Parlays

A parlay is a combination bet where all the bets fall under a single wager. Each bet must cover to win the wager. For example, a three team parlay involves three bets and if all three cover, the bettor collects six times the wager amount. Sounds good except for the fact it takes only one losing game to lose the parlay and the total wager amount. Important to note is that depending on the book, a push in a game of the parlay may result in either a no bet situation or the bet is pushed down to a fewer games parlay. Under the push down rule, a push in a game of a three team parlay converts the bet into a two team parlay.

The inevitable question arises to whether a parlay bet is a sound investment strategy. In order to answer this question, the important number to consider is the projected success rate for picking pointspread winners. If a bettor is picking less than 52.38% winners against the spread (ATS), straight bets are better than parlays as the straight bets will lose at a slower rate than the parlays. The consolation for making straight bets in this inevitable losing situation would be the bankroll won’t be wiped out as fast. The bottom line is that both straight bets and parlays will be losing propositions for failure to pick consistent winners.

For the situation where the bettor can pick consistent winners, let’s use some statistical mathematics to crunch the probability numbers. Let’s consider a two team parlay. The first step is to determine all the possible outcomes for each of the two bets as shown below:

2 Team Parlay Bets

   Game 1        Game 2

W                  W                    1 combination of 2 wins

W                   L                     2 combinations of 1 win

L                    W

L                     L                     1 combination of 0 wins

There are a total of four win-loss combinations, assuming there are no pushes. If a bettor picks 54% winners over a season, the individual bet success rate is 0.54 and the failure rate is 0.46. Applying the success and failure rates to the four possible combinations shows the following:

probability of two winners:                                                                                                           0.54 x 0.54 x 1 combination = 0.291 (29.1%)

probability of one winner and one loser:                                                                                    0.54 x 0.46 x 2 combinations = 0.497 (49.7%)

probability of two losers:                                                                                                                0.46 x 0.46 x 1 combination = 0.212 (21.2%)

Since a winning two team parlay pays 13/5 odds, this means a successful parlay will pay out 2.6 times the wager amount. The 13/5 odds also show that 5 out of 18 (27.8%) two team parlays are required to win to break even. For a $110 parlay wager, a winning parlay will pay out $286 and if either game loses, the $110 wager will be lost. If 54% ATS winners over time are anticipated, the expected rate of return on the two team parlay bet is computed as follows:

0.291 x  $286  =    $83.23 (bettor has a 29.1% chance of winning $286 on successful parlay)

0.497 x -$110 =   -$54.67 (bettor has a 49.7% chance of splitting the games and losing $110)

0.212 x -$110 =   -$23.32 (bettor has a 21.2% chance of losing both games and losing $110)

Summing the three returns yields an expected profit of $5.24 per parlay bet. If a bettor played 12 two team parlays at $110 each (gross risk = $1,320), the expected profit would be $62.88 (12 bets x $5.24).

The question begs would the bettor make more money playing straight bets? If the bettor chose straight bets for the same games, there would be 24 single game wagers at $55 each (same gross risk = $1,320) and 54% winners would show 13 winning bets and 11 losing bets. With a 10% juice ($55 to win $50), the profit would compute to (13 x $50 – 11 x $55) = $45.00. This calculation shows that at 54% winners, a two team parlay has a higher expected rate of return than straight bets, $62.88 versus $45.00.

Actually, a 52.7% ATS winning rate is the breakeven point for two team parlay bets as compared to a 52.38% ATS winning rate for straight bets at a 10% juice (11:10 payout). In other words, if a bettor can win more than 52.7% of the plays, the two team parlay has a higher expected rate of return than straight bets.

Moreover, three team parlays have an even higher expected rate of return than two team parlays when picking 54% winners ATS. Hitting a three team parlay returns six times the wager amount. The possible outcomes for three plays follows:

3 Team Parlay Bets

Game 1    Game 2    Game 3

W            W             W                    1 combination of 3 wins

W            W              L                     3 combinations of 2 wins

W             L              W

L              W             W

W             L               L                     3 combinations of 1 win

L              W              L

L               L              W

L               L               L                     1 combination of 0 wins

There are a total of eight win-loss combinations, assuming there are no pushes. If a bettor picks 54% winners over a season, the individual bet success rate is 0.54 and the failure rate is 0.46. Applying the success and failure rates to the four possible combinations shows the following:

probability of three winners:                                                                                                         0.54 x 0.54 x 0.54 x 1 combination = 0.1575 (15.75%)

probability of two winners and one loser:                                                                                    0.54 x 0.54 x 0.46 x 3 combinations = 0.4024 (40.24%)

probability of one winner and two losers:                                                                                    0.54 x .046 x.046 x 3 combinations = 0.3428 (34.28%)

probability of three losers:                                                                                                             0.46 x 0.46 x 0.46 x 1 combination = 0.0973 (9.73%)

The 6 to 1 payout shows that 1 out of 7 (14.3%) three team parlays are required to win to break even. A winning parlay will pay out $660 and if any game loses, the $110 wager will be lost. If 54% ATS winners over time are anticipated, the expected rate of return on the three team parlay bet is computed as follows:

0.1575 x  $660  =   $103.95 (bettor has a 15.75% chance of winning $660 on successful    parlay)

0.4024 x -$110 =    -$44.26 (bettor has a 40.24% chance of winning two games and losing $110)

0.3428 x -$110 =    -$37.71 (bettor has a 34.28% chance of winning one game and losing $110)

0.0973 x -$110 =    -$10.70 (bettor has a 9.73% chance of losing all games and losing $110)

Summing the four returns yields an expected profit of $11.27 per parlay bet. If a bettor played 12 three team parlays at $110 each (risking $1,320), the expected profit would be $135.24.

The calculation shows that at 54% winners ATS, a three team parlay has a higher expected rate of return than two team parlays and straight bets. But the worth of parlays ends here. Avoid four or more team parlays at all costs. The expected rate of return diminishes and a bettor is playing the lottery at that point.

Before everyone forsakes straight bets to play all parlays, extreme words of caution need to be expressed. First of all, there is no guarantee that 54% winners will directly translate into winning 29.1% of the two team parlay bets or 15.75% of the three team parlay bets as shown above. Consider the 12 three team parlay plays above which means there are 36 individual pointspread plays. Assume the bettor will win 20 out of the 36 individual plays (55.55% winners ATS). Believe it or not, a worst case scenario shows the bettor could lose all 12 parlay bets. Eight of the parlay bets could feature two pointspread winners and one loser and the other four could have one pointspread winner and two losers. Voila, 12 parlay bet losers even though the bettor picked 55.55% winners in the individual games.

The major pitfall of betting parlays is that the expected rate of return analysis does not guarantee the distribution of the winners and losers within the parlay bets.

POINTSPREADWINNERS.COM advocates straight bets.