100 bets in one day - kelly adjustment?

[BigCap]

I've seen your posts on other forums and you seem like a smart guy. But no offense, Buddy, you just don't undertand some very simple math.

And anyway you haven't show sh*t. You gave a little qualitative argument with no matematcial reasoning for why you believe what you do but still obviously haven't didn't read that Ganch post linked on how to properly measure a bankroll, or his proof decimates your argument completely.

If you believe that considering an outcome that will not happen makes sense, then you can agree with Ganchrow's theoretical application. I don't, and I am right. Also, I understand all of the math necessary to determine the bet ratio for these 100 bets to maximize growth, and it is not < 1% because losing 100 of these bets will simply not happen.

So if you think ganch amd monkey are both wrong then wheres your mathematical reasoning? Or are you one of those people who "don't believe that math always tells the whole story" or some other such drivel?

The "drivel" you describe is simply stating the simple fact that losing 100 51.5% independent bets will not happen in any real world situation. As such it should not be considered in an expected growth calculation. Simple as that.

[BigCap]

Huh? That's not admitting anything. That's saying that it would be the same. And 1.01%?? BASED ON WHAT FORMULA?

Since when does < 1% equal > 1%? Have you lost it completely?

Maximize growth omitting the 100 losing event outcome and this will yield 1.0204% bet ratio. That is the formula. I think you have enough resourcefulness to generate this result using Excel or some other program.

My point is that with every amount that you risk beyond the amount that you can pay back, your win % must be that much higher just to avoid total devastation.

Not if you rule out the 100 losing event outcome.

My point is that you adjust bankroll first. THEN APPLY KELLY. If you have 100 bets they CANNOT be greater than 1%.

No, you assign an array of outcomes, and the probabilities of each like what Ganchrow did. The only problem with his model was he considered losing 100 events as a potential outcome, which it is not.

THEN WHAT ARE THE LIMITS FOR THE 1279th TIME?!?!!?

Any limit has absolutely no impact on how much I wager, only what my bankroll is. This is true because I must pay off any losses the next day with my existing bankroll. I can't believe you don't realize this by now.

[BigCap]

No kneecaps get broken in our scenario. Only this unrealistic dream world you've concocted here. Remember?

Sure, don't pay off a bookie when he comes for the money and see what happens. You've certainly lost it completely.

And the rules change YET AGAIN. So now it's multiple books offering unspecified credit. Uh huh.

No, again you miss the point completely. Do you really have no clue on this, or are you just playing dumb? Since when does book (A) offer me a parlay using odds for another event at book (B)? Please, save the strawman arguments for somebody else. Just put yourself in the player's shoes and either you have the right answer or you don't. And < 1% is not the right answer.

[BigCap]

Look. We've asked multiple times for you to provide mathematical proof to your assertions. Until you do, everything you've said is nonsense. The onus is on you here. The Kelly Criterion has been time tested.

And again, I told you that Kelly Criterion cannot be applied here due to the fact that the 0-100 scenario will not happen. How many times do I need to repeat this for it to get through your thick skull?

Please, just stop.

[BigCap]

That's a lot of arrogance for someone who is challenging the Kelly Criterion and proclaiming victory without one single equation proposed. Please inform us of this magical utility formula that can omnisciently predict every players' risk of ruin comfort level universally. I hope you realize that is exactly what you are professing to know here and that it's utterly obtuse.

And it is a lot of arrogance on your part to completely ignore my question. If you had this opportunity, how much would you wager on each bet as a percentage of your bankroll ($100,000)? Why don't you just answer the question, and stop your nonsense? And please stop with "not real world", "infinite limits", etc. The question as posed is sufficient for a correct answer that is not <1%.

[MonkeyF0cker]

WE ALREADY ANSWERED THE FUKKING QUESTION, NITWIT!!!!!!! UNFUKKING REAL!

Try to prove us wrong with math, retard. How many fukkin times do we have to say it?

You keep twisting the shit I say, changing the fukkin storyline along the way, and provide absolutely nothing in terms of theory or proof. So let's fukkin see it, hotshot.

[Ganchrow]

And again, I told you that Kelly Criterion cannot be applied here due to the fact that the 0-100 scenario will not happen. How many times do I need to repeat this for it to get through your thick skull?

Please, just stop.

So why stop at claiming the 0-100 outcome will never happen?

Why not also omit the 1-99 outcome? I mean that only happens with probability ~ 3.98×10^-30?

And then while we're at it, what about omitting 10-90 outcomes? Those only occur with probability ~ 1.18×10^-18?

And 20-80 outcomes occur with probability ~6.68×10^-11? Is that rare enough to exclude?

