100 bets in one day - kelly adjustment?

[Ganchrow]

But I know that this is NOT how much you would bet. This is the question I am asking. Thanks again in advance for your providing this answer.

Why are you so certain "that this is NOT how much I would bet"?

Are you suggesting that I'm not look to maximize bankroll growth?

[BigCap]

How is this a "real world" scenario precisely, BigCap? You're proposing a situation that is as likely as hitting the four Powerball numbers that you are railing against. It is certainly POSSIBLE to lose every bet no matter how slim the liklihood may be. AGAIN, there MUST be some bounds to the credit availability. And if there weren't, although I'm not quite certain how, you'd need a utility function that would be independent for each person's level of comfort with risk of ruin.

You are getting a bit closer to the answer. Betting on books' credit and clearing the books the next day is how the business was run for years. It is still being done this way for many books. Again, you are misconstruing books' credit with one obtaining credit against future net worth. The books providing you credit are not adding to your net worth or increasing your bankroll; they are only facilitating placing of wagers in a convenient way so you do not need to drive up to their location and drop the cash.

It is not possible in the real world to lose 100 bets as described, and there is no real point in discussing the possibility. I think we have moved on from that discussion.

[Ganchrow]

And actually, your original question was, ""How much should I bet on each assuming I want to maximize growth?"

The answer of course remains a tad less than $1,000 per bet.

[BigCap]

Why are you so certain "that this is NOT how much I would bet"?

Are you suggesting that I'm not look to maximize bankroll growth?

Because I am certain you would never consider losing 100 bets as described as a potential outcome. This I am absolutely certain.

[BigCap]

And actually, your original question was, "How much should I bet on each assuming I want to maximize growth?"

The answer of course remains, a tad less than $1,000 per bet.

Again, I think we have moved past considering losing all 100 bets as a possible real world outcome. This is why "a tad less than $1,000 per bet" is not the correct answer.

[MonkeyF0cker]

You are getting a bit closer to the answer. Betting on books' credit and clearing the books the next day is how the business was run for years. It is still being done this way for many books. Again, you are misconstruing books' credit with one obtaining credit against future net worth. The books providing you credit are not adding to your net worth or increasing your bankroll; they are only facilitating placing of wagers in a convenient way so you do not need to drive up to their location and drop the cash.

It is not possible in the real world to lose 100 bets as described, and there is no real point in discussing the possibility. I think we have moved on from that discussion.

If you are risking the credit available to you through the book in excess of your actual bankroll, then it must be considered a portion of your bankroll. If you are looking to exceed the limitations of your bankroll, there is absolutely no correct answer to this question, as it relies on individual utility.

[MonkeyF0cker]

Please provide the math which proves the assertion that losing 100 bets is not possible. Thanks.

[BigCap]

If you are risking the credit available to you through the book in excess of your actual bankroll, then it must be considered a portion of your bankroll.

This is not correct. Again, the books are providing a convenience to you. For example, this convenience in no way would change how you would determine how much to place on a single bet, as a percentage of your true bankroll.

If you are looking to exceed the limitations of your bankroll, there is absolutely no correct answer to this question, as it relies on individual utility.

As already described, the book allows me to bet on credit. This you were already aware of.

There is a correct answer, and it can be demonstrated. I am reasonably certain now that you and others here can now answer this question, once Kelly Criterion application is recognized as not providing the correct answer.

[Ganchrow]

We're running around in circles here.

But to be crystal clear, in answer to your initial question, "How much should I bet on each [of these 100 independent 3% edge even odds bets] assuming I want to maximize [bankroll] growth?"

The answer is a tad less than 1% of bankroll per bet.

I'd be more than happy to entertain and critique (and of course ultimately refute) any mathematical proof to the contrary. The same I'm sure would for Monkey.

[BigCap]

Please provide the math which proves the assertion that losing 100 bets is not possible. Thanks.

Again, this is not possible in the real world. Any reasonable person should be able to recognize this. Let's move on from this pointless discussion as I am sure you would agree that you would never consider this possibility in any of your future planning. It really is nonsense.

