Please figure this out

[RedeemerKing]

I figured there would be a lot of math guys in here who might be able to figure this one out.

This is a math question related to sports, particularly money lines. I can usually narrow it down to 4 picks on a given day. My EV would be -10%, assuming dime lines, of what I risked if I was to do 4 straight bets, right? What would be my expected value if I did a round robin with 3 team combinations of the same 4 teams and risked the same amount. I'm pretty sure it would be lower, but cant mathematically figure it out. Any help would be appreciated

PS If u dont know..... A round robin would give me every possible 3 team combination in a parlay of the original 4 teams for a total of 4 3team parlays

[gaming_mouse]

How much do you get payed for picking a round robin correctly?

When you make a straight wager, do you have to wager 110 to win 100?

When you make a round robin wager, what do you have to pay and what will you win?

[RedeemerKing]

to keep it simple lets say i pick 4 teams, 1234, all straight 11$ to win 10$ for 44$ to win 40$ total.

I have 4 parlays
teams 123 $11-$66
teams 124 $11-$66
teams 134 $11-$66
teams 234 $11-$66

so any 3/4 nets $33 profit. 4/4 nets $264 profit. and anything else I lose $44

[gaming_mouse]

[ QUOTE ]
to keep it simple lets say i pick 4 teams, 1234, all straight 11$ to win 10$ for 44$ to win 40$ total.

I have 4 parlays
teams 123 $11-$66
teams 124 $11-$66
teams 134 $11-$66
teams 234 $11-$66

so any 3/4 nets $33 profit. 4/4 nets $264 profit. and anything else I lose $44

[/ QUOTE ]

So let's say you can pick a team correctly with 55% accuracy.

EV_straight_wagers = 4*(10*.55 + (-11)*.45) = 2.2

Now let's get the EV for the parlay.

The chance that you choose exactly 3 teams correctly is:

4*(.55)^3*.45 = 0.299475

All 4 correctly:

(.55)^4 = 0.09150625

Thus:

EDIT AGAIN (I was confused by how the odds were working. I'm assuming now that you risk 11 to get 66 in profit):

EV_parlays = (66-33)*.299475 + (66*4)*0.09150625 + (-44)*(1-0.09150625-0.299475) = 7.2435

[Stephen H]

Using the same math as gaming_mouse with a straight 50/50 accuracy on picking games, though, I get:

4 Individual game bet EV: -$2
4*(10*.5-11*.5) = -2
4 3-team parlay game bet EV: -$5.50
4*(.5)^3*.5 = .25
(.5)^4 = .0625
(66-33)*.25 + (66*4)*.0625 - 44*(1-.25-.0625) = -5.5

Which makes it worse EV to make the parlay bets if you have no edge on picking the games.