Oh, good catch, I will edit that. What is the EV from those offers, then? It seems to still be nearly +$1000 and nearly risk-free with the following approach: bet $1000 on something very unlikely (EV of the payout will be $1000, but as something like a 1% chance of $100000). If you lose, bet the $1000 of site credit on something extremely likely, so you end up with $1000 cash. Then withdraw that.
For BetMGM, repeat the same approach but do 5x very safe bets of $200 with the site credits.
That still works for $1000 expected profit, right?
One thing to note is that some books have different definitions of āfree betsā or āsite credit.ā If you place a $100 free bet on a +100 market on FanDuel it pays out $200 (your $100 stake, and your $100 winnings). But on BetMGM a $100 free bet on a +100 market pays out $100, because you donāt get your free bet stake back.
This means that on sites like BetMGM or DraftKings (and I believe some others), āfree betsā or āsite creditā are not as good as cash. Theyāre value in cash typically 70-80% of the face value of the credit because you can convert them into that amount of cash. See good markets for free-bet conversion here.
In this case BetMGM seems to be negative EV. In OPās 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.
Perhaps Iām misunderstanding your example above or @martin_gluskerās comment about the free bets. As I understand Martinās comment, you donāt get your free bet stake back, so if you bet on something extremely likely youāll just get the small winnings but not the notional value of your wager. For instance, if you bet on something at ā1000 with $1000 of free bet, youāre likely to win, but youād 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 martinās 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 youād 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.
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 /ā risk profiles.
As @KaseyShibayama originally noted above, this isnāt risk-free, so these ārisk-free betā offers differ from the deposit bonuses OP describes, where one gets āfree betā 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; OPās example is indeed correct. Any positive value on the site credit drives the total EV positive (assuming the original bet is 0 EV).
Oh, good catch, I will edit that. What is the EV from those offers, then? It seems to still be nearly +$1000 and nearly risk-free with the following approach: bet $1000 on something very unlikely (EV of the payout will be $1000, but as something like a 1% chance of $100000). If you lose, bet the $1000 of site credit on something extremely likely, so you end up with $1000 cash. Then withdraw that.
For BetMGM, repeat the same approach but do 5x very safe bets of $200 with the site credits.
That still works for $1000 expected profit, right?
One thing to note is that some books have different definitions of āfree betsā or āsite credit.ā If you place a $100 free bet on a +100 market on FanDuel it pays out $200 (your $100 stake, and your $100 winnings). But on BetMGM a $100 free bet on a +100 market pays out $100, because you donāt get your free bet stake back.
This means that on sites like BetMGM or DraftKings (and I believe some others), āfree betsā or āsite creditā are not as good as cash. Theyāre value in cash typically 70-80% of the face value of the credit because you can convert them into that amount of cash. See good markets for free-bet conversion here.
In this case BetMGM seems to be negative EV. In OPās 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.
It is not negative EV. You are either misunderstanding the offer or someoneās example.
Perhaps Iām misunderstanding your example above or @martin_gluskerās comment about the free bets. As I understand Martinās comment, you donāt get your free bet stake back, so if you bet on something extremely likely youāll just get the small winnings but not the notional value of your wager. For instance, if you bet on something at ā1000 with $1000 of free bet, youāre likely to win, but youād 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 martinās link, but as shown there they mostly top out around 80% of the value.
Thus in your example above
in this case youād 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.
I think I understand your confusion @shrek. There are two stages: the initial risk-free bet and then then free bet (if necessary).
--
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
--
2nd bet (only necessary if lost 1st bet), $1000 free bet on +100 odds
Win: Payout is $1000 cash
Lose: Payout is $0
--
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 /ā risk profiles.
As @KaseyShibayama originally noted above, this isnāt risk-free, so these ārisk-free betā offers differ from the deposit bonuses OP describes, where one gets āfree betā money immediately and can keep the original deposit money to withdraw without risking any of it.
I still thinkOPās example here isnāt quite right, because you canāt easily convert the $1000 of site credit to $1000 of cash.Edit: I see now the error in my calculation; OPās example is indeed correct. Any positive value on the site credit drives the total EV positive (assuming the original bet is 0 EV).
I agree with that analysis (and someone risk-neutral should bet the 2nd game on whatever game has the lowest vig).
Worth considering taxes, though.