100 bets in one day - kelly adjustment?

[BigCap]

I'm not attempting to answer your initial question, I'm trying to understand your reasoning. You state that 0 - 100 will not happen. Fair enough. Am I to assume, then, that 1 - 99 might, and should be considered?

Simple yes or no please.

Again, the question is for you to answer, not me. I posed the question to get responses from others. Some were reasonable about this, others were not. When someone posts the correct solution I will answer your specific question. The solution should be obvious by now, so I anticipate it will be posted soon.

[MonkeyF0cker]

Fukkin ridiculous. This thread could have consumed two posts. Instead, you fukkin play games only to come full circle and agree with what I've been saying the ENTIRE TIME. You're a fukkin joke, BigCap. Take your fukkin kids games elsewhere.

[sofos]

Assuming that you have the $100,000 bankroll and bet a bit more than 1% on each bet you cannot make 100 bets because by the time you have made 99 bets you just don't have enough left for the 100th bet. Therefore, since you only made 99 bets, there is no way for you to go 0 and 100.

[Pokerjoe]

Again, the question is for you to answer, not me. I posed the question to get responses from others. Some were reasonable about this, others were not. When someone posts the correct solution I will answer your specific question. The solution should be obvious by now, so I anticipate it will be posted soon.

Poseur of the year?

[BigCap]

Fukkin ridiculous. This thread could have consumed two posts. Instead, you fukkin play games only to come full circle and agree with what I've been saying the ENTIRE TIME. You're a fukkin joke, BigCap. Take your fukkin kids games elsewhere.

I guess you can't type or read. I have stayed completely consistent, whereas you have bounced around like somebody just cut your head off.

And I thought you gave up? Why don't you post at an appropriate (read: lower) level.

[BigCap]

Anyone who clings to "theory" claiming that >1% is not correct can be proven wrong for the following reasons:

1. There are countless instances where application of theory is inappropriate. A very simple example: application of pi. In theory, pi is an irrational number with infinite non-repeating decimal digits. However, application of pi in approximate form is appropriate in many instances. It would be inappropriate for someone to waste time and calculate pi to n digits when only 3 is sufficient. On the other hand, there are some applications in which pi needs to be expressed in very precise form. No rational person would ever say that the crude application of pi was not correct. Even though they are not precise in any way, the application of pi was sufficient to produce the correct result. In the case of Kelly, the original application of this theory involved signal degradation over long distance phone lines. Due to the nature of this application, a strict adherence to theory was appropriate to achieve minimum signal loss. (i.e. maximum gain) However, this does not mean that application of Kelly needs to be as strict in all situations. A frequent bettor, in his lifetime, may place 200,000 bets. This pales in comparison to the number of iterations in which a long distance signal could lose strength. This means that any "out of this world" event (e.g. 3.75E-32) should never be considered as a potential outcome for this bettor if he wants to maximize growth, because it will simply not happen. And this application is perfectly appropriate. Another example: there are many cases where the binomial search does not yield the correct (i.e. quickest) result, if some pattern about the population is known beforehand. So applying theory in this case would not achieve the optimal result. The same applies in this example.

2. Let's assume for a moment that some "tad below 1%" wager for this scenario was correct. Going completely with theory, the actual amount to wager would be as close to 1%, but not over. So let's assume that we found a book that took bets in cents, with the standard $1 minimum. So I would bet $999.99 on each event. Now, the only reason why betting this amount would ever hold true (compared to betting 1% or more) would be if we go 0-100. So in this case, we are left with exactly $1. Now, in theory, we have not gone broke. But in fact anyone with only $1 to their name is indeed functionally broke. And even if you do not consider this person broke (which they are), their next bet will be $1 and they will risk complete ruin anyways. So they are effectively "broke" from a theoretical risk of ruin context as well.

