Thanks for bringing this up, I feel like such an analysis could enable many more EAs to participate. If you take the standard deduction you basically have to ask yourself “Is a promo worth it if individually, bets won are worth my marginal tax rate % less than they actually pay out?”
For example, lets say your marginal tax rate (including state tax) is 28% and you’re considering the Wynnbet $1,000 risk free first bet promo for site credit that does not return the stake. If you make your first bet and free bet at +100 odds you have:
(.5 win probability) ($1000 profit *.72 take home) +(.5 lose probability)((-$1000 loss but unlock free bet) + (.5 free bet win probability)($1000 free bet profit *.72 take home))
=.5(720) + .5(-1000 + 360) = $40 EV (compared to the $250 EV of making these same bets if itemizing.)
This is profitable but not worth the time. However this is also not an efficient betting strategy.
Let’s say instead you make your first bet and your free bet at +300 odds. The math would look like:
(.25 win probability) ($3000 profit *.72 take home) = $540
(.75 lose probability) [(-$1000 loss but unlock free bet) + ((.25 win probability)($3000 profit on risk free bet *.72 take home) + .75 lose probability (0 because it was a free bet))] = $-352.5
Total is $540-$352.5 = $187.5 EV ( compared to the roughly $562.5 EV of making these same bets if itemizing.)
In theory this is potentially worth the time, depending on the opportunity cost of the bettor. You will have to pay taxes on aggregate profits even if you itemize so this $187.5 after tax EV return is better than it looks. Many caveats though:
Risk of after-tax loss is much higher. This matters to the extent that we care about the experience of the EAs placing these bets, and humans hate the realistic possibility of losing thousands of dollars.
Tighter margins puts more strain on our assumptions. If bets are losing to the vig by 7% on a certain book (due to an absence of beatable lines) rather than breaking even, these bets have a chance to be unprofitable and a high chance of no longer being worth the time.
The bettor needs to be very aware of the tax implications of her bet. The variance of a bet actually effects the expected value of that bet, since only profit is taxed and losses cannot be written off (basically, you’re incentivized to lose as infrequently as possible.) This works fairly well for deposit match promos that return the stake, and risk free first bets for site credit that returns the stake, as these bets can be made efficiently on short odds.
Overall, I think the risk free first bets that do not return the stake are not worth doing, and the deposit match bonuses with more than 1x rollover requirements, or that match 50% or less are not worth doing.
Risk free bets win or lose seem that give non-stake-returning site credit seem worth doing but with significantly lower EV, as do 100% 1x rollover deposit matches that give non-stake-returning site credit
100% 1x rollover deposit matches that give stake-returning site credit and risk free first bets that give stake-returning credit seem like they’re still worth doing (your hourly rate when making these bets on short odds is reduced by a bit more than your marginal tax rate. So if $300ish/hour is still worth it for you, these are probably worth doing.)
Thanks for bringing this up, I feel like such an analysis could enable many more EAs to participate. If you take the standard deduction you basically have to ask yourself “Is a promo worth it if individually, bets won are worth my marginal tax rate % less than they actually pay out?”
For example, lets say your marginal tax rate (including state tax) is 28% and you’re considering the Wynnbet $1,000 risk free first bet promo for site credit that does not return the stake. If you make your first bet and free bet at +100 odds you have:
(.5 win probability) ($1000 profit *.72 take home) +(.5 lose probability)((-$1000 loss but unlock free bet) + (.5 free bet win probability)($1000 free bet profit *.72 take home))
=.5(720) + .5(-1000 + 360) = $40 EV (compared to the $250 EV of making these same bets if itemizing.)
This is profitable but not worth the time. However this is also not an efficient betting strategy.
Let’s say instead you make your first bet and your free bet at +300 odds. The math would look like:
(.25 win probability) ($3000 profit *.72 take home) = $540
(.75 lose probability) [(-$1000 loss but unlock free bet) + ((.25 win probability)($3000 profit on risk free bet *.72 take home) + .75 lose probability (0 because it was a free bet))] = $-352.5
Total is $540-$352.5 = $187.5 EV ( compared to the roughly $562.5 EV of making these same bets if itemizing.)
In theory this is potentially worth the time, depending on the opportunity cost of the bettor. You will have to pay taxes on aggregate profits even if you itemize so this $187.5 after tax EV return is better than it looks. Many caveats though:
Risk of after-tax loss is much higher. This matters to the extent that we care about the experience of the EAs placing these bets, and humans hate the realistic possibility of losing thousands of dollars.
Tighter margins puts more strain on our assumptions. If bets are losing to the vig by 7% on a certain book (due to an absence of beatable lines) rather than breaking even, these bets have a chance to be unprofitable and a high chance of no longer being worth the time.
The bettor needs to be very aware of the tax implications of her bet. The variance of a bet actually effects the expected value of that bet, since only profit is taxed and losses cannot be written off (basically, you’re incentivized to lose as infrequently as possible.) This works fairly well for deposit match promos that return the stake, and risk free first bets for site credit that returns the stake, as these bets can be made efficiently on short odds.
Overall, I think the risk free first bets that do not return the stake are not worth doing, and the deposit match bonuses with more than 1x rollover requirements, or that match 50% or less are not worth doing.
Risk free bets win or lose seem that give non-stake-returning site credit seem worth doing but with significantly lower EV, as do 100% 1x rollover deposit matches that give non-stake-returning site credit
100% 1x rollover deposit matches that give stake-returning site credit and risk free first bets that give stake-returning credit seem like they’re still worth doing (your hourly rate when making these bets on short odds is reduced by a bit more than your marginal tax rate. So if $300ish/hour is still worth it for you, these are probably worth doing.)