Effective value of "50% CASH bonus if your first bet is a win" bonus

[xyz]

betEd currently is running a sign up promotion named "50% CASH bonus if your first bet is a win". The details are as follows:

Whatever you win from your first sports bet, we’ll add another 50% of your winnings on top! Applicable to your first "Point Spread" or "Over/Under" wager only. This only applies to a single "Straight Wager". Bonus has a maximum value of $250.

I want to compute the effective value of this bonus if I were to hedge my bet somewhere else. Assuming "Point Spread" or "Over/Under" odds is around even. Then I would put $500 on one side in betEd, then put $625 on the other side somewhere else. There is no profit if the game pushes. So I must find a spread or total that falls on a half point. Then this would guarantee a profit of $125, which is effectively a 25% cash bonus ($125/$500).

Is this the most we can get out of this type of bonus? Are there ways to extract more value? Thank you for your help.

[Ominous]

IF you do not hedge your bet you will get better value.
Unless you find an off market line the hedge bet will be -EV because of the bookie juice.
However, I would prolly hedge anyway considering the risk.

Your actual value is lower than what you have computed btw, as you pay juice not only on the hedge bet but also on the Bonus bet. You will need to bet 550$(at -110) to win 500$ = 250 bonus and then you need to be slightly more than 625$ on the other side to ensure same profit

[Justin7]

If the max payout is $250 and you win half the time, the cash value is $125 for a 50/50 bet. Can you play big favorites? If you can do this on the moneyline, you can get your equity closer to $250 (e.g. a "fair" line of -1000 gets about 90% of the equity, or $225).

[xyz]

It doesn't allow moneyline plays. Unless they have alternative spreads, the odds are going to be close to 50/50.

[Ganchrow]

We'll assume no rollover on winnings.

Were you not to hedge and bet $550 at -110, your EV would be:

50%*-$550 + 50%*$750 = $100

This would be the equivalent of receiving odds of 100* $750 $550 ≈ +136.36 on a $550 bet.

If you did choose to fully hedge then to do so you'd need to wager about $680.95 on the other side of the bet at -110. This would the guarantee you a risk-free profit of $69.05.

Of course, if you could somehow bet at shorter odds then -110 then you'd be able to slightly increase your expectation.

For example, betting to win $500 at -120 off a -120/+100 line set would yield you an EV of about $104.35, which if fully hedged at +100 would yield a risk-free profit of $75.