EV Formula For Parlay?

Hello Sport Wizards!

I just dipped into sports betting realm!

I couldn't figure out the EV formula for parlay bets. Especially the winning and losing odds part. I saw somewhere if the odd is -110 and let's say you made a two team parlay bet then the winning odd is 50% x 50% => 25%. However, I couldn't find info how to figure out the winning odd if Team A's odd is +400 and Team B's odd is +130. So far I have the EV formula as...

Bet Amount: $10
Team A: +400
Team B: +130
Payout: 10.50 (I got this info from Parlay Calculator)
Winning Odd: I haven't figured it out
Losing Odd: I haven't figured it out

EV = (Bet Amount x Payout x Winning Odd) + (-Bet Amount x Losing Odd)

EV =($10 x 10.50 x Winning Odd) + (-$10 x Losing Odd)

Two questions:
1) Is my EV formula correct?
2) How do I get winning/losing odds if Team A is +400 and Team B is +130?

Thanks & Happy Betting!

Quote: JustALuck

Hello Sport Wizards!

I just dipped into sports betting realm!

I couldn't figure out the EV formula for parlay bets. Especially the winning and losing odds part. I saw somewhere if the odd is -110 and let's say you made a two team parlay bet then the winning odd is 50% x 50% => 25%. However, I couldn't find info how to figure out the winning odd if Team A's odd is +400 and Team B's odd is +130. So far I have the EV formula as...

Bet Amount: $10
Team A: +400
Team B: +130
Payout: 10.50 (I got this info from Parlay Calculator)
Winning Odd: I haven't figured it out
Losing Odd: I haven't figured it out

EV = (Bet Amount x Payout x Winning Odd) + (-Bet Amount x Losing Odd)

EV =($10 x 10.50 x Winning Odd) + (-$10 x Losing Odd)

Two questions:
1) Is my EV formula correct?
2) How do I get winning/losing odds if Team A is +400 and Team B is +130?

Thanks & Happy Betting!

1) Assume fair odds - +400 would be 1/5 chance to win (4 chances to lose 100 and 1 chance to win 400 = even)
+130 would be 10/23 (100 base bet) / (130 payout + 100 base bet) chance to win.
Combined probability of winning both would be 1/5 * 10/23 = 10/115

plug that into your formula
10 * 10.5 * 10/115 + -10 * 105/115 = 0

Adjust accordingly - for example a 10 cent line would put fair payout at +140 for the second team so only 10/24 chance to win. +400 would become 10/41. combined win = 10/41 * 10/24 = 100 / 1722

ev = 10 * 10.5 * 100/1722 - 10 * 1622/1722 = -3.321718931475029

2) (100 + 400) * (100 + 130) - 100 = 1050 / 100 base bet = 10.5

Thanks wudged!!! Your post was very helpful!