Swings in NLCASH

[TNixon]

[ QUOTE ]
You obviously have a different definition than every 2+2'er on what it means to drop x buy-ins .

[/ QUOTE ]
No, actually, you are the one using an incorrect definition here, because you keep trying to equate "a 20 buy-in drop" with "going bust when starting with 20 buyins".

Again, I think I've given you far too much credit, after swearing the last time that I would never overestimate you again.

Because I assumed that *you* knew what everybody was talking about when discussing a 20 buyin drop, and that you were just being stubborn about trying to relate risk of ruin calculations to the odds of having a 20BI drop over X hands.

I'm talking about a 20 buyin drop, which is obvious to everybody else here, except you (since you keep giving answers that have ABSOLUTELY NOTHING WHATSOEVER to do with the question), and you keep coming in with crap like this:

[ QUOTE ]
So given the numbers in my original post , your risk of busting with 23 buy-ins becomes 0.006029 or about .6029%

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As if the chance of busting with 23 buyins is in any way relevant to what's being asked whatsoever.

Once again, not a single person in this thread is asking about the chance of busting. That is a bankroll question. The odds of an X buyin drop over Y hands is a variance question. You're giving a bankroll answer to a variance question.

And the amusing part is that you don't even seem to understand the difference. You're so stuck in this "oh, that freak doesn't know what he's talking about" mindset, that you aren't even willing to explore the possibility that you might not understand what's being asked. (and clearly you don't, because the answers you're giving have nothing to do with the question at all)

I'm not trying to give you a probability lesson. I'm trying to make you see that you're being an ignorant jackass, answering a question that's not even being asked, and then acting indignant about it, like I'm the one being an idiot here.

I'm asking a question, you're giving an answer to a question that I'm not asking. Who's wasting who's time here?

The question is:

Given a specific winrate and std deviation, what are the odds of having a 20 buyin drop over X hands.

This question is exactly the same as:

Given a specific winrate at HUSNGs, what are the odds of having a 4 buyin drop over X games.

So far, you have avoided the actual question entirely, and have only said that the chance of dropping 20 buyins *has* to be lower than the risk of ruin. I have already proved, both mathematically and logically, that your statement is absolutely false, but here's yet another attempt to help you see the light.

The 20 buyin drop question over X hands is exactly the same as asking the odds of dropping 4 buyins over X games at HUSNGs. Both situations have the same variables, winrate, std deviation, buyins, and time constraints. Whatever math you use to solve for one would be appropriate to solve the other.

As a refresher, you have said that the chance of a 20 buyin drop over X hands *HAS* to be less than the total risk of ruin.

This is equivalent to saying that the chance of a 4 buyin drop over X HUSNGs *HAS* to be less than the total risk of ruin for when starting with 4 buyins.

So, what is the risk of ruin if you start with 4 buyins, and have a 60% win rate? You determined in another thread that the SD of a 60% win rate is very close to 1, so the risk of ruin is .00823, or 0.823%.

For your statement to be true, I should not be able to find any number of games where the chance of dropping 4 buyins at any point during that number of games is greater than .823%.

But you know, I just don't have to look very far at all to find a number of games where the chance of losing 4 buyins is greater than .823%.

Because the chance of losing 4 games in a row *at any point* is 2.56%, which is over 3 times the odds of your total risk of ruin.

And if X only has to be 4 to prove your statement false, then clearly you have a HUGE logic flaw somewhere. Since you don't seem to be capable of figuring it out on your own, here it is again:

The risk of ruin has absolutely zero bearing whatsoever on figuring out the odds of a 20BI drop over X hands. At least, certainly not in the way you're trying to apply it, as an upper bound to the odds of a 20BI drop.

Which would be painfully obvious to you if you had actually comprehended anything I've said up to this point (which you've made absolutely no attempt whatsoever to do, or you're completely incapable of understanding in the first place), or if you actually understood what was going on underneath the sheets in your precious formulas, or if you even recognized that you were giving an answer to a completely different question than the one being asked.

You know what? If you don't know how to answer the question being asked, that's perfectly fine. If it weren't a hard question, I would have just figured it out myself.

What's pissing me off is that not only are you not answering the question, but that you're either pretending I'm the idiot here because you don't actually know how to answer the question, and you need to save face for whatever twisted reason you might have in your thick skull, or that you really are being a complete moron in not realizing that you're not actually even attempting to answer the question being asked, and that your "answers" have no bearing whatsoever on the problem.

So which is it? Ego or ignorance? Because I've just given incontrovertible proof that your most basic statement in this thread is completely false, and that all of your RoR calculations are completely irrelevant, because your basic assumption (that the chance of having a 20BI drop over X hands has to be lower than the RoR) is quite flawed.

[Wu36]

all these numbers make my head hurt

[jay_shark]

Tnixon , please post in the probability forum .

I have no more patience with you .

[TNixon]

Already did. They can't *all* be like you over there.

Maybe you'd like to spout your "the probability can't possibly be higher than the risk of ruin" crap over there too, so somebody who you might actually think about listening to can rip it apart just as thoroughly as I have.

