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# Casino Bonus calculation

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Trying to calculate the average value of a casino bonus.

Bonus is 100 and you have to turn over 3600 (100x36) for the bonus to become real money.

The average return for each bet is 97% (3% margin for the casino).

Lets say I want to calculate the value for 5000 bonuses (100*5000), is my formula correct? 500000*(0.97^36)

Some players will lose all money before being able to turn over the amount 36 times and some will win more whilst doing so, does this change the formula? In the end the average margin is 3%.

Thanks

Nov 1, 2021

#1
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... 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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Nov 1, 2021
#2
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GA are you GingerAle?

Guest Nov 1, 2021
#3
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Thanks, I might have been unclear when I said 5000 bonuses. What I mean was I want to calculate the cost of giving out five thousand bonuses worth 100 each, i.e 500000 total with a turnover requirement of 36 times the bonus.

Does this mean the formula should be EV = 50000 - (1800000 * 0.03)?

Using the described formula would mean the EV of a 100 bonus is -3392 which doesnt make any sense, should be positive. EV = 100 - (3600*0.03)

My original formula 100*(0.97^36) gives an EV of 33.4 which seems to be in the right ballpark for a 100 bonus?

Guest Nov 2, 2021
#4
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...  I want to calculate the cost of giving out five thousand bonuses worth 100 each, i.e 500000 total with a turnover requirement of 36 times the bonus.

Well... obviously the cost (to the house) would be 500,000, if all the gamblers meet the turnover requirements.

For this case,

EV = 100 – (3600 * 0.03) = -8

This means house can expect to pay out a net (500,000 – (5000 * 8)) = 460,000, if all 5000 gamblers meet the turnover requirements.

This would be an incentive for new and long-gone gamblers to visit and return. This type of promotion would be paid for via an advertizing and promotion account. It would not be for the casino to realize a short term profit.

My original formula 100*(0.97^36) gives an EV of 33.4 which seems to be in the right ballpark for a 100 bonus?

I’m unfamiliar with this ballpark, and this is not an EV formula that I’m aware of.

Where did you find this formula?

This formula is depicting a return payout pattern of (0.97) on the first wager, and (0.97 * 0.97 = 0.9409) on the second wager, and (0.97 * 0.97 *.097 = 0.912673) on the third wager..., etc... etc..., thirty-six times in sequence.   This could happen but it’s very unlikely. It certainly isn’t an expectation for the above parameters.  A pay out like this would be a major disincentive to gamblers –exactly the opposite of what casinos want.

GA

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GingerAle  Nov 3, 2021