100 bets in one day - kelly adjustment?

[tomcowley]

Wow. I take the simple step of not considering 0-100 outcome, which can happen exactly one way, which has 3.75E-32 probability, and you extend that reasoning to exclude 2^100-1 other outcomes? Look, there will be an outcome sequence, that is known. What we also know is that the sequence which generates 0-100 will not occur in this example. Much like winning at lotto. There will be a winner, picking the person ex ante is an entirely different story. Another fallacy you are making is that ALL outcomes will occur. This is complete nonsense.

Every ordered outcome can happen exactly one way. They're all similarly likely, and if the bets were flips at +odds instead if 51.5/48.5 at even, they would all be equally likely. So yes, I am extending your "logic" to say that if I can ignore one ~E-30 outcome, I can ignore any ~E-30 outcome. How can you argue? They're equally likely, and I can ignore one, but not the other? Yeah, that makes sense.

This is not how margin investing works, but even if it did your argument that it applies here reduces the case to consider risk of ruin for a kelly bettor. If you adhere as closely as possible to a theoretical kelly bankroll, then you will have mortgaged everything you own, borrowed against all of your future income, etc. What happens then if your "fantasy" outcome of 0-100 occurs and you have $0.10 left? Does it not stand to reason that YOU would claim bankruptcy, and stiff your lenders, and start over? Of course you would, just like you claim above. So in effect the results are the same if you consider 0-100 outcome or don't. Since it does not serve in one's best interest to consider 0-100 (as it reduces one's expected growth), one should ignore it, with the added comfort that it it WON'T HAPPEN.

No, I would consider it, and every other outcome, and discount the negative aspects of the outcome if they're covered by effective bankruptcy. If I could "declare bankruptcy" and effectively only had to pay out at worst, say, a 20-80 result, then of course I would overbet my nominal roll. If me, my friends, and my family would be getting buttraped and tortured every day for the rest of our lives if I didn't pay on time, then I'd be.. a bit more circumspect. I already said this- what's your point?

Again, either you consider 0-100 as a potential outcome, with 3.75E-32 probability of its occurence, or you don't. It is as simple as that. And it is completely logical to deduce that it WON'T HAPPEN.

The most likely configuration in your example is 1.5E-29. That's SO much more likely. I think I'll just ignore all of those super-rare outcomes. Oh, wait, something has to happen, but I ignored it because it was so rare.

[BigCap]

Every ordered outcome can happen exactly one way. They're all similarly likely, and if the bets were flips at +odds instead if 51.5/48.5 at even, they would all be equally likely. So yes, I am extending your "logic" to say that if I can ignore one ~E-30 outcome, I can ignore any ~E-30 outcome. How can you argue? They're equally likely, and I can ignore one, but not the other? Yeah, that makes sense.

Sure, using the same logic you can exclude one outcome sequence with 3.75E-32 probability from your array of potential outcomes and build an expected growth model. But what purpose would that serve? Would it improve your expected growth? There is exactly one outcome that, by not considering, maximizes expected growth, and that is 0-100.

No, I would consider it, and every other outcome, and discount the negative aspects of the outcome if they're covered by effective bankruptcy. If I could "declare bankruptcy" and effectively only had to pay out at worst, say, a 20-80 result, then of course I would overbet my nominal roll. If me, my friends, and my family would be getting buttraped and tortured every day for the rest of our lives if I didn't pay on time, then I'd be.. a bit more circumspect. I already said this- what's your point?

You brought up the specter of bankruptcy as though it applies only to one who does not follow the theoretical kelly growth model, but in fact would apply to anyone in this situation (i.e. you only got $0.10). Another example: say you lose 500 consecutive bets, and you got $0.01 to your name. I know you are stickler for considering all possible outcomes, so what to do in this case? Do you have a few $ saved up somewhere (which means that you were not following theory) and get back in action, or do you walk around with one less kidney? Or do you claim BK?

The most likely configuration in your example is 1.5E-29. That's SO much more likely. I think I'll just ignore all of those super-rare outcomes. Oh, wait, something has to happen, but I ignored it because it was so rare.

