A question for you math geeks....

[AaronBrown]

That's why we're in poker theory. In practical poker, everyone goes broke or dies first. Which would you rather do?

[tarheeljks]

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That's why we're in poker theory. In practical poker, everyone goes broke or dies first. Which would you rather do?

[/ QUOTE ]

indeed, i kind of see his point though. examples like this are a little too contrived for my taste and amount to intellectual masturbation

[Andrew1593]

Seems like the question has been pretty adequately answered, but I thought I'd share this anyway. It's an applet for the Gambler's Ruin problem which allows you to enter in your starting bankroll, the house's bankroll, and the house's probability of winning.

Try putting in 100 for your starting bankroll, 1,000,000 for the house's bankroll, and 0.5 for the house's probability of winning. Then run a simulation of ~100,000 games. Even though I understand pretty well the math behind random walks, I still think it's interesting to see how often you end up broke in a game like this.

Gambler's Ruin Applet

[AaronBrown]

Just to be precise, the applet does not demonstrate gambler's ruin. It demonstrates the difficulty of beating a negative EV game when playing against a much larger bankroll. While that's interesting, I think most people grasp intuitively that you have the worst of it in that situation.

Gambler's ruin is the counterintuitive idea that you will go broke without bankroll management, even if you have the edge. The major casino games have house edges ranging from 0.5% to 6% (excluding things like slots and keno), with 0% and even negative edges possible. Yet if you walk into a casino with $100, the casino figures to take $40 to $60 on average, depending on the casino.

If you kept your bet the same size, you'd just lose the house percentage times the total amount you bet. But if you keep betting until you lose all your money, which is a very common strategy, raising your stakes when you win but not cutting your stakes when you lose, you might as well just hand your money over to the house at the beginning and find some better use of your time.

[jstill]

well first ur statement doesnt make sense intuitively as condition 2 is a condition by which players wont all go bust... if there was a finite amount to be won (which there is) and losing players eventually stop playing (and are replaced by a diminshing number of losing players), which seems to be the trend, winning players edges diminish and former slight winners will become slight losers and that process will extrapolate until only the very best are actual winners as everyone else plays well now, and eventually even they would bust. Fortunately there are tons of live donks, tourists, part time hobbeyist where we dont have to worry about that any time soon, and really even online games are still super viable (obviously) but again only like 10% of players if even will beat the rake in limit, NL or sngs (as many slight winners at lower levels move up til they have no edge, and most players arent playing winning poker even at the smallest stakes).

The question of the sustainability of poker is its own thread however.

as for question one, as you probably know its nearly mathematical impossible to conceive of many occurances, for example flipping heads 50 times in a row will happen 1/2^50, so basically hardly ever, but still that one time in however many...

what prevents us as poker players from reaching that almost mathematically impossible occurance are using bankroll management to assure a nearly 0% risk of ruin based on an underestimated winrate of ours and using 99%+ confidence intervals to feel pretty safe about it. Sure with this outline theres still a chance approaching infinity we could bust, but thats only if we never moved down which prolongs this process of bustoing (and ideally increases our edge/ winrate to create even less variance).

Really with good BR management assuring a nearly 0% risk of ruin and moving down after a prolonged downswing (multiple levels if neccessary) any winning poker player should be able to avoid the gamblers dilemna (cant return from zero). And most of us will play over a million hands in our carreer (or every couple of years really with multitabling, most on here probably play like 500k/yr or close), so you can basically look at many players short term ( a year or less) as the long run since they are playing a million + hands.

So there is plenty of means by which even a good player can plan to assure even if he ran as badly as anyone could ever concieve (or would even believe because it lies beyond the nth imaginable std deviation), ie being over rolled and moving down during long bad runs.

really most of the reason people bust is 1) withdrawing, if you cap your BR you're hurting your long term viability 2) moving up diminishing ones edge 3) probably the largest factor poor BR management and usually 4) a long bad run that causes declining play, but wouldnt have resulted in busto with proper BR management.