Is There a Sweet Spot for Bet Size for Online Promotion

[Midwest Player]

Assume an online casino is offering a $20 deposit bonus with $1,000 play requirement. This would be a positive value promotion assuming a house edge of a half a percent. You should make $15 on it.

Now I'm wondering if there is a sweet spot for bet size for playing it. You could play it in one hand at a $1,000 a hand and would lose $1,000 over half the time or grind it out at $1 a hand over several hours. Is there a sweet spot somewhere in between which balances time and risk so you will most likely win?

[DSchles]

Without doing the math, it seems quite obvious to me that, despite the fact that, no matter how you bet, your e.v. is identical, the greatest probability for being ahead when you've finally bet the $1,000 is by betting the smallest permissible amount on each hand. But that takes the longest amount of time.

In the end, it comes down to how much you value your time. To me, betting $1 a hand, 1,000 times, in order to win $15, would be an insane waste of my time. So, the more you bet per hand, the more valuable your time becomes, but the variance of outcomes obviously becomes much greater. No one can tell you how to balance that tradeoff.

Don

[Mr. Ed]

Hmm. I think it’s not so much how valuable your time is, but how comfortable you are losing $1000. Personally, I’m not comfortable with a 50% chance of losing $1000, so I would not make the $1000 bet, with a 50% chance of losing it all.

However, making ten $100 bets with a roughly 0.5^10=0.1% chance of losing it all, that would be my personal comfort zone.

Personally, I am more about finding ways to “beat the system on their own terms” than I am about the time value of money. I guess that’s why I have not been backed off yet. I am happy taking nickels from the casino.

[DSchles]

However, making ten $100 bets with a roughly 0.5^10=0.1% chance of losing it all, that would be my personal comfort zone.

It's not always an all-or-nothing proposition. Would you be comfortable losing nine of the 10 hands for an $800 loss? Eight of the 10, for -$600?

Don

[Archvaldor]

Assume an online casino is offering a $20 deposit bonus with $1,000 play requirement. This would be a positive value promotion assuming a house edge of a half a percent. You should make $15 on it.

Now I'm wondering if there is a sweet spot for bet size for playing it. You could play it in one hand at a $1,000 a hand and would lose $1,000 over half the time or grind it out at $1 a hand over several hours. Is there a sweet spot somewhere in between which balances time and risk so you will most likely win?

You say "deposit bonus". A deposit bonus is by definition given upfront for a minimum deposit. You haven't said what the minimum deposit is.

This changes the optimal strategy quite a bit. Please clarify.

Generally speaking the more aggressively you play the higher the expectation from a deposit bonus is. However you wouldn't bet $1000 because normally if you lose your bonus and deposit there is no reason to continue playing. So if the deposit was $20 and the bonus $20 and you lose $40 you have lost the bonus so quit.

Generally speaking the optimal strategy with this type of bonus hustling is bet as much as your bankroll can stand while leaving enough money for doubles and splits.