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.
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).
I think I understand your confusion @shrek. There are two stages: the initial risk-free bet and then then free bet (if necessary).
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1st bet, $1000 on +100 odds (50% implied probability)
Win the bet: Payout is $2000 ($1000 stake, $1000 winnings)
Lose the bet: Payout is $0 cash, $1000 free bet
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2nd bet (only necessary if lost 1st bet), $1000 free bet on +100 odds
Win: Payout is $1000 cash
Lose: Payout is $0
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The EV calculation is then: 0.5 x 2000 + 0.5 x ((0.5 x 1000) + (0.5 x 0)) = $1250
Thus we see that it is positive EV.
This can get much fancier, and you can optimize it for higher EV, lower risk, etc, but this shows the basic intuition.
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 thinkOP’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).