[Izverg04]

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now how do you incorporate the house edge into this argument? ... Would you first calculate the simple expected end amount of playing out the wagering requirement as

E_end_amount = (B+D) - WR*HA

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I think a better strategy is to aim for T+WR'*HA, where WR' is the remaining wagering requirement after betting. Either bet everything, or bet just what you need to reach T+WR'*HA. Once you reach T+WR'*HA, grind out the wagering requirement with tiny bets.


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The wagering requirement and the +EV gained by busting early should be taken into account the same way whether the bonus is sticky or cashable.

When you bust, you don't have to complete the wagering requirements saving yourself WR'*HA. So you deal with this gain exactly the same way as you would with B'=WR'*HA sticky bonus. In the context of sticky bonuses, you recalculate the target as

T=(B+B') + sqrt(BR*(B+B'))/2.

In practice, sticky bonuses are usually offered by Playtech-powered casinos, which offer zero-HA games, so this is not a concern.

In the context of zero-HA games, pzhon's advice to go immediately for the target and then grind it out with tiny bets is not optimal, since all you are concerned with now is speed. It's much faster on average to reach the target with $20 bets than making a couple of $200 bets and grinding out $1 bets when you win.