300BB downswings are not normal. PERIOD!

[MaxPower]

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You're more likely to have a 300 BB downswing than go broke with a 300 BB bankroll.

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Huh?

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To go broke with a 300 BB bankroll, you will almost always have to have a downswing >300 BBs. Example: If you win 20 BB when you start, you have to go on a 320 BB downswing to go broke. OTOH, you can never go broke with a downswing < 300 BBs.

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Here is another example that illustrates how likely a 300BB downswing is. Lets say I have a 5% risk of ruin with a 300BB bankroll.

Let also assume that every time I win 100BB, I cash out and round my bankroll down to 300BB.

Each time I do this I start out with a 5% risk of ruin. What happens if I do this 30 times?

The chance of my not going broke each time is .95, so the chance that I don't go broke in all 30 trials is .95 to the 30th power which equals .21.

So there is a 79% chance that I will go broke (and experience a downswing of 300BB or more) during one of the 30 trials. Wow, that is depressing.

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First, as I understand it, the ROR with a 300BB bankroll if based on the assumption of never cashing out.

That aside, even if it did not, your example is not correct. What you have done is artificially inflate the number of "trials" by indexing it to something totally unrelated to variance--in this case a cashout at 100BBs. You might as well say that the player should cash out any surplus at the end of any 24 hour period when they are over 300BB, or every time the buffet serves mussels, or based on the phase of the moon. It still doesn't affect variance or the ROR.

To make this point clear, you could just as easily say "Hey what if you cashed out 1+ BB every single time you were at 301+ BB". Then you'd have an absurdly high number of "trials" in a very short period of time, and by your logic the player would be virtually guaranteed to go broke extremely quickly. Clearly, something has gone wrong. One cannot use artificial benchmarks like a cashout to calculate one's chances of losing 300BB over a certain period of time.

The 5% rule is, imho, quite unclear as it has been stated on here and elsewhere. Everyone's risk of ruin is different. It depends on SD, true winrate (which we can never really know), and a host of other factors. I am not fully familiar with the math behind it (though now I think I will become familiar with it), but it seems the 300BB/5% rule gets tossed around here rather indiscriminately sometimes, and the math/logic in the discussions of it is often pretty sketchy.

For what it's worth, I agree with the OP. A 300 BB downswing should be an extremely rare occurance for a good player (particularly one with a low variance, low SD style), and many of the "downswings" I see posted on here are probably the result of the snowballing of bad luck, bad play, and the resultant bad image causing opponents to take more shots/play better.

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To me, my logic makes sense, but I could be calculating things wrong.

Neverless, I think you agree that when you take your winnings out of your bankroll your overal risk of ruin increases. In fact, I think if you did cash out every time you were up 1BB, it would have pretty large effect on your risk of ruin after a while. Someone better than me at math could probably compute this.

SoBeDude is disputing the fact that your risk of ruin increases when you remove your winnings from your bankroll. He should check page 51 of Gamblng Theory and Other Topics and see what Mason has to say about it.

No one is saying that 300BB downswings are not rare. They are, but even rare things are somewhat likely to happen if you play enough.