And how about 33-77? I mean that only happens with p = 0.008%, which is less than one hundredth of one percent of the time? I mean surely we can exclude those outcomes, too, right?

Anyway, I'm sure you see where I'm going with this. the line? What probability needs to be associated with a given event in order it be considered sufficiently "rare" to completely omit it from calculations of expected bankroll growth?

[Ganchrow]

Maximize growth omitting the 100 losing event outcome and this will yield 1.0204% bet ratio. That is the formula. I think you have enough resourcefulness to generate this result using Excel or some other program.

Actually, and FWIW, if one were to omit the 100 losing event outcome (say we called it a push) then the full-Kelly optimal stake would be strictly bounded from above by 1 99 ≈ 1.0101%.

For the upper bound on the Kelly stake to be 1 98 ≈ 1.0204% as you suggest, one would in fact need to exclude the two worst possible outcomes (i.e., not only the 0-100 outcome but also the 1-99).

As long as we're going to do that, heck, why not include the 20 worst outcpmes, or even the 50 worst outcomes? Anyway, please see my previous post.

[MonkeyF0cker]

Exactly, Ganch. That's what I was saying originally. That you'd need a utility function for that person who chose to risk those outcomes occurring by omitting them when they are wagering beyond their means with this credit. BigCap seems to think he knows what type of risk is best suited for everyone in this obscure situation that is as likely to occur as going 0-100.

[MonkeyF0cker]

Perhaps, we should build a Monte Carlo sim and see if it never happens. What do you think, BigCap?

[reno cool]

It's hard to believe that just omitting the 0-100 would make much of a difference in anything, as others have said.
Why throw in "expected growth"? Why not just say what you would bet and why it makes sense?

[BigCap]

WE ALREADY ANSWERED THE FUKKING QUESTION, NITWIT!!!!!!! UNFUKKING REAL!

Try to prove us wrong with math, retard. How many fukkin times do we have to say it?

You keep twisting the shit I say, changing the fukkin storyline along the way, and provide absolutely nothing in terms of theory or proof. So let's fukkin see it, hotshot.

Really? Who brought up "infinite limits?" Who brought up "Martingale?" Who brought up $200,000 bankroll instead of $100,000 bankroll? Who brought up parlays when they were not even part of the question?

You tried to strawman, distort, and exaggerate just about every simple constraint on the example, and you still have not conceded that 0-100 will not happen? Come on, IT WILL NOT HAPPEN! Let's move on...

[BigCap]

So why stop at claiming the 0-100 outcome will never happen?

Why not also omit the 1-99 outcome? I mean that only happens with probability ~ 3.98×10^-30?

And then while we're at it, what about omitting 10-90 outcomes? Those only occur with probability ~ 1.18×10^-18?

And 20-80 outcomes occur with probability ~6.68×10^-11? Is that rare enough to exclude?

And how about 33-77? I mean that only happens with p=0.008%, which is less than one hundredth of a percent of the time? I mean surely we can exclude those outcomes, too, right?

Anyway, I'm sure you see where I'm going with this. the line? What event can be considered sufficiently "rare" to completely omit them from calculations of expected bankroll growth?

Well, does this mean that you concede that 0-100 will not happen? Please let me know, because I thought somebody else conceded this point but now I'm not so sure.

But you are getting closer to answering the question...

[BigCap]

Actually, and FWIW, if one were to omit the 100 losing event outcome (say we called it a push) then the full-Kelly optimal stake would be strictly bounded from above by 1 99 ≈ 1.0101%.

For the upper bound on the Kelly stake to be 1 98 ≈ 1.0204% as you suggest, one would in fact need to exclude the two worst possible outcomes (i.e., not only the 0-100 outcome but also the 1-99).

As long as we're going to do that, heck, why not include the 20 worst outcpmes, or even the 50 worst outcomes? Anyway, please see my previous post.

The answer (if 0-100 is correctly omitted) is 1.0204% (100/98) if TIES ARE NOT POSSIBLE. The answer is 1.01% (100/99) if TIES ARE POSSIBLE.

I was initially considering ties, but for simplicity my bets as originally stated in the question were win/loss (no tie). So I am just trying to be consistent, so 1.0204% is the correct answer omitting 0-100 outcome.

[BigCap]

Perhaps, we should build a Monte Carlo sim and see if it never happens. What do you think, BigCap?

Sure. While you're at it, run your Monte Carlo and get all of today's MLB results, and let it print some money for you as well.

Get real. 0-100 WILL NOT HAPPEN. This is quite simple, really. Please stop with this. Either you get it or you don't.

[BigCap]

It's hard to believe that just omitting the 0-100 would make much of a difference in anything, as others have said.
Why throw in "expected growth"? Why not just say what you would bet and why it makes sense?

