Many people have asked about a sticky bonus formula. This is not as simple as a basic strategy expected value. There have been many opinions on the board.

I'd like to see what other people see as the expected value of the new rules at Golden Palace.

Golden Palace Rules:

Sticky 300% bonus on first $100.

Wager Requirement are 20x's bonus and deposit ($8000 on maximum bonus plus deposit)

Hypothetical Example:

Let's say GP offered a bet on a coin flip with no house edge. Heads you win, tails you lose.  You bet ALL of it on heads, $100 plus $300 bonus for a total of $400.

If you win:

you'll have $800 in your account.  Now you'll have to play that money 19x's more.  If you play blackjack, you'll lose an average of (19 x $400 x 0.52% house edge)= $39.52.

$800 - $39.52 = $760.48.

Subtract the sticky bonus money, and your deposit to calculate your profits:

$760.48- $300 - $100= $360.48

Your average profits is $360.48

If you Lose:

You lose all $100 of your original deposit.

Calculated overall expected value:

Half the time you lose $100, half the time you win $360.48

$360.48-$100= $260.48.

$260.48/ 2 = $130.24

My calculation for you expected value in this hypothetical situation is a profit of $130.24. Not bad for a deposit of $100!

Of course, GP doesn't offer you a coin flip wager on the first wager.  That's why the calculation gets more confusing. Plus, some games have a table limit lower than $400.

Comments Welcome:

All you math geeks out there, I'd love to see a formula for the expected value of a sticky bonus.

Mark

As I have stated elsewhere, the EV of a sticky is based on your target. I believe it's impossible to get an exact calculation without doing simulations, but in general, the higher you play the sticky, the higher the EV.

Using your coin toss situation, if you went to 3x, your EV would be 400*3=1200

1200-340 (bonus+expected loss)= 860

860 * 1/3 (chance of tripling up)= 286.6

286.6-100 (original deposit) = 186.6= EV.

The problem with these calculations is, of course, they do not account for house advantage. And there is no way to calculate the effect of house advantage without a simulation, because it may take you 25 hands to quadruple, or it may take you 100. (unless there's some way to do it with a frequency distribution, which I don't think there is)

The absolute best way to play a sticky is probably to play it up to around 10-12x deposit+bonus. But, this could feasibly result in bankroll swings of 5k or so, most bankrolls would do well to triple or quadruple. Also, you may want to consider quitting once you have played out the WR if you are up by a good deal.

One more thing: do not bet it all! Unless you are playing baccarat, this raises the house advantage to over 2% (no doubles or splits). You should bet half, or bet 1/3 of your buy in each time.

You are correct that we need sims, but what you are pointing to is the effect of compounding the house advantage over many hands. For most people, I think the best strategy is to quit when you're somewhat ahead (2-3x* deposit+bonus) if you have finished the WR. On the other hand, if you bankroll can handle it, it is still correct to milk those sticky chips for all they're worth, and keep going.

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