Now, let's say that we will not bet so close to 1%, but instead we will bet $999.98 so we are left with $2, so we will not risk going broke betting $1. Well, what happens if you lose that bet? You are down to $1 again, and again you are in the state where you cannot avoid risk of ruin. Following mathematical induction one should be able to see that there is no "safe" amount to bet, because you will eventually reach a point where you cannot avoid risk of ruin in the 0-100 outcome. So considering the 0-100 outcome as possible does not serve any purpose, and in fact only reduces the growth opportunity available to the bettor if he rationalizes these potential outcomes and correctly identifies which outcomes should be ruled out. Also, anyone not betting as close to 1% would not be following strict application of theory, so any "holding back" of funds in case of a 0-100 outcome is "fudging" and reducing their expected growth vs. theoretical Kelly expected growth.

And if you don't believe that $1 is "theoretically broke", I can choose any number as small as you want to make this example hold true.

[BigCap]

Assuming that you have the $100,000 bankroll and bet a bit more than 1% on each bet you cannot make 100 bets because by the time you have made 99 bets you just don't have enough left for the 100th bet. Therefore, since you only made 99 bets, there is no way for you to go 0 and 100.

Please read the original question again, if you believe this to be the case. (the bettor can bet on book's credit to be cleared the next day)

[MonkeyF0cker]

Can you please inform us as to the liklihood that this would ever be applicable? I would certainly love to know how often one should anticipate coming across 15 simultaneous wagers with equivalent edge much less 100. Thanks.

[reno cool]

I'm not a proponent of Kelly for gambling purposes. But, isn't the reason you're betting less in case of simultaneous bets due to the fact you're unable to adjust bet size after a losing streak? Not that you're afraid to run out of $ that day? And for your example above, if you're able to bet cents as in 999.99 why would you bet your last dolor whole?

[BigCap]

I'm not a proponent of Kelly for gambling purposes. But, isn't the reason you're betting less in case of simultaneous bets due to the fact you're unable to adjust bet size after a losing streak? Not that you're afraid to run out of $ that day? And for your example above, if you're able to bet cents as in 999.99 why would you bet your last dolor whole?

Because you would have exactly $1 left if you went 0-100.

This scenario is the reason why it's silly to consider 0-100 as a potential outcome. Because even if it did, you would be ruined.

[BigCap]

So basically, this is what we have:

(1)If you exclude 0-100 from array of outcomes to be considered, you should bet more than 1%.

(2)If you do not exclude 0-100 from array of outcomes to be considered, you should bet as closely to 1% as possible but not more. But this position would only improve on (1) if 0-100 DID happen, which would leave you ruined anyway.

So the only logical choice is (1), because (2) offers no advantage.

[reno cool]

so why not indeed bet 3%. 33-66 hardly likely.

[BigCap]

"hardly likely" and "will not happen" describe two quite different outcomes, do they not?

Even if 0-100 was considered a potential outcome, it still leaves you ruined.

[Art Vandeleigh]

Once when I was in Vegas I was down to my last $1.00 and went to a nickel keno machine and turned it into $40.

Went and had me a nice buffet.

OK, I wan't rich. But I didn't feel ruined.

[jimbojpc]

The answer to the question? Questions the answer

[BigCap]

Some more evidence that the risk of ruin argument is silly:

With $100,000, one would place $3,000 on a 3% edge bet paying even money. After losing, this bet, one would place $2,910 on the same edge bet, and so on. After losing 264 consecutive bets, one would be forced to bet under $1. After 434 bets, one would no longer be able to bet because they wold only have $0.16 and their bet would not equal $0.01. So I am in state of ruin.

But, hey, 8.4011E-126 != 0, so I guess I am in an unavoidable state of risk of ruin!

[BigCap]

Once when I was in Vegas I was down to my last $1.00 and went to a nickel keno machine and turned it into $40.

Went and had me a nice buffet.

OK, I wan't rich. But I didn't feel ruined.

...and then you turned your $40 (less buffet cost) into...?

I guess the keno machine you found was +EV, which frankly I have never encountered.

[Art Vandeleigh]

Oh OK, let's say instead of video keno I went to a bank of nickel video poker machines that were linked together and had a progressive jackpot (for a Royal Flush) large enough to make the overall return 103% (max coins) and I played 5 nickels for a few hands until I caught 4 of a kind Aces and left with $40.

So in this case I played a +EV game and got myself $40 away from "absolute" ruin of $0.00. Chip and a chair that's all we need, right?

