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
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,
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
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.