.

Here is your expected probability table and possible results.

Result of Game Prob. Jets Raiders sum
Jets win by 4 or more 45% +$100 -$120 -$20
Jets win by exactly 3 10% +$100 +$100 +$200
Raiders cover +2.5 45% -$110 +$100 -$10

If the Jets win by exactly 3, then you win both bets. Any other outcome means you lose one side and win the other. Since you are paying the juice on both bets, winning one and losing the other will give you a small loss. These two bets should be looked at as a tandem. The true risk is whether or not the Jets will win by exactly three. Here is the EV calculation of the two bets given the probability distribution shown in the table above.

The EV of the two bets combined equals:

= (45% x -$20) + (10% x +$200) + (45% x -$10) = +$6.50

If your expectation of the probability distribution of the game is correct, then you have a positive-EV middle. Unfortunately, 90% of the time you will lose small. But the other 10% of the time, you will win big. The big wins will cover the losses by a nice margin if your probability distribution is on target. If your numbers are incorrect, you may have a negative-EV middle.

This is part of an occasional series of articles.

Excerpted with permission from the e-book version of Weighing the Odds in Sports Betting by King Yao, edited for this format.


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