[MasterLJ]

jay_shark, TNixon,

You both have it wrong.

The correct definition is: Swongs, they are one thing.

[daveT]

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all these numbers make my head hurt

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If you don't pay attention to the numbers, skim a few lines, and marvel at the size of the posts, the arguments are very entertaining. Even more so because I never know who to root for.

[TNixon]

Thanks to people in the probability forum who are actually capable of understanding what is being asked, and providing answers...

According to a formula generated in this thread:

http://forumserver.twoplustwo.com/sh...age=0&vc=1

If I managed to get the formula typed in right into excel (I'm fairly confident, since my output matched his numbers for the few examples he did run, but anything's possible, and I've screwed up far simpler things than transitioning a formula into excel)...

With a winrate of 8PTBB/100, and a std dev of 50PTBB/100, the chance of having a 20 buyin downswing in 50k hands is about 4.2%. Over 100k hands, it's 8.25%. Which (assuming the math is even close) basically means that one in twelve people will have a downswing that big in their first 100K hands. So yeah, that seems fairly common-ish. Of course, 100k hands is a *lot* of hands, so this probably shouldn't be a monthly occurence, but if you play enough, you could very easily see a swing that big multiple times.

And btw, this does depend HEAVILY on your actual variance. If the std. dev is increased to 75PTBB/100, the odds shoot through the roof, with an 57.3% chance of having a 20BI downswing over just 50k hands, and a 15.6% chance over just 10k hands. 75 does seem pretty high though, just based on the very few real std. devs I have heard.

Oh yeah, and just because I'm a bitter bastard, I'll say that I'm not at all surprised that these numbers are higher than the risk of ruin with 20 buyins. Which should leave jay_shark thinking something along the lines of...

"What? How is that possible? It can't be higher than the risk of ruin. I "proved" it. I am a probability god, and cannot possibly be wrong? Mortal fool, you dare try to give me lessons in probability?"

[TNixon]

[ QUOTE ]
My winrate for 31k(25 days) hands is 8.19. My S.D. is 99.62 big bets/100 hands. Usually I'm in good vs villains' hands. but lots of suck outs. I play mostly agro's(wannabee's and total fish). The biggest downswing I've had was about 9-12 buy-ins(btu there were 2-3 mistakes for stacks), also I could've had S.D. 150bb/100, if played more agro. So I feel that 20 buy-in swings is possible once a month (considering how bad I was running sometime, and it COULD'VE BEEN even worse), and 30 buy-ins downswings once in a quarter(playing 30K hands a month). But if to play agro-fish and maniacs more nitty, then it's very possible to not go trough such swings at all with WR of 8ptbb/100.

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With the statistics you gave for winrate and std dev, it would seem you are quite correct in figuring on at *least* one of these a month. Extrapolating your hand count to 40k for a month gives an 88% chance of having at least one.

Bumping the std. dev to 150 makes it a near-certainty. (99.9%)

[jay_shark]

Tnixon , I'm embarrassed for you .
Have you ever thought about getting into law ?

You may need to read Pzhon's post and RE-READ Jason1990's thread again because his "approximation" formula is a function of time t for when the downswing occurs . Jason's solution computes the probability of a downswing of size b given time t which is not necessarily 0 .

What I've learned after all this is that you're one of the biggest idiot I know .

[TNixon]

Are you a COMPLETE goddamned idiot jay_shark? Or just pretending?

Because this:

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Jason's solution computes the probability of a downswing of size b given time t which is not necessarily 0 .

[/ QUOTE ]
Is exactly what we want here, where t is equal to a number of hands (or, more specifically, 100s of hands, since winrates and std devs are measured per 100 hands).

I mimicked this section of jason's post:

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where M = E[T]. You have played 163,293 hands, so you would like to know p = P(T < 1632.93), the probability that you would have a 360BB downswing in your first 163,293 hands. Using the above estimate for this probability, here are some numbers.

m = 1.95 and s = 16 ==> p = 0.187
m = 1.95 and s = 18 ==> p = 0.418
m = 1.50 and s = 18 ==> p = 0.616

[/ QUOTE ]

Exactly, and verified that I got the formula into excel correctly by plugging those numbers in (along with 1632 as t, and 360BB as b) and getting those exact same probabilities.

The numbers I've given here were from the same damn formula, and mean the same damn thing, and you absolutely have to be a complete retard to STILL be confused about what is going on here. If you disagree with the formula's applicability for the question at hand, feel free to say so. (If you do, you'll only further prove that you have absolutely no clue about what's actually being discussed here, but please, be my guest). If you feel I've misapplied the formula, then feel free to say so as well. But you better be prepared to defend that statement with a "correct" application, and numbers different from what I just gave.

For hell's sake.

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What I've learned after all this is that you're one of the biggest idiot I know .

[/ QUOTE ]

What I have learned from this is that you are a far bigger idiot than I ever even imagined was POSSIBLE.

STFU monkey.