whats the best way to compare two different wagers?

same size wager:

a $100 3team parlay getting 6.5:1 and a $100 straight up bet


same payout:

a $100 3team parlay getting 6.5:1 and a $392 straight up bet

$100(6.5) + $100 = $750

$392(10/11) + $392 = ~$750


same EV:

a $100 3team parlay getting 6.5:1 and a $137.50 straight up bet

$100(1/8)(6.5) - ($100)(7/8) = -$6.25

($137.50)(1/2)(10/11) - ($137.50)(1/2) = -$6.25


same variance:

a $100 3team parlay getting 6.5:1 and $260 straight up bet

(1/8)*(650)^2+(7/8)*(-100)^2+((1/8)*(650)+(7/8)*(-100))^2 = ~61601

(1/2)*(260*10/11)^2+(1/2)*(-260)^2-(1/2*(260*10/11)+1/2*(-260))^2 = ~61601

Wouldn't you need to wager $715 to win $650 on a straight bet?

I note that at a probability of winning per pick of 50.45%, the house edge of both bets is almost the same, at 3.7%. If you think you can beat 50.45%, and don't mind the variance of the parlay, then the parlay is the better bet. You need only 51.1% to have zero house edge on the parlay. I think you would achieve that just flat betting underdogs.

hey mike. thanks for the response.

like i thought it was kindof an interesting topic. its kind of like comparing apples to oranges. whats the best way to compare two different wagers? maybe comparing the same size wager and the EV of both isnt the best approach.

maybe its better to figure out the size of the wager where their variance is the same. then figure out the EV of each bet to compare them to eachother.

but then it would seem like betting one number in roulette is better than betting on red or black since theres less variance. when usually were taught it doesnt matter what u bet on in roulette since the house edge remains the same. but maybe thats not the only thing to consider.

another thing im confused about. i always thought longshots had more variance than coinflips. but when i computed variance for this sports bet. u needed a larger wager on a straight up bet to have the same variance as a longshot. not sure if i did something wrong or what.

i got something to email u in a bit. just updating it one last time.

like comparing rolling a 7 on two dice to flipping a coin. in 90 trials getting 14 or 16 7s compared to 51 heads and 49 tails or 49 heads and 51 tails. that one away from the mean is going to be +/- 5 for the dice but in the coinflip one away from the mean is gonna be +/- 1. seems like rolling the dice has more variance.

Makes sense as there are 11 possible outcomes (2-12) with dice, but only two with the coin.