... is my formula correct?
No. It’s not.
You are describing what appears to be a “Cashable Bonus”
The formula for this is...
EV = Bonus – (Wagering Requirement * House Edge)
Your example above (appears to be) ...
5000 bonus, 500,000 Wagering Requirement, 3% house edge.
If so, then ...
\(EV = 5000 – (500000 * 0.03) = -10000\)
The expected value is a loss of 10,000 (dollars, pounds, drachmas). The loss is twice the bonus ... A fool’s gambit for sure.
\(EV = 0 \text{ at } 33 \dfrac{1}{3} \;{ turnovers}\) .
Note: This does not factor in bankruptcy (busting).
Bankruptcy probability is based on the game probabilities, bank roll, and the minimum wager (bet). However, you still get the bonus if you bankrupt as long as it happens on or after the minimum number of turnovers.
GA
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