[BigCap]

We're running around in circles here.

But to be crystal clear, in answer to your initial question, "How much should I bet on each [of these 100 independent 3% edge even odds bets] assuming I want to maximize [bankroll] growth?"

The answer is a tad less than 1% of bankroll per bet.

I'd be more than happy to entertain and critique (and of course ultimately refute) any mathematical proof to the contrary.

Because I am aware that you do not consider losing 100 bets as described a real world possibility, this is obviously not the correct answer, or at least not consistent with logical reasoning on the matter.

If you do consider losing 100 bets as described a real world possibility, then you are not being reasonable as no reasonable person would ever consider this a real world possibility. So either choice is incorrect.

[MonkeyF0cker]

Again, this is not possible in the real world. Any reasonable person should be able to recognize this. Let's move on from this pointless discussion as I am sure you would agree that you would never consider this possibility in any of your future planning. It really is nonsense.

Actually, I would consider each and every permutation of the results of those 100 bets to be within the realm of possibility.

[BigCap]

Actually, I would consider each and every permutation of the results of those 100 bets to be within the realm of possibility.

Then you would be short-changing yourself, as these events would never happen, and thus not possible in the real world. Again, I think we can dismiss this part of the discussion as I am certain all of us agree it will never happen.

I am certain you agree this event will never happen in your lifetime, which is sufficient to conclude it will not happen for your planning. Any disagreement to this is just being disingenuous.

[MonkeyF0cker]

That's absurd. You can't maximize growth by ignoring possible outcomes.

[BigCap]

That's absurd. You can't maximize growth by ignoring possible outcomes.

It is perfectly reasonable, logical, and correct to dismiss the outcome of losing 100 consecutive 51.5% events, as I have noted in my example.

Anything otherwise is not reasonable.

No one would ever consider this outcome in this situation.

[MonkeyF0cker]

Please provide the math which proves otherwise.

[BigCap]

Please provide the math which proves otherwise.

Are you being unreasonable, i.e. considering the possibility of losing 100 consecutive 51.5% bets? This is my only explanation to why you have posed this question. I already answered this, in that no logical, reasonable person would ever consider this a possibility in their planning. I know for certain that you would never consider this in your planning, i.e. if you were in the situation I posed above. I am certain you would bet more than 1% of your bankroll because you would want to maximize growth. Considering losing 100 consecutive bets would be absurd. You may post otherwise, but I would appreciate some honesty in this case.

This is a perfect assumption that will never fail for this example. You are trying to apply theory for a practical situation in which the theory does not apply (e.g. Kelly).

[Ganchrow]

Simple mathematical proof as to why bet size need be less than 1% of bankroll in order to maximize bankroll growth:

Expected bankroll growth would in this case be defined as:

Now if we allow x = 1%, then the 1st term of the summation (i=0) reduces to:

(1+(2*0-100)*.01)^{combin(100,0)*0.5150*0.485100}
=0^1*1*0.485100
=0

As the product of any given set of finite numbers that includes zero equals zero then our E(growth) equals:

0 - 1
= -100%

In other words a bet size = 1% would imply -100% expected bankroll "growth", (which in full Kelly terms equates to -∞ utility).

Hence, bet size must be < 1%.

QED

[BigCap]

Simple mathematical proof as to why bet size need be less than 1% of bankroll in order to maximize bankroll growth:

Expected bankroll growth would in this case be defined as:

Now if we allow x = 1%, then the 1st term of the summation (i=0) reduces to:

(1+(2*0-100)*.01)^{combin(100,0)*0.5150*0.485100}
=0^1*1*0.485100
=0

As the product of any given set of finite numbers that includes zero equals zero then our E(growth) equals:

0 - 1
= -100%

In other words a bet size = 1% would imply -100% expected bankroll "growth", (which in full Kelly terms equates to -∞ utility).

Hence, bet size must be < 1%.

QED

Again, either you are considering losing 100 consecutive bets as a real world possibility (which is not reasonable), or you are not being honest with your intention of betting more than 1% in this case.

