Very interesting question!
Does anyone know of an easy was to calculate the true EV of a bonus considering the house edge and playthrough requirement?
For example, lets say we receive a BTC1 bonus to play a game with a 10% HE and 10x playthrough.
We can expect to lose BTC1 for every BTC10 wagered at this game, BTC10 is the amount we have to wager, but that doesn't make the EV of our bonus = 0
I
think it's 0.563 bitcoin.
Am I doing it wrong?
If I'm doing it right, it there an easy way to calculate Bonus Value with 100x or more?
(Variance and deposit/no deposit are not relevant.)
Yeah, I think you're doing it wrong. But it's late, I've had a few beers and I'm sleepy so I very well might be wrong. I'll try provide some working tomorrow if you're interested.
For what it's worth I get:
1x roll over: 0.90 BTC
10x roll over: 0.563 BTC
100x roll over: 0.315 BTC
1000x roll over: 0.196 BTC
Which seems strangely high. But I guess the important thing to note, is a player can never lose money, as your worst case is losing the free 1 BTC bonus. So the EV is the average of a bunch of weighted >= 0 numbers.
In a real casino, it might be a 100% deposit bonus ... which means although you get some "free" money you have to gamble like crazy to the point you risk your actual deposit (and can have a loss), to the point that the "free" bonus money might cause you more harm than good!