It most certainly is an expected growth calculation. Assuming the 0-100 outcome is not considered with no ties, and I bet EXACTLY 1.0204%, then my expected growth is 2.55%. If I reduce my bet to 1.0%, then my expected growth is reduced to 2.51%.

This is why it makes sense to bet 1.0204%, because it maximizes growth.

[BigCap]

Exactly, Ganch. That's what I was saying originally. That you'd need a utility function for that person who chose to risk those outcomes occurring by omitting them when they are wagering beyond their means with this credit. BigCap seems to think he knows what type of risk is best suited for everyone in this obscure situation that is as likely to occur as going 0-100.

One more time: Are you conceding that 0-100 WILL NOT HAPPEN? If not, please stop.

[BigCap]

It's funny how a very simple question in a real world situation cannot be answered, or that there is even so much dispute over a very simple (and correct) assumption that losing 100 consecutive 51.5% independent bets will never happen.

Why is this so difficult? These are quite simple assumptions to make, really. Everybody knows that nobody will EVER win 4 successive powerballs, much less identifying the specific person ex ante, which is actually the equivalent probability.

Of course the answer involves a utility function. But nobody would EVER CONSIDER 0-100 as a possible outcome. To say anything else is a complete joke and reveals the complete mis-application of theory to a real world problem.

Enough said.

[Ganchrow]

The answer (if 0-100 is correctly omitted) is 1.0204% (100/98) if TIES ARE NOT POSSIBLE. The answer is 1.01% (100/99) if TIES ARE POSSIBLE.

I was initially considering ties, but for simplicity my bets as originally stated in the question were win/loss (no tie). So I am just trying to be consistent, so 1.0204% is the correct answer omitting 0-100 outcome.

Mea culpa. A shade under 1 98 would indeed be the optimal bet size were one to strictly condition on the nonoccurrence of the 0-100 outcome.

[Ganchrow]

Well, does this mean that you concede that 0-100 will not happen? Please let me know, because I thought somebody else conceded this point but now I'm not so sure.

But you are getting closer to answering the question...

No ... I'm saying that a 0-100 outcome happens with probability 3.75×10^-32, which (perhaps at the risk of understatement) is clearly a rare occurrence.

But going 1-99 is a rare occurrence, too, occurring with probability 3.98×10^-30, which in your parlance I would also think would constitute an event that "will not happen in the real world".

So my question once again to you would be why not just exclude these 1-99 outcomes as well? This (conditioning on the 0 win and 1 wins outcomes not occurring) would imply an optimal bet of a shade under 1 96 per wager and conditional BR growth of 2.59%.

And so the point of my question remains. Under your "rare event conditioning" of Kelly, at what level rarity of an event ought one draw the proverbial line?

I mean, if you can draw the line at p = 3.75×10^-32, why not also at p = 3.98×10^-30, why not also at p = 2.70×10^-10? Heck, while we're at it, why not at p = 8.8×10^-03?

Et cetera.

Obviously, if you condition on a given event not occurring (e.g. 0 wins and 100 losses, or 90 wins and 10 losses, or 100 wins and 0 losses, etc.) then that will certainly change your outcome set, and so too your optimal bet size and expected growth.

But what makes this conditioning in any way mathematically proper? Just because an event is highly unlikely to happen, doesn't mean one can simply omit it from one's outcome set and tout the concomitant "improved" results.

So the question I once more pose to you is exactly what level of rarity does your conditional brand of expected bankroll growth maximization require for you to feel justified in ignoring a given outcome?

[Pancho sanza]

Technically Ganchrow is correct, 0-100 is THEORETICALLY possible.

Remember that insurance policy Porky pig took out? Hey shit happens.

http://en.wikipedia.org/wiki/Fool_Coverage

[BigCap]

No ... I'm saying that a 0-100 outcome happens with probability 3.75×10^-32, which (perhaps at the risk of understatement) is clearly a rare occurrence.

I now know you are not being honest about this; any reasonable person would completely exclude 3.75E-32 event (0-100) in my example. If you would please be upfront and just concede this simple point, we can move on.

But going 1-99 is a rare occurrence, too, occurring with probability 3.98×10^-30, which in your parlance I would also think would constitute an event that "will not happen in the real world".

This line of reasoning led me to believe that you were getting closer to solving the problem. But if you cannot concede a very simple, logical point, then I guess not.

So my question once again to you would be why not just exclude these 1-99 outcomes as well? This (conditioning on the 0 win and 1 wins outcomes not occurring) would imply an optimal bet of a shade under 1 96 per wager and conditional BR growth of 2.59%.