Again, this theory does not apply because of the reasons noted.

I would appreciate an honest answer to the question posed, WITHOUT THEORY. Just put yourself in the player's shoes and make a logical choice on how much you would bet. I know what the theory produces, and I know why I can logically dismiss it.

[Ganchrow]

Again, either you are considering losing 100 consecutive bets as a real world possibility (which is not reasonable), or you are not being honest with your intention of betting more than 1% in this case.

Again, this theory does not apply because of the reasons noted.

I would appreciate an honest answer to the question posed, WITHOUT THEORY. Just put yourself in the player's shoes and make a logical choice on how much you would bet. I know what the theory produces, and I know why I can logically dismiss it.

Not sure what more I can say.

We're talking about maximizing expected bankroll growth, which is a rather straightforward mathematical concept.

Perhaps your own personal bankroll management goals do not encompass the maximization of bankroll growth. That's fine by me, and certainly in no normative manner is either "better" or "worse" than a set of goals that does.

But go ahead ... argue how that's not how you'd personally behave if faced with such a scenario and you won't hear a peep out of me. Such is simply a matter of personal preferences and I have no more right to dictate yours when it comes to bankroll management than I have when it comes to your choice between flavors of ice cream or methodology for consuming Oreo cookies.

BUT:

That was NOT your original question. YOU asked about the maximization of bankroll growth and I (and Monkey) responded with the correct answer. Whether YOU like it or not, whether YOU would behave this way or not, whether it ultimately angers YOU to no end or not, that the maximization of expected bankroll growth necessitates betting less than 1% of bankroll per wager remains an immutable mathematical fact that I easily proved in post #53 of this thread.

[BigCap]

Not sure what more I can say.

We're talking about maximizing expected bankroll growth, which is a rather straightforward mathematical concept.

Perhaps your own personal bankroll management goals do not encompass the maximization of bankroll growth. That's fine by me, and certainly in no way normative manner either "better" or "worse" than a set of goals that do.

So go ahead ... argue how that's not how you'd personally behave if faced with such a scenario and you won't hear a peep out of me. Such is simply a matter of personal preferences and I have no more right to dictate yours when it comes to bankroll management than I have when it comes to your choice between flavors of ice cream or methodology for consuming Oreo cookies.

BUT:

That was NOT your original question. YOU asked about the maximization of bankroll growth and I (and Monkey) responded with the correct answer. Whether YOU like it or not, whether YOU would behave this way or not, and no matter how much it might anger YOU, that the maximization of expected bankroll growth necessitates betting less than 1% of bankroll per wager remains an immutable mathematical fact.

Again, we are going in circles here. You never answered my question honestly, so I can only conclude you just want to misapply theory to mask what your intentions would be for this specific case.

Losing 100 events as described will NOT HAPPEN IN THE REAL WORLD. This is why the theory cannot be applied. I am not going to beat an apparent dead horse here with trying to obtain your non-theoretical answer to this question. Again, I am certain you would always rule out losing 100 of these bets in your planning. You never disputed this so I can only conclude it true. As such you would always bet (correctly) at more than 1%. I believe this a logical conclusion as you never provided an honest answer in this way.

Either you recognize this event will never happen (and construct an appropriate model for the solution), or you don't want to admit such (and thus are unreasonable).

[MonkeyF0cker]

AGAIN, any wagers of 1% or greater come down to personal utility. If you had proposed a realistic situation, then perhaps your argument of a "real world" approach could hold some weight. But you haven't and it doesn't. What remains is that your idea of bankroll is misconstrued and that if this scenario were ever encountered in the "real world," anyone wishing to exceed their bankroll would need to factor in their own utility in determining how much risk of ruin they wish to take on. There is no denying there is risk there, no matter how small it may be. That amount of risk also increases exponentially the more possible outcomes that person is willing to write off.

[RickySteve]

Pretty much the best thread ever.

[BigCap]

AGAIN, any wagers of 1% or greater come down to personal utility.

