You can guarantee a profit on the promotion by doing the following. I figured this out for a free $1100 bet, because it is easier to follow. To use it for a $1250 bet, simply increase the bet size of the opposite bets by 13.63%. All bets are at -110 odds. (.91 to 1.0 ROI) There are 3 ways this can play out.
Scenario #1 (W)
Scenario #2 (L, L)
Scenario #3 (L, W)
Scenario #1 (W)
Bet the $1100 bet
Bet the opposite team for $880
Win the free bet +$1000
Lose the other bet -$880
Scenario #1 (W) is complete. Your profit is $120. You won your $1100 bet, and lost an $880 bet.
Scenario #2 (Loss, Loss)
You lost the $1100 bet
Won $800 on the opposite bet. You are -$300 right now.
Use the free bet $1100
Bet the opposite team for $440
You Lose the free bet. Your total loss on the promotion is $1100
Opposite bets are +$800 and +$400= +$1200
Scenario #2 (L, L) is complete. Your profit is +$100
Scenario #3
You lost the $1100 bet
Won $800 on the opposite bet. You are -$300 right now.
Use the free bet $1100
Bet the opposite team for $440
You win the free bet. You get $1000 minus the $1100 you lost. You are -$100 on the promotion.
You lost the $440 opposite bet, but you won $800 on the first opposite bet, so $800-$440= $360 profit from your opposite bets.
Scenario #3 (L, W) is complete. Your profit of $260 $360 minus $100= $260
I'm pretty sure this covers it. If I'm wrong, I'm sure someone will let me know. As a 38 year resident of Las Vegas, NV, I have never received free bet promotions. They know if you live here, you are already addicted to sports betting, so they don't offer big promotions.