Again, what purpose does it serve ignoring events that won't happen if you cannot benefit by it? If I was told that I could earn $1 billion in a day, but to do so I would be required to risk my entire bankroll of $100,000 with a 3.75E-32 chance, would I do this? OF COURSE I WOULD, AND YOU WOULD TOO. Come on, let's get real. I don't want this to get into a silly battle of some slippery slope argument that since I ignored 3.75E-32 then I must exclude ALL outcomes. I'm sure you can see the folly in that.

Before this degenerates further, you are on record that YOU would consider the 0-100 outcome when building your expected growth model of 2.51%. I do not, and I earn 2.55%. And I will never go 0-100. Enough said.

[tomcowley]

Sure, using the same logic you can exclude one outcome sequence with 3.75E-32 probability from your array of potential outcomes and build an expected growth model. But what purpose would that serve? Would it improve your expected growth? There is exactly one outcome that, by not considering, maximizes expected growth, and that is 0-100.

It serves no purpose because it's complete nonsense to ignore any possible outcome, or to preferentially ignore one of two equally likely outcomes.

You brought up the specter of bankruptcy as though it applies only to one who does not follow the theoretical kelly growth model, but in fact would apply to anyone in this situation (i.e. you only got $0.10). Another example: say you lose 500 consecutive bets, and you got $0.01 to your name. I know you are stickler for considering all possible outcomes, so what to do in this case? Do you have a few $ saved up somewhere (which means that you were not following theory) and get back in action, or do you walk around with one less kidney? Or do you claim BK?

I never claimed that. The concept of your Kelly bankroll (including present value of future potential earnings) being .01 is pretty hard to translate to the real world. If you could declare bankruptcy and stiff, you would have done it long before this point. (Or if you haven't, declare now and reload your roll with future earnings). If you can't, then what can you do? Your future earnings for the rest of your life are .01 present value above the present value of your debts. Enjoy.

Again, what purpose does it serve ignoring events that won't happen if you cannot benefit by it? If I was told that I could earn $1 billion in a day, but to do so I would be required to risk my entire bankroll of $100,000 with a 3.75E-32 chance, would I do this? OF COURSE I WOULD, AND YOU WOULD TOO. Come on, let's get real. I don't want this to get into a silly battle of some slippery slope argument that since I ignored 3.75E-32 then I must exclude ALL outcomes. I'm sure you can see the folly in that.

Of course- because if I punted my entire current net worth, I could get a job, a poker stake, or whatever, and come back. The real question is that if I imagined the absolute worst case scenario (whatever infinitely negative utility corresponds to), then the answer is no. The problem is coming up with a real-world scenario that's bad enough- if there's a high enough lower bound on negative utility (akin to a form of bankruptcy), then "going all-in" isn't really going all-in, and losing isn't infinitely bad, in which case it's trivially correct in some scenarios. It's not because the case can't happen- it's because the real-world consequences of that case wouldn't be as bad as theory.

Before this degenerates further, you are on record that YOU would consider the 0-100 outcome when building your expected growth model of 2.51%. I do not, and I earn 2.55%. And I will never go 0-100. Enough said.

Of course I consider it, and of course it would happen if enough people took the opportunity enough times. Somebody wins the lotto, after all. I would weigh the consequences of stiffing if I ran badly enough, and depending on what I came up with, overbet by some amount- and know full well that they could come true, not live in a fantasyland where they never could (until they do).

[BigCap]

It serves no purpose because it's complete nonsense to ignore any possible outcome, or to preferentially ignore one of two equally likely outcomes.

"Nonsense" to consider an event with 3.75E-32 probability? How old do you expect to live? Really, you need to get serious here. It serves a distinct purpose of INCREASING your expected growth. If it won't happen, why do you need to worry about it?

I never claimed that. The concept of your Kelly bankroll (including present value of future potential earnings) being .01 is pretty hard to translate to the real world. If you could declare bankruptcy and stiff, you would have done it long before this point. (Or if you haven't, declare now and reload your roll with future earnings). If you can't, then what can you do? Your future earnings for the rest of your life are .01 present value above the present value of your debts. Enjoy.

That would translate in "real world' to some outcome that would not need to be considered either, e.g. 3.75E-32. The point is "out of this world" events serve no useful purpose in the expected growth calculation, because they simply won't happen, just as you do not need to consider the fact that you are always at risk of ruin because you could theoretically lose 500 consecutive bets.