Correct, which led me to believe you were on the right course. But anything less than 1% is not logically correct under any reasonable cirrcumstances.

If you had proposed a realistic situation, then perhaps your argument of a "real world" approach could hold some weight. But you haven't and it doesn't.

This is definitely a real world situation (which I already noted this is how books ran their operation for years), and as such a real world approach is quite appropriate. This is not logically disputable. In fact this is how I wagered for years, so you are completely wrong here.

What remains is that your idea of bankroll is misconstrued and that if this scenario were ever encountered in the "real world," anyone wishing to exceed their bankroll would need to factor in their own utility in determining how much risk of ruin they wish to take on. There is no denying there is risk there, no matter how small it may be. That amount of risk also increases exponentially the more possible outcomes that person is willing to write off.

Again, I already demonstrated how getting credit from a book for betting with the requirement that win/loss is cleared the next day does NOT increase your bankroll. Additionally, the fact this event will never occur supersedes any approach which considers the potential outcome of this event.

Let me pose another example, which you will probably post a rejection either because (a) it is not "real world" (but your attempted application of theory to this problem is not real world at all), or (b) proves your approach to be in error (which I am reasonably certain you would not admit to anyway). It has no logical answer other than a confirmation that I am correct:

Portfolio manager: Joe, I have some potential investment opportunities that will increase your portfolio by 25% each year over the next 10 years.

Joe: Sounds good, but what is the risk?

Portfolio manager: Well, we modeled this investment and the only risk we came up with is a 10E-500 chance of losing everything.

Joe: Everything?

Portfolio manager: Yes, everything you own, or ever could own would be gone. Your effective net worth would be zero.

Joe: Can you give me an example of what 10E-500 chance would be?

Portfolio manager: Sure. It would be about the same chance that you would play one ticket each week on powerball, win this week, then win next week, and so on for the next 80 weeks.

Joe: I think I can live with that. That is never going to happen, so why worry about it?

Portfolio manager: Exactly, it will never happen.

Anyone who does not agree with Joe needs to re-evaluate their thought process on this matter. Unfortunately I believe you fall into this category, but I am certain you will not admit to such.

[MonkeyF0cker]

This is laughable. Seriously. If you ONLY exclude the 0 wins combination out of your risk calculation, guess what? Your optimal wager will still be very close to 1% of your bankroll. And really? That's the ONLY risk here? Please. What if you're extending your bankroll to wager $200k on these events with this credit and go 29-67-4? Is that within the "real world" possibilities maybe? What have you stated in regards to utilizing the credit as a portion of your bankroll? It is indisputable that it would now be considered a portion of your bankroll. What else is it? You can't extend your bankroll without that money being considered a part of it. And NO IT ISN'T REALISTIC. I've never heard of a book that offered credit with infinite limits. Certainly, such a book DOES NOT EXIST. If there were such a book, why not just Martingale all day long? Not only that, but this book also will not offer parlays? Please don't tell me this is due to risk aversion. LOL. You're in outer space on this one. This isn't a black and white question, and it's certainly not realistic.

[MonkeyF0cker]

And by the way, what we're proposing is close to a zero net worth possibility at 3.75E-32. What you're proposing is a negative net worth at far better odds.

[BigCap]

This is laughable. Seriously. If you ONLY exclude the 0 wins combination out of your risk calculation, guess what? Your optimal wager will still be very close to 1% of your bankroll.

More precisely, it would be 1.01%, which is more than 1%. Is this your way of admitting you were wrong about < 1% being the correct answer?

And really? That's the ONLY risk here? Please. What if you're extending your bankroll to wager $200k on these events with this credit and go 29-67-4? Is that within the "real world" possibilities maybe?

And what exactly is your point here? That with $100k bankroll my position is correct, but with $200k it is not? This is laughable.

What have you stated in regards to utilizing the credit as a portion of your bankroll? It is indisputable that it would now be considered a portion of your bankroll. What else is it? You can't extend your bankroll without that money being considered a part of it.

