With Fixed Bankroll, You Will Definitely Go Broke

[AcesUp46 0]

Here's something that I've thought about. I've searched this forum and 2+2 and couldn't find a precise answer to this issue. I'd appreciate your thoughts on this matter. I suspect that I have made an error in my reasoning somewhere, please point it out to me.For the purposes of this discussion, let's limit the poker game to full-ring limit holdem. However, the concepts are relevant to all forms of poker. Let us assume that there is only 1 game that we can play in and that our poker player has a positive expectation per hour. Most books/authorities recommend a bankroll of 300 Big Bets (BB) when playing limit holdem. By keeping a bankroll of 300 BB, we will be optimally balancing the following opposing 2 factors : 1) Minimize risk of ruin and 2) Playing at a large enough level to maximize our expectation per time period. Given our playing style and bankroll, there exists a risk of ruin of x%. Our playing style will affect the standard deviation of our session outcomes and if we become more LAGgy, our deviation will increase and consequently, our risk of ruin increases too. Also, if our bankroll decreases, our risk of ruin increases too. So far, all these concepts should be familiar to most FCPers. Here's what's been troubling me. Given a risk of ruin of x% over a time period, our chances of NOT going bust is trivially (100-x)% or similarly (1 - [x/100] ). Ok, now let's assume that our poker player always keeps a constant bankroll of 300 BB. If he were to play for n time periods, the chances that he will NOT go bust is (1 - [x/100] ) ^ n. As you can see, for any risk of ruin x>0, as n tends to infinity, the probability that our poker player will NOT go bust approaches ZERO, ie he will necessarily go bust.Now, let us loosen our earlier assumption that our poker player can only play in 1 game and assume that there are many different limits that our poker player can choose from, ie if he makes enough, he can move up to the next level with 300 bigger BBs or if he loses, he drops down one level with 300 smaller BBs. Let's take the case where he drops down one level with 300 smaller BBs. All this does is "reset" his risk of ruin (not precisely reset since the risk of ruin at the smaller limit will be different from that at the higher limit, but it will still be lower than just before he dropped down one level). Now he's back to the earlier predicament where if his bankroll in constant, he will eventually go bust. For the case where he does well and moves up, well, the moment he moves up one level with 300 BB, we come back to the same problem, ie fixed bankroll with a fixed risk of ruin over an infinite time period.I can't seem to see a solution to this predicament. One possible solution would be to take out less money from our bankroll and let it grow to 400 or 500 BB before we move up to the next level. But all this does is simply reducing the risk of ruin and we are still stuck with the same predicament.I strongly suspect that I am missing something in my reasoning. Any comments are appreciated.

[GrinderMJ 0]

The only thing I can see is that you have started 5 seperate threads today.

[showstopper24 0]

Yea.

[AcesUp46 0]

Mods, can you move this to Strat? Been posting too much in General that I auto-posted this here.

[Yoda 1]

Your whole theory is flawed by ^ n. Why would you be exponentially more likely to bust on each subsequent session? This should be constant, not exponential.

[Simpleton 0]

This is dumb to ^nth degree. What are we supposed to be Einsteins to understand that jibber jabber and flibber flabber.

[crimethink_ 0]

"It happens to everyone, from time to time, everyone goes bust."

[AcesUp46 0]

Your whole theory is flawed by ^ n. Why would you be exponentially more likely to bust on each subsequent session? This should be constant, not exponential.

I don't think it's wrong. You must consider the indefinite time period. Consider this analogy. If you use a condom during sex, the risk of the girl getting pregnant is about 1%, ie the probability of her NOT getting pregnant is 99%. Now, if you have sex with her 100 times, the probability of her NOT getting pregnant by now is 0.99 ^ 100 = 0.37. As you can see, the more times you have sex, with her, the more likely that she is to EVENTUALLY get pregnant.This is analagous to the bankroll issue.

[Sluggo 0]

No, there's a large chance you won't go broke.

[Yoda 1]

I don't think it's wrong. You must consider the indefinite time period. Consider this analogy. If you use a condom during sex, the risk of the girl getting pregnant is about 1%, ie the probability of her NOT getting pregnant is 99%. Now, if you have sex with her 100 times, the probability of her NOT getting pregnant by now is 0.99 ^ 100 = 0.37. As you can see, the more times you have sex, with her, the more likely that she is to EVENTUALLY get pregnant.This is analagous to the bankroll issue.

Yes, but you are flawed at basic common sense. In poker every session isn't go broke or nothing. There is that little thing called winning you should consider.

