Yep, that makes sense, thank you. I agree with your calculation and the positive EV result in this example, and I agree you could construct other bets with different EV / risk profiles.

As @KaseyShibayama originally noted above, this isn't risk-free, so these "risk-free bet" offers differ from the deposit bonuses OP describes, where one gets "free bet" money immediately and can keep the original deposit money to withdraw without risking any of it.

I still think OP's example here isn't quite right, because you can't easily convert the $1000 of site credit to $1000 of cash.

Edit: I see now the error in my calculation; OP's example is indeed correct. Any positive value on the site credit drives the total EV positive (assuming the original bet is 0 EV).

Thank you, those examples make it much clearer.

Perhaps I'm misunderstanding your example above or @martin_glusker's comment about the free bets. As I understand Martin's comment, you don't get your free bet stake back, so if you bet on something extremely likely you'll just get the small winnings but not the notional value of your wager. For instance, if you bet on something at -1000 with $1000 of free bet, you're likely to win, but you'd only get $100 of winnings, not $1000 of stake plus $100 of winnings.

I can see how bets could be constructed that would recover more value using martin's link, but as shown there they mostly top out around 80% of the value.

Thus in your example above

If you lose, bet the $1000 of site credit on something extremely likely, so you end up with $1000 cash.

in this case you'd end up with around $800 of cash (by careful construction of bets; much less if you just bet one something likely with low payout) in the much more likely losing case.

I can see how the offer could be used in a way that is positive EV (e.g. bet opposite sides with another free bet offer so you win on one side and get the free bet credit on the losing side), but I think the example you posed is not positive.

OP, could you elaborate on how exactly you ended up with $4400? It would be interesting to know the bets / payouts involved, as well as how much of your own money you had to temporarily deposit (you say $2000, but it seems like for each bonus in the screenshot it's necessary to deposit an amount roughly equal to the bonus amount).

Also, you say six bonuses and $5800, but I only count five and $4800 in the screenshot.

In this case BetMGM seems to be negative EV. In OP's example above, if the $1000 of site credit is only worth $800 or so, you have 1% chance of +$1000 and 99% of -$200.

Edit: bad arithmetic on my part here, it should be 1% of +$99000, for total EV +$792.