Again, we do not need to dwell on this further. My bet ratio to my bankroll for a single bet would not change one bit if I had the convenience of placing my bets with a book and clearing them the next day. I think you should be able to rationalize this by now. Get serious.

And NO IT ISN'T REALISTIC. I've never heard of a book that offered credit with infinite limits.

Who on earth is talking about "infinite limits"? You are way off base here.

Certainly, such a book DOES NOT EXIST. If there were such a book, why not just Martingale all day long?

Books still exist that offer the convenience of clearing the next day. You cannot be this ignorant. Sure, Martingale and see what happens to your knee caps when tomorrow comes and you can't pay. Maybe somebody will go further and find a nice hole in the desert.

Not only that, but this book also will not offer parlays? Please don't tell me this is due to risk aversion. LOL. You're in outer space on this one. This isn't a black and white question, and it's certainly not realistic.

I'm sure you are aware that book (A) will not be so kind to offer you a parlay a bet with the same odds as book (B), each of which offer the favorable odds. And I'm in outer space? Wow, get a clue, really. You are clearly wrong on each and every point.

[BigCap]

And by the way, what we're proposing is close to a zero net worth possibility at 3.75E-32. What you're proposing is a negative net worth at far better odds.

At least you got 3.75E-32 right, which is a bit of a surprise. It does not change the fact that the event won't happen, and should not be considered in any future planning.

Other than the above figure you have been 100% wrong. You are clearly reaching on this, trying to distort my initial question with pointless exaggerations and untruths. Every point you have attempted has been easily refuted. You already acknowledged you were wrong about the < 1% figure. At this point I would save some grace because it will not get any better for you on this one.

Enough said.

[Dazzez]

So hey BigCap. Are you saying that Ganchrow, Monkeyfocker and Kelly are all wrong when they say that to maximize BR growth you should bet less than 1% of BR per bet?

[BigCap]

So hey BigCap. Are you saying that Ganchrow, Monkeyfocker and Kelly are all wrong when they say that to maximize BR growth you should bet less than 1% of BR per bet?

If you cannot deduce this, then I would put you in that group as well.

Kelly applied to this question is incorrect, as I have shown. So it should not be included in the above group. And Monkey... already admitted as such that > 1% is correct.

[Dazzez]

If you cannot deduce this, then I would putyou in that group as well.

Kelly applied to this question is incorrect, as I have shown. So it should not be included in the above group. And Monkey... already admitted as such that > 1% is correct.

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.

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?

[MonkeyF0cker]

More precisely, it would be 1.01%, which is more than 1%. Is this your way of admitting you were wrong about < 1% being the correct answer?

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

And what exactly is your point here? That with $100k bankroll my position is correct, but with $200k it is not? This is laughable.

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.

Again, we do not need to dwell on this further. My bet ratio to my bankroll for a single bet would not change one bit if I had the convenience of placing my bets with a book and clearing them the next day. I think you should be able to rationalize this by now. Get serious.

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

Who on earth is talking about "infinite limits"? You are way off base here.

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

[MonkeyF0cker]

Books still exist that offer the convenience of clearing the next day. You cannot be this ignorant. Sure, Martingale and see what happens to your knee caps when tomorrow comes and you can't pay. Maybe somebody will go further and find a nice hole in the desert.

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

I'm sure you are aware that book (A) will not be so kind to offer you a parlay a bet with the same odds as book (B), each of which offer the favorable odds. And I'm in outer space? Wow, get a clue, really. You are clearly wrong on each and every point.

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

[MonkeyF0cker]

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.

[MonkeyF0cker]

At least you got 3.75E-32 right, which is a bit of a surprise. It does not change the fact that the event won't happen, and should not be considered in any future planning.

Other than the above figure you have been 100% wrong. You are clearly reaching on this, trying to distort my initial question with pointless exaggerations and untruths. Every point you have attempted has been easily refuted. You already acknowledged you were wrong about the < 1% figure. At this point I would save some grace because it will not get any better for you on this one.

Enough said.

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.