slot dollar reimbursement promo math -- help!
A casino is offering a loss reimbursement promo. If you lose $100 at slots, you are reimbursed 100 slot dollars. The promo applies to video poker games.
Say you put exactly $100 into a 9/6 JoB machine, with the intention of either losing all of it to redeem for slot dollars, or walking away when you hit a certain amount. Some time later, you have $X in the machine. What is the expected value of continuing to play $X rather than walking away? (For the sufficiently masochistic, what's the certainty equivalent?)
I do believe the information in the above paragraph isn't sufficient. I think the bet size is needed. I also think the exact probabilities and payouts of all the hands are needed; or, at least, the probability of a loss. Thankfully all that information is easily obtainable.
Things that are obvious to me:
When $X < $100, expected value of continuing to play is >$99.54 (the return of JoB times $100).
EV of betting $100 in one shot is at least $153.84, since you replace the 0 on a loss with $99.54 (the expected value of the slot dollars you'll get back). It's possible that it's greater than that number, since EV(playing $153.84) could be greater than $153.84.
Quote: foxfan20I can't figure out the math on this for the life of me.
A casino is offering a loss reimbursement promo. If you lose $100 at slots, you are reimbursed 100 slot dollars. The promo applies to video poker games.
Say you put exactly $100 into a 9/6 JoB machine, with the intention of either losing all of it to redeem for slot dollars, or walking away when you hit a certain amount. Some time later, you have $X in the machine. What is the expected value of continuing to play $X rather than walking away? (For the sufficiently masochistic, what's the certainty equivalent?)
I do believe the information in the above paragraph isn't sufficient. I think the bet size is needed. I also think the exact probabilities and payouts of all the hands are needed; or, at least, the probability of a loss. Thankfully all that information is easily obtainable.
Things that are obvious to me:
When $X < $100, expected value of continuing to play is >$99.54 (the return of JoB times $100).
EV of betting $100 in one shot is at least $153.84, since you replace the 0 on a loss with $99.54 (the expected value of the slot dollars you'll get back). It's possible that it's greater than that number, since EV(playing $153.84) could be greater than $153.84.
I'll help you out, and this is not the type of promo that you need to delve into very far to see if it has value or not.
First off, game EV is meaningless for what you're doing. Whether it's 99.54% or 102.68% is irrelevant. For the amount of time you're playing yes, find the best paytable and least volatile game if you really intend to take a profit with you. But rationalizing it by applying long-term theory to such a short-term reality is of no value whatsoever.
The only way to play this is to play until and if you lose $100. You never know--you may stay ahead the entire time. But if you do lose $100 AND NO MORE PLEASE, then go get your $100 in freeplay, play it thru once (which will be required) and leave the place with whatever that affords you.
Keep in mind, these are sucker promotions for most people. The typical player will, regardless if a royal or other big winner is hit, continue playing until they lose at least a hundred dollars, then go to the slot club with a great big smile on their faces as if they knew they were going to make a comeback with the free slot play.
Play wisely.
That is possible. And I surmise that at some value greater than $100, I should stop, because the value of attempting to play it further is not as great as the value of keeping it. I'm trying to determine that value.
Obviously you stop playing at 0, since you aren't reimbursed for anything beyond that.
Let say another casino, the $100 credit is paid after losing $100.01, one cent more. This is also +EV.
Let say another casino, the $100 credit is paid after losing $100.02, another cent more. This is also +EV.
Let say there is a million casino more, each require you to lose 1 cent more than previous.
Obvisouly there will be a point where the game becomes negative EV. That would be same as you walk away amount from your current game.
You can work out when the game becomes negative EV mathmatically. I cannot do that with confidence.
However it is trivial to write a computer simulator to play VP with fix basic strategy and just change the walk away amount; to see which walk away amount is best.
However the above ignores risk. Let say we work out the break even amount is $300. Profit at $299 is 1 cent. Would you risk lost $299 to gain a profit of 1 cent?
I won't. I suspect bill gate would, if the bet doesn't waste any of his time/effort.
Note the chance of losing $299 is not 50%.
If you win another dollar, you reach $300, you walk away. So maybe 99% chance of walking away after wining 1 dollar. 1% chance of losing $299 and get the $100 credit.