Of course- because if I punted my entire current net worth, I could get a job, a poker stake, or whatever, and come back. The real question is that if I imagined the absolute worst case scenario (whatever infinitely negative utility corresponds to), then the answer is no. The problem is coming up with a real-world scenario that's bad enough- if there's a high enough lower bound on negative utility (akin to a form of bankruptcy), then "going all-in" isn't really going all-in, and losing isn't infinitely bad, in which case it's trivially correct in some scenarios. It's not because the case can't happen- it's because the real-world consequences of that case wouldn't be as bad as theory.

Getting struck by a comet going to your mailbox to pick up your withdrawal check is something I'm certain you don't worry about, but it is orders of magnitude more likely than 3.75E-32? Why is that? I cannot imagine a scenario that would justify you turning down $1 billion given an event with probability 3.75E-32. It simply won't happen, and you know that. And you would take this offer in a heartbeat, even if all of your bankroll was locked in with future earnings, your property, etc. And your argument that going "all in" is not really "going all in" only supports my argument further, in that following a theoretical kelly model ASSUMES YOU ARE ALL IN, but in reality one is not. Funny, how you describe a 3.75E-32 event as "punting", when in fact it is more of sure thing than any human could possibly imagine.

Of course I consider it, and of course it would happen if enough people took the opportunity enough times. Somebody wins the lotto, after all. I would weigh the consequences of stiffing if I ran badly enough, and depending on what I came up with, overbet by some amount- and know full well that they could come true, not live in a fantasyland where they never could (until they do).

And that is the basic point: given this scenario it WILL NOT HAPPEN. Your lotto example is quite weak; an equivalent probability would require you to identify ex ante somebody who would win 4 successive lottos. That indeed will never happen.

[BigCap]

I can see it now:

Investor: Ok, I mortgaged everything, borrowed against all of my future income, put a deed on my kidney, and I got $100,000.00.

Billionaire: Very good, so just hand over that $100,000.00 and tomorrow morning you will get the wire for $1 billion deposited to your account. Only if the moon collides with the earth and venus do you lose out.

Investor: Well, you see, I follow the kelly theoretical growth model, and if I invest all $100,000.00 of my money, I will be ruined. So how about $99,999.99?

Billionaire: Sorry, $100,000.00 or nothing.

Investor: Wow, that's too bad, I just can't. I could have been billionaire if he would have let me save $0.01. I'll watch the news tonight to see if I made the correct decision.

[tomcowley]

"Nonsense" to consider an event with 3.75E-32 probability? How old do you expect to live? Really, you need to get serious here. It serves a distinct purpose of INCREASING your expected growth. If it won't happen, why do you need to worry about it?

Every outcome is a ~E-30 result.

That would translate in "real world' to some outcome that would not need to be considered either, e.g. 3.75E-32. The point is "out of this world" events serve no useful purpose in the expected growth calculation, because they simply won't happen, just as you do not need to consider the fact that you are always at risk of ruin because you could theoretically lose 500 consecutive bets.

Every outcome is a ~E-30 result.

Getting struck by a comet going to your mailbox to pick up your withdrawal check is something I'm certain you don't worry about, but it is orders of magnitude more likely than 3.75E-32? Why is that? I cannot imagine a scenario that would justify you turning down $1 billion given an event with probability 3.75E-32. It simply won't happen, and you know that. And you would take this offer in a heartbeat, even if all of your bankroll was locked in with future earnings, your property, etc. And your argument that going "all in" is not really "going all in" only supports my argument further, in that following a theoretical kelly model ASSUMES YOU ARE ALL IN, but in reality one is not. Funny, how you describe a 3.75E-32 event as "punting", when in fact it is more of sure thing than any human could possibly imagine.

Getting struck by a comet is irrelevant to a wager. Also, every result is an ~E-30 result.

And that is the basic point: given this scenario it WILL NOT HAPPEN. Your lotto example is quite weak; an equivalent probability would require you to identify ex ante somebody who would win 4 successive lottos. That indeed will never happen.

That sequence of 4 lotto winners was a ~E-30 result.

Repeat after me. They're all ~E-30 results.

[tomcowley]

I'll watch the news tonight to see if I made the correct decision.

Oh, the irony. If the bet wins, the odds were good.

[BigCap]

Every outcome is a ~E-30 result.

