Probability Question

Let's say you're playing blackjack against the house. Each game you play, you have a 51% chance of winning. The house has a 49% chance of winning. Each game you must bet $10 (you lose $10 every time you lose a game and win $10 every time you win a game) and your starting bankroll is $10,000. The house has infinite money, and you must keep playing forever unless you bust. That is, you can't ever quit the game unless you go busto.

What's the probability that you will go busto playing this game?

miniscule

100%?

^brain fart of an answer by the way... i need to think more

cool question

100% ez

Obviously 100%. A better question might be, how many hands maximize your EV in such a case? Obviously playing just 1 hand is +EV, and 2 hands even more so, but playing unlimited hands will make you go bust. I don't know what the answer is here.

100% came to mind first, but i'm not sure about it.

You need to lose 100 times more than you win to go broke. It's extremely unlikely this will happen in the first 100 or 200 times. However, when you play an infinite amount of times, you will have won 51% as the infinity cancels out all variance. But in between those 2 extremes there may be a moment where it does happen. Im not good enough at limit poker math...

playing infinite hands u will always go busto, but also to maximize your ev you would also never stop playing

the answer has to be never or always

that said im leaning more towards never

you would have to run really really bad to go busto but its still possible fuck

i think it has to be 100% doesn't it? that seems so fucking wrong though, awesome question

isn't it effectively 0? you have a slightly better than coinflip chance of winning, and you need to lose 1000 times in a row to go bust. On a whim I'd say (0.49)^1000? I'm not sure if thats right or not..

make that 1-(0.49^1000)

the beauty of infinity is that you will at some point have a run bad enough to go busto, no matter if you start with 100000000000000000000000000000 x the bet

i'd say an incredibly small nonzero number. your expectation is always positive, so the longer you play the further you will be away from busto, requiring that much worse of a downswing to busto you. id say like 1/10^500 or something.

its a mindfuck because all things either can or cannot happen and although in the course of infinity hands we are maximizing our value we are at the same time putting ourselves at the definite risk that we will go busto because it has to happen over the course of infinity just because it can.

sorta like the monkeys with a typewriter writing shakespeare theory

If you run it out long enough you will always go bust.

so this means its theoretically impossible to win at poker, investing, or anything really amirite

Based on the info you provided, you would never go busto.

On September 10 2008 18:26 CrownRoyal wrote: so this means its theoretically impossible to win at poker, investing, or anything really amirite

sick point