To be more precise, expected growth in this case would be 2.5923%.

And so the point of my question remains. Under your "rare event conditioning" of Kelly, at what level rarity of an event ought one draw the proverbial line?

I mean, if you can draw the line at p = 3.75×10^-32, why not also at p = 3.98×10^-30, why not also at p = 2.70×10^-10? Heck, while we're at it, why not at p = 8.8×10^-03?

Et cetera.

If you cannot make a simple logical conclusion that 3.75E-32 will never happen in this scenario, then I'm not sure I can help you on this.

Obviously, if you condition on a given event not occurring (e.g. 0 wins and 100 losses, or 90 wins and 10 losses, or 100 wins and 0 losses, etc.) then that will certainly change your outcome set, and so too your optimal bet size and expected growth.

But what makes this conditioning in any way mathematically proper? Just because an event is highly unlikely to happen, doesn't mean one can simply omit it from one's outcome set and tout the concomitant "improved" results.

And this is where I believe you are failing. You are trying to apply a theory to a real world problem, in which the theory considers an event that will not happen. If you can just be honest and accept the fact that 0-100 will not happen, then we can move on.

So the question I once more pose to you is exactly what level of rarity does your conditional brand of expected bankroll growth maximization require for you to feel justified in ignoring a given outcome?

I already hinted above the course to solving this problem. I'm sure you know how to solve it. You are just reaching on this 0-100 event as a possible outcome.

Please read post #88 as it seems we are going in circles again. This should address your questions here.

[BigCap]

Technically Ganchrow is correct, 0-100 is THEORETICALLY possible.

Remember that insurance policy Porky pig took out? Hey shit happens.

http://en.wikipedia.org/wiki/Fool_Coverage

Note quite. Nice try, though.

And we are talking specifically about INDEPENDENT events. 0-100 WILL NOT HAPPEN AND SHOULD NOT BE CONSIDERED AS A POSSIBLE OUTCOME. Anything else is really just folly.

[BigCap]

Mea culpa. A shade under 1 98 would indeed be the optimal bet size were one to strictly condition on the nonoccurrence of the 0-100 outcome.

It actually is a limit problem, so 100/98 is correct as I can basically get as close to this ratio as I want.

[maxdalury]

why not eliminate the 100-0 and 99-1 outcomes that will "never" happen in the real world.

[BigCap]

why not eliminate the 100-0 and 99-1 outcomes that will "never" happen in the real world.

Solid reasoning, but (un)fortunately this has a negligible effect on expected growth.

[Dazzez]

Why not eliminate the 1-99 outcome that will "never" happen in the real world?

[BigCap]

Why not eliminate the 1-99 outcome that will "never" happen in the real world?

Do you agree that 0-100 will not happen and should be excluded from the array of potential outcomes?

[MonkeyF0cker]

BigCap,

Enough with your superiority complex. Either discuss your thoughts or drop the subject. This isn't rocket science and you're not exactly Einstein in removing 0-100. So either get to the point so it can be refuted or go away.

[BigCap]

BigCap,

Enough with your superiority complex. Either discuss your thoughts or drop the subject. This isn't rocket science and you're not exactly Einstein in removing 0-100. So either get to the point so it can be refuted or go away.

I think the government could do well by taxing your http posts.

So, we are in agreement then that 0-100 should be excluded from the array of potential outcomes? I would say the odds of you being Einstein are about 3.75E-32, so this should not be a major hurdle for you to get past.

You are right, this is not rocket science. I don't know what the big deal is about calculating expected growth. Ganchrow did it (2.55% using 1.0204% bet ratios), so you should be able to follow along here.

[BigCap]

Hey Monkey,

Do you have any idea what it means when an optimum investment strategy indicates investing more than 100% of your portfolio? Does this make any sense to you? Do you not realize this is possible?

Maybe we should get some facts straight before I go about assuming you can fairly assess this problem.

[MonkeyF0cker]

Great. More superiority bullshit. Are you going to get to the fukkin point or is THAT it? Remove 0-100 if you're ever faced with 100 simultaneous wagers at multiple books that offer overnight credit. Gee, thanks.

[BigCap]

Great. More superiority bullshit. Are you going to get to the fukkin point or is THAT it? Remove 0-100 if you're ever faced with 100 simultaneous wagers with multiple books that offer overnight credit. Gee, thanks.

How many teeth did you lose on that admission?

And did you read post #101?

And btw what is your guess on the bet ratio for the 3% advantage bets?

[MonkeyF0cker]

It's not an admission, bonehead.

[MonkeyF0cker]

So AGAIN, where is the threshold? What happens when you're faced with 98 simultaneous wagers?