Which adds what to your point, exactly? I already told you to go ahead and exclude any potential outcome that won't happen, so go ahead and do it. Only the 0-100 outcome INCREASES your expected growth, while excluding any of the others does not. So guess what outcome I won't consider?

Every outcome is a ~E-30 result.

Again, 0-100 won't happen and you know it. Just accept it and move on.

Getting struck by a comet is irrelevant to a wager. Also, every result is an ~E-30 result.

Not to your bankroll, it isn't. And what about losing 500 consecutive bets, or all of the books going south, or Obama instituting an executive order today shutting down all withdrawals? Did you do the math for that? You are in a constant state of unavoidable risk of ruin, but you of course would say those are "different". You are completely missing the point if you can't understand this.

That sequence of 4 lotto winners was a ~E-30 result.

No, it was an E-8 result, and you did not identify the person ex ante, so your example was useless.

Repeat after me. They're all ~E-30 results.

3.75E-32 will not happen in this example. Once you admit to this simple fact, all of the rest falls into place. If you deny this fact, then you have failed. Simple.

[BigCap]

Oh, the irony. If the bet wins, the odds were good.

Complete failure. Actually your comment bolsters my point, in that the investor who failed to make the correct move here was indeed "results oriented".

Of course you would not agree with the investor's decision to skip earning $1billion, would you?

[BigCap]

This really boils down to accepting the fact that 3.75E-32 event will not occur in this example. If you don't accept this fact, then you have no correct course in maximizing growth for this scenario. And I have already proven that even if you did accept this as a potential outcome, it holds no advantage over not considering it, as the consequences are equal assuming worst case (which won't happen anyways), and never better than rejecting the potential outcome otherwise.

Even if one follows the Kelly theoretical growth model to size wagers, they are always in a state of risk of ruin, whether they accept that fact or not.

[tomcowley]

LOL. Obviously a ~E-30 result will occur in this example. You just don't know which one.

I'm going to hold my own Lotto.. and since I know the odds of any 4 particular consecutive winners is E-30, I'll just ignore one configuration. And I'll ignore that other configuration. And that other one. Eventually I'll ignore every outcome where I ever have to pay out, since it's impossible for any of those E-30 events to ever happen (it just boils down to accepting the fact that a E-30 event won't occur in this example, after all), so I get to keep all the money, which is AWESOME for my expected growth. You with me?

[maxdalury]

the october 1987 stock market crash where the s&p fell over 20% in one day was estimated to have been E-160 likely to happen. And that happened in our likelihoods and it was many many order of magnitudes more unlikely then your scenario. Even you believe in 'fat tails' that was certainly more unlikely than your example.

[BigCap]

Going 0-100, which is 3.75E-32, will not occur in this example. It can be ruled out. Also, it serves the bettor who rules it out because that bettor increases their expected growth in this example. That same person can safely rule out ANY specific outcome that also would be 3.75E-32 probability, and they would be correct in doing so. However, ruling out any other sequence does not serve in the best interest of the bettor, because no other sequence can increase expected growth than ruling out 0-100.

Nobody will ever identify ex ante the winner of 4 successive powerball lottos. That is the scale we are discussing here. Any statements contrary to that are plainly false.

[BigCap]

the october 1987 stock market crash where the s&p fell over 20% in one day was estimated to have been E-160 likely to happen. And that happened in our likelihoods and it was many many order of magnitudes more unlikely then your scenario. Even you believe in 'fat tails' that was certainly more unlikely than your example.

Whoever told you this, I would scratch from your "get reliable information from" list. Simple analysis of stock market returns should allow you to easily refute E-160 claim.

[maxdalury]

a simple analysis of the stock market would tell you that it was over 25 standard deviations from normal returns. mark rubinstein, a man much smarter than yourself who has actually done the research has shown that it was 27 standard deviations away from mean hence E-160.

[BigCap]

a simple analysis of the stock market would tell you that it was over 25 standard deviations from normal returns. mark rubinstein, a man much smarter than yourself who has actually done the research has shown that it was 27 standard deviations away from mean hence E-160.

So how does one explain that (a) this was not even the biggest single day % drop in the 20th century, and (b) several other times single day % drops over 8% have occurred?

Someone failed to get adequate historical data, it appears.