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How High Would You Go


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hi general forum dorks.How greedy/needy/risk adverse are you?Say:You start with $1.You roll a die.Each time you don't roll a 6, your money will be doubled.If you roll a 6, you lose all your money that you've won doubleing upAnd game is over.At any time before rolling a 6, you can take your winningshow much money would you need to have won before walking away ?$512, $4096, $65,536, $1,048,576 *********as an add on, if we assume you can come back and play the game a total of 3 times; but only if you don't bust, would that change your walk-away amount ? So, if you bust after 2nd time, you still keep the first times winnings, but you can't go a 3rd time. If you bust 1st time, well, too bad.

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For the record, being able to play the game multiple times wouldn't make a difference for me on the first play. The fact that I might have a chance to double 9 times to make $16,000 won't affect whether I attempt to double once to reach that number. Actually, I'd say if i only go once, I keep going until $32,000.If I get multiple chances, I go for $32,000 the first time, $260,000 the second time, and $1,000,000 the third time.

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makes for intereesting Expected Value Calculationintuitively it's 0 if you never stop and increasing at least early on.Is there a max ? Where?ok..back to question.Iggy, I like stoppnig earlier if I'm going 2 more times, it gives me a bit more incentive to risk more the next time.. but then again, I have to start over at $1 again...hmmm.. yeah.... Probably dumb to stop so much soonerSo, I'll revise.Go 3xstop at$ 16,384$ 65,536$ 524,288about 93% of the time though, I'd bust witrh nothing before reaching 16k... lol..man.. this is tough*************

you really are an actuary aren't you.
so, what are you saying? :club::D
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I can't imagine ever being able to stop. 5/6 chance of doubling your money is tough to say no to. I guess the difference between 1 million and 2 million wouldn't make much (relatively speaking...) of a difference in my life, so I guess I'd stop at 1 million. No I wouldn't, I'd go broke.I like this question.

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makes for intereesting Expected Value Calculationintuitively it's 0 if you never stop and increasing at least early on.Is there a max ? Where?
I can't get past the unbounded answer.2^x * (5/6)^x = (5/3) ^ xAs X goes to infinity, so does (5/3)^x.hmmm. But certainly you go broke. It's a Infinity * 0 special case...maybe I should not be combinig them into (10/6)^x.... more later.... carry on.
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it is an interesting question however because it is always +EV to do it, but we know that you'll eventually go broke.It's kinda of like playing poker in a way.If you play above your bankroll all the time with a huge edge over the competition, you will probably win each time you play. But we know that eventually you will lose your roll and go broke.I think this is where this question is heading

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this is purely a lifestyle question. i'd probably stop at 64K or 128K because those are the amounts i'd need to make a significant change in my life. if i had a consistent income of, say $60K+, i'd probably go closer to half a million before i even considered it.being able to play the game multiple times (if I lost) would significantly change things. I'd be far more willing to 'gambooool'

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Bascomeb, I wan't heading to a bankroll question; but I see the analogy.************Danny,that seems like a gambling mindset there.even if you made 60k per yr, it's not as if an additional 60k above that is meaningless.************I can't prove we will go broke eventually, but surely we do.any math wizards?LLY ?Copernicus?Rod?others?I get (5/3) ^ x as our Amount, unbounded as x goes to infinity. X being the number of rolls we takeOk, so the EV is unbounded but the likelihood of going broke is still 100% as x goes to infinity.***

$1,099,511,627,776 sounds about right.
lolyou know first thing I did was verify that it's on the sequence
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Bascomeb, I wan't heading to a bankroll question; but I see the analogy.************Danny,that seems like a gambling mindset there.even if you made 60k per yr, it's not as if an additional 60k above that is meaningless.************I can't prove we will go broke eventually, but surely we do.any math wizards?LLY ?Copernicus?Rod?others?I get (5/3) ^ x as our Amount, unbounded as x goes to infinity. X being the number of rolls we takeOk, so the EV is unbounded but the likelihood of going broke is still 100% as x goes to infinity.***lolyou know first thing I did was verify that it's on the sequence
Yeah, I don't know how to make sense of this intuitively. I think infinity is screwing with our minds again. I think what you said is right though.Our EV approaches infinity while our chances of growing broke approach 1. It is easier to understand if we just let x = 1000 or something.
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Our EV approaches infinity while our chances of growing broke approach 1. It is easier to understand if we just let x = 1000 or something.
even at x=478 (477 dbls)EV = 6,635,193,109,306,990,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 lol.that's nonsenseI"m missing sometthing
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