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Gambling Math - Part 1: RETURN ON INVESTMENT

When you bet $100 flat on a single game you get back $91.  When you bet $100 flat on a 2-team parlay, you get back $260.  Do you know which has the higher return on investment (ROI)?  The answer is not as easy as it looks.

 ROI is calculated by dividing your total win by your total amount invested.  The total amount invested is another way of saying "the total amount you put at risk."

ROI for Straight Bets

With the straight bet, you put $100 at risk.  If you played just one game and won $91, your return on investment for that game is 91/100 = 91%.  If you played just one game and lost, your return on investment is 0/100 = 0. 

If you played two games for $100 each and won both, then your return on investment is your win of 91 x 2 = 182 divided by the $200 you put at risk.  That's 182/200 = 91%.  It doesn't matter that you won the first game and used the same $100 to bet both games.  You still put $200 at risk -- $100 on the first game and $100 on the second game.  You risked the $100 twice.  Your return on investment at a 100% win percentage will always be 91% no matter how many games in a row you win. 

ROI for Parlays and "If" Bets

Now lets look at calculating the ROI for parlays.  Many people assume that because they put $100 through the window when they bet the parlay, their risk/investment is only $100.  That is not true, because it doesn't take into account the fact that you will not get anything back for the first win if the second game loses. 

Obviously, needing to win 2 games or more cannot be the same risk as needing to only win one game in a straight bet.  In a parlay you risk $100 on Game 1.  If you lose Game 1, then your ROI is 0/100 = 0%.  If you win Game 1, then the entire amount of your win plus your original bet is placed on Game 2.  That's why you get back $0 if Game 2 loses, whereas with two straight bets you would get back the $91 you won on Game 1 if Game 2 loses. 

 The increased risk on Game 2 is what makes a parlay different from simply betting two games straight, or betting the same two games in a common "if " bet. 

In a common "if" bet, you put $100 on Game 1 and IF Game 1 wins you automatically put $100 on Game 2.  If both games win and you win $91 for each game for a total win of $182, you can clearly see that even though you put only $100 through the window, the bookmaker automatically risked $100 for you on each of the two games in the bet.  In fact, in making the bet that's exactly what you told him to do.  You say "Bet $100 on Game 1, and if it wins Bet $100 on Game 2."  Thus, the winning "if" bet ROI is no different from the ROI on betting two games separately for $100 each.  With the common "if" bet, if Game 1 wins and Game 2 loses, you still get back $91 from your win on Game 1. 

A parlay is really a type of "if" bet.  The actual bet is: 

Put $100 on Team 1 and IF Team 1 wins then put the whole $100 bet plus my $100 win on Team 2.  Note that, in a parlay, the bookmaker subtracts the vig at the end if you win, and not game by game.  Therefore, on Game 1, you win a full $100 for your $100 bet.  As previously stated, it is as a result of the increased risk of  $200 on Game 2 that you get back $0 if Game 2 loses.  If anything less than $200 were risked on Game 2, there would be something left for you to get back in the end just like with the regular "if" bet described in the paragraph above.

Your total risk in a 2-team parlay is $100 on the first game and, if you win, then $200 on the second game.  If you win the second game also, the total payout at true odds would be $400.  The book then subtracts the 10% vig he charges on parlays from the total returned to you.  The amount returned to you is thereby reduced by 10% of $400 = $40.  The book gives you back $400 - $40 = $360.  That breaks down as $100 as your original bet, and a win of $260.  The total risk in a 2-team $100 parlay is $100 on the first game and $200 on the second game for a total of $300.  Your ROI is the win of $260 divided by the total risk (investment) of $300 = 86.67%.  This is less than the ROI of 91% on two straight bets, and therefore the ROI on straight bets is higher than the ROI on parlays. 

The ROI would be higher for straight bets even if you doubled up your second straight bet.  If you bet $100 on Game 1, and then $200 on Game 2, your total win would be $91 on Game 1 plus $182 on Game 2, which equals $273.  Divide $273 by your risk of $300 and you get an ROI of, you guessed it, still 91%.    

The ROI always being higher for straight bets is as it should be, since the house edge on a 2-team parlay is 10% compared to just 4.54% on straight bets.  In the next article I will discuss how to calculate the house edge.

RULE 1:  The Return on Investment is always higher for bets with a lower house edge. (This rule is a mathematical absolute.  It has no exceptions.) 

RULE 2:  The theoretical ROI moves opposite the house edge.  The lower the house edge, the higher the theoretical return on investment will be for any given win percentage.  The higher the house edge, the lower the theoretical return on investment will be for any given win percentage 

In a 3-team parlay the amount you risk is $100 on the first game, $200 on the second game, and $400 on the third game, for a total of $700.  If you win $600 on the parlay, your ROI is 600/700 = 85%.

ROI for Teasers

The ROI for teasers is calculated the exact same way as for parlays.  In a 2-team teaser, you risk $100 on the first game at the adjusted line, and $200 on the second game at the adjusted line.  Instead of paying you a $300 win plus your bet, the bookmaker gives you just $91 plus your bet in a 6-pont teaser.  He takes 400-191 = $209 as his commission.  Incredibly, when you bet a teaser the bookmaker gets more as his commission than you get back for your win plus your original bet.  The question with teasers is whether the line adjustments are sufficient to compensate you for the huge vig.  That's a discussion for another article, but suffice it to say that in the vast majority of football teasers and all basketball teasers the line adjustment is not even close to sufficient compensation.   

If you win $91 on a $100 2-team teaser, your ROI is 91/300, which equals a comparatively tiny 30.33 % based on a win percentage of 100%. 

Now that you know the math, you should be starting to understand why, except under some very limited circumstances, competent professionals don't bet parlays or teasers.

(c) Robert Crowne & Assoc., April, 2009.  Published by permission.

 

 

A professional sports bettor and card player for 24 years, Rob is known as being as an expert handicapper and bettor, as well as one of the few sources for picks of the professional sports betting groups... Read more

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