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.
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