Well, that's true, but it is calculated a bit differently for bonuses.
OK, so I think I understand what you are saying now. It goes like this - correct me if I'm wrong:
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I have two choices:
a) I can deposit 1 BTC, reject the bonus, play as much or as little as I like, and withdraw my whole balance.
b) I can deposit 1 BTC, accept the bonus, and have 4.01 in my balance. If I happen to wager enough to unlock the bonus I can withdraw whatever is in my balance up to 4.01 but no more. But at any time I can opt to cancel the bonus, which subtracts 3.01 from my balance and then I am free to withdraw whatever is left.
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Is that correct? Does "cancel the bonus" mean "subtract 3.01 from my balance" in this case?
If I have all this right, then the bonus does seem to be +EV compared to not accepting it. The worst that can happen is that I lose 1 BTC in both cases, but having accepted the bonus there's a chance I lose more than 1 BTC but then recover it, using the bonus money.
So what happens in this hypothetical situation:
I depost 1 BTC, you give me 3.01 extra, so I have 4.01. I wager 387 times the bonus amount, and end up with 1000 BTC in my balance. I haven't unlocked the bonus yet because I need to wager 388 times to unlock it. I cancel the bonus. You take 3.01 off my balance. I have 996.99 left. I withdraw it.
Is that allowed? If not, why not? According to my new understanding of your bonus it seems like it should be allowed.
Edit: none of the above can be right. It's easily abused. And I see in the terms:
"If you do not meet the requirements you will not be able to withdraw your winnings, but you will always be able to withdraw your own deposit amount"
and so "cancel the bonus" in this case means "if my balance is greater than 4.01, set it to 1, else subtract 3.01 from it". Is that right?
If so, then the deposit bonus *is* -EV, and should never be accepted - because it's very unlikely you will be able to make any profit at all. You have to wager a massive amount before it is possible to keep any profit you might happen to make, and even then you can only keep up to 3.01 of whatever you are lucky enough to make after wagering over 1500 BTC.
You see, the EV when you reject the bonus is close to zero (it's only around -0.0188 per BTC wagered) because wins cancel out losses. But if you accept the bonus the EV is much lower, because there's almost no possibility of winning, and a decent chance of losing.
You wrote:
Most players will withdraw their funds long before they get to this point. When the prospects are not good, withdrawal is the best option
Not a single one of these players who cancel their bonus before unlocking it are profiting from the bonus are they? They are ending up with the same or less than they deposited. That's why it's a bad deal to take the deposit bonus.
You compare it to the lottery, but that's not really valid.
In the lottery you pay $1 for a 1 in 2 million chance of winning $1 million. Crappy odds, the payout is only half of what it "should" be. The house take is 50%. You're unlikely to win, but when you do you get a good multiplier. 1 in 2 million to win, with a million times multiplier. Bad, but not horrible.
With your bonus, you say you have a 1 in 500 chance of 'winning' (ie. clearing the bonus) but when you do win, you only get a 4.1x payout. 1 in 500 chance of 4.1x is horrible odds. And so I'm back at my original position that nobody should take the deposit bonus, and that it is actually harmful to their expected value to do so.