Hypothetical Gambling Situation
 

Kinda embarassed to post this up, but my eyes have been opened to a whole different side of gambling recently, so hopefully some of the guys who have been around a while will find this neat. It's a gaming theory question:

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You have a net worth of $10k, when you get to $30k, you're going to buy a car. You care just slightly about money between $10k and $30k, but you care about $30k A LOT. You also don't particularly like or dislike gambling.

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Your buddies are going to the casino and they like slots and you're hanging out with them. You sit down at a Video Poker machine near the slots so you can talk and stuff. Holy crap! You just hit a Royal Flush worth $5k. Your net worth is now $15k and you're $15k away from your goal of having the car.

Video Poker offers something called "Double Up", which is where you can choose to rewager your jackpot, at even money on whether the next card will be red or black. 1:1 odds (and a reshuffled deck) make this completely even money, and the house doesn't take a commission on the bet. You can "Double Up" as often as you please, and for as many iterations as you please. You can also "Quadruple Up" by betting on the next suit (again, 3:1 odds, this is even money).

Neither of these options risks any money other than what you just won at the machine (so you can't lose your initial $10k).

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Firstly, what should your goal be? To get to $30k. For the purposes of this question, let's assume that you don't just take your $5k over to the poker tables. Now, here's the interesting part. What should you do, and why?

a) Double up twice. ($5->$10->$20) (25% chance)

or

b) Quadruple up once. ($5->$20) (25% chance)

There's two factors that I consider worth evaluating here, but one of them is much more important than the other. I feel quite strongly that there is only one correct answer.

Edit: Try not to read the replies before you reply yourself, this is kinda a neat question. Any observations that you want to make on the situation from a gaming theory context would be neat too.

Re: Hypothetical Gambling Situation
 

I quadruple up once and take clubs....

running a simulation now to see....

WOOOO!!! 4c!! FOUR OF CLUBS! i won!

but wait... if i put this 20k on the quadruple up... i could win 90k!!!! thats enough for 3 cars!

this time i take spades, running simulation....

6c.... i lose. i knew i shoulda just stuck with my lucky suit =(

Re: Hypothetical Gambling Situation
 

This should probably (heh) like be in the probability forum, but I'm curious anyhow.

This is a BR stats type of question (risk of ruin) that I basically have no clue about. I think the ROR is greater for the 2nd option (quadruple up) is higher because the SD is bigger. We would expect to go bust 3/4 times. Now if we do the former (double double), we expect to go bust 1/2 times on the first bet. When we don't go bust, we have the same shot at going bust 1/2. Bah, see, I really have no clue actually.....

Re: Hypothetical Gambling Situation
 

If you are sure you are going to take the doubling up option twice, and not quit if you won the first time, then they are exactly the same. 1/4 of the time you will quadruple up with either option, the other 3/4 of the time you will bust out.

I'd like to hear another way of interpreting this that sticks to probability though. [img]/images/graemlins/smile.gif[/img]

Re: Hypothetical Gambling Situation
 

In both cases you have the same probability of winning the 20k total (15k more). In both situations you have no bankroll ror because this is a one-shot thing and you're not going to be doing it infinitely (or even at all with your original $10k bank that you started with, you're just out on a night with the guys trying to blow as little cash as possible and still be in the slots parlour with them, but you got [censored]-hot lucky, and it looks like you have a chance at your car, keep in mind that it would be nice, but not really a big deal, if you came home tonight with $5k extra, but that you've got a chance at going for the car, and you've decided to do it... how do you do it?).

So, the EV and ROR is the same with both options, yet there's still one correct answer.

btw, eskimo, you rock! [img]/images/graemlins/smile.gif[/img]

Re: Hypothetical Gambling Situation
 

Going for the quadruple up saves me a button press [img]/images/graemlins/cool.gif[/img]

Re: Hypothetical Gambling Situation
 

Doubling up twice would decrease your standard deviation. If you come across this situation many times. I guess I still don't prefer one to the other for that reason. I see it as you're going all the way to 30k and it's a 25% chance. I go for the quadruple up and save the suspense. I could just imagine that damn "Who wants to be a millionaire" music and those lights as I was going for the second double up. Then I pick red and it's a SPADE! Wah wah waaahh. Whammies start running around and take all my cash. I'll take the quadruple up. Much easier to deal with the loss of $5k instead of $10k since just winning $5k is not an option.

Related Interesting Problem:
Is the Monte Hall Question already posted here? The one with the three doors (2 donkeys 1 car) and you pick Door 1 hoping there's a $30k car behind it(assumption: you don't want the donkey). He shows you door #2 with a donkey behind it, he then asks do you want to switch to door #3? Well do ya?

Re: Hypothetical Gambling Situation
 

What if a DeathDonkey is behind it though? [img]/images/graemlins/smile.gif[/img]

Yeah of course you switch. Go from a 1/3 to a 50/50 shot. Or is it to a 2:1 favorite I dunno.

If you pick the car and switch you lose everytime. But you only pick the car 1/3 of the time. If you pick a donkey and switch, it will be the car. So yeah you go from a 2:1 dog to a 2:1 favorite.

Edit: DaveC, wtf is going on here. You smoking the good stuff again or is there really a correct answer here? It looks to me like no strategy even slightly dominates the other. And I've been doing game theory all damn day so I know [img]/images/graemlins/smile.gif[/img]

Re: Hypothetical Gambling Situation
 

why the hell not, lets answer this

First off, the door question, always switch. I vaguly remember the math, but I know it improves your odds.

As for the double/quadrouple, since mathmatically they are the same, I'd do what Eeegah did and save myself a button press.

Crovax

Re: Hypothetical Gambling Situation
 

You take that 5K and stick it in your f---ing pocket!