[AcesUp46 0]

Yes, but you are flawed at basic common sense. In poker every session isn't go broke or nothing. There is that little thing called winning you should consider.

It doesn't matter. Consider all poker sessions as just one super long lifetime session. EDIT : Also, consider the term "time period" as I had used in my first post as any arbitrarily chosen time frame or number of hands.Perhaps I need some clarification with regards to the concept of risk of ruin. I think I read somewhere that it refers to the probability that you will go bust before tripling your bankroll. Someone enlighten me on this as I feel this is where I may be tripping up.

[sdnuol 0]

too much math and %, # and stuff for me

[Yoda 1]

too much math and %, # and stuff for me

It's a pretty ridiculous idea regardless of math..Unless of course nobody in the history of poker has ever tripled their bankroll without going broke.

[crimethink_ 0]

It's a pretty ridiculous idea regardless of math..Unless of course nobody in the history of poker has ever tripled their bankroll without going broke.

No, actually it makes perfect sense.

[AcesUp46 0]

No, actually it makes perfect sense.

Glad to find someone who understands the situation.

[RodReynolds 87]

I didn't read your whole post, but, assuming that in any give time period you have a chance, x%, of going broke, no matter how small, and if you play an infinite number of these time periods, then of course you will go broke. But most people don't play this much poker, and have to stick to a finite number of sessions. Then the BB rule mimimizes this risk, apparently adequately enough to avoid bankruptcy for most solid players. Maybe I missed your point.

[crimethink_ 0]

Glad to find someone who understands the situation.

Being willing to move down in limits, though, will reduce your odds of going broke so much that it becomes a non-issue.

[SpiderGuard 0]

Technically your math looks fine, but there are a few problems with the assumptions of your model.The assumption that the player maintains a constant bankroll of 300BB is your flaw. You would have to have one long miserable session to lose 300BB in one sitting, but in your analysis the bankroll resets after each one. The same goes for winning. The reason people don't go broke is because they don't maintain the constant 300BB bankroll. You go down to 280 one day, up to 330 the next. Also, you never approach an infinite number of sessions. Depending on where you set the probability of going broke in that one session, it would take a ridiculous amount of sessions to even give you a 5% chance of going broke.The math is fine, but the assumptions behind the model are incredibly flawed. It's not that the other people in this thread don't get your math, it's that the math is irrelevant when you create such an unrealistic model.

[bascomeb 0]

Being willing to move down in limits, though, will reduce your odds of going broke so much that it becomes a non-issue.

bingo, topic closed

[PotDragon 0]

It's a pretty ridiculous idea regardless of math..Unless of course nobody in the history of poker has ever tripled their bankroll without going broke.

Then there's this.Since when does anyone have their whole bankroll on the table at once ? I have a bad run or play like a donk...I lose 3 to 5 BUY INS. Call it a night. Just like the condom worked. This has no effect whatsoever on my overall bankroll.Now my girl dumping me...that crushed it. and the stomach churns.

[xtxoxpxd 0]

all you proved was that risk of ruin is >0%. given infinite playing time, everyone will go broke. duh.if i have a million dollar bankroll and flip coins for 1 cent forever, i will go broke. doesn't mean its even close to likely.

[PotDragon 0]

if i have a million dollar bankroll and flip coins for 1 cent forever

Wonder if you could get a suite comped forever ?

[crimethink_ 0]

all you proved was that risk of ruin is >0%. given infinite playing time, everyone will go broke. duh.if i have a million dollar bankroll and flip coins for 1 cent forever, i will go broke. doesn't mean its even close to likely.

Yes. That.

[AcesUp46 0]

Technically your math looks fine, but there are a few problems with the assumptions of your model.The assumption that the player maintains a constant bankroll of 300BB is your flaw. You would have to have one long miserable session to lose 300BB in one sitting, but in your analysis the bankroll resets after each one.

No, it is not an unrealistic assumption. A lot of players maintain a constant bankroll. After a winning session, they will take part of the winning and move it elsewhere and add part to an increasing bankroll. And if they have a losing session, they will not replenish this bankroll.

bingo, topic closed

No, you will simply move back to the same problem but at lower limits.

[sdnuol 0]

No, it is not an unrealistic assumption. A lot of players maintain a constant bankroll. After a winning session, they will take part of the winning and move it elsewhere and add part to an increasing bankroll. And if they have a losing session, they will not replenish this bankroll.No, you will simply move back to the same problem but at lower limits.

im not disagreeing or agreeing with anything. i havent the slightest idea what my opinion is on this. havent really tried to figure one out either