Anyway, I think I'm following what your trying to get across but I want to see the 100k bankroll go under 25 cents before I become your ruined disciple.

Or maybe there is some more clear technical definition of "ruined" I'm not familar with, that could very well be.

[BigCap]

Oh OK, let's say instead of video keno I went to a bank of nickel video poker machines that were linked together and had a progressive jackpot (for a Royal Flush) large enough to make the overall return 103% (max coins) and I played 5 nickels for a few hands until I caught 4 of a kind Aces and left with $40.

So in this case I played a +EV game and got myself $40 away from "absolute" ruin of $0.00. Chip and a chair that's all we need, right?

Anyway, I think I'm following what your trying to get across but I want to see the 100k bankroll go under 25 cents before I become your ruined disciple.

Or maybe there is some more clear technical definition of "ruined" I'm not familar with, that could very well be.

Using your definition of "ruin", in fact you could go to zero, find some video poker coupons and still be able to grow your bankroll. So in that case the theory does not even apply at at all. Supports my point even more that the theory is misapplied.

And your other point about bankroll "go under 25 cents" indeed would never happen, which again supports my point that there is no need that potential outcome, so there would be no risk of ruin.

[reno cool]

Seems that we're arguing about the possibility of going broke that day. There's no chance of that. The question is are you exposing yourself too much in the sense of risking too high a % of bankroll? I miss the significance of the whole 0-100 example.

[BigCap]

Seems that we're arguing about the possibility of going broke that day. There's no chance of that. The question is are you exposing yourself too much in the sense of risking too high a % of bankroll? I miss the significance of the whole 0-100 example.

If you plug in the numbers, maximum expected growth on the 100 independent bets with 3% edge paying even money is 2.51%, if you consider that 0-100 could happen. If you rule out 0-100, you can get your expected growth up to 2.55%. So if you know 0-100 won't happen, why would you be satisfied with 2.51% expected growth if you can get 2.55%?

[reno cool]

Could you increase it further by eliminating 1-99?
It seems to me that if anything you're showing that the idea of "expected growth" is trivial.
'

[BigCap]

Could you increase it further by eliminating 1-99?

Yes.

It seems to me that if anything you're showing that the idea of "expected growth" is trivial.
'

Not by any means. The 2.55% figure I gave you is the correct number if you do not consider 0-100 as a potential outcome.

Let's look at another type of investment to illustrate my point. Say you want to invest in the stock market, and you want to use a fairly diversified instrument in which to invest. So, you choose the S&P 500 index. Now, if you invest without margin, you will certainly not go broke (because S&P 500 will not go to zero). However, you do not maximize your growth opportunity because you acknowledge S&P 500 will not go to zero. This implies that you can invest "more" than your bankroll, i.e. you invest on margin. Now, how much margin you use in your investment depends on your understanding of the actual risk S&P 500 value could drop to a point where you cannot recover. The same principles in this type of investment apply to my example.

[tomcowley]

If you plug in the numbers, maximum expected growth on the 100 independent bets with 3% edge paying even money is 2.51%, if you consider that 0-100 could happen. If you rule out 0-100, you can get your expected growth up to 2.55%. So if you know 0-100 won't happen, why would you be satisfied with 2.51% expected growth if you can get 2.55%?

(assuming your numbers are right- I didn't run them myself)

If you rule out 0-100, then it's not expected growth anymore. It's fantasyland. You can see from your numbers that the 0-100 case is relevant- if it weren't, then your numbers wouldn't change visibly, but you only have 98.5% of the growth in the real world that you would have in fantasyland- and that difference is solely due to the "irrelevant" 0-100 case.

[BigCap]

(assuming your numbers are right- I didn't run them myself)

If you rule out 0-100, then it's not expected growth anymore. It's fantasyland.

It's only "fantasyland" if you consider 0-100 as a potential outcome.

You can see from your numbers that the 0-100 case is relevant- if it weren't, then your numbers wouldn't change visibly, but you only have 98.5% of the growth in the real world that you would have in fantasyland- and that difference is solely due to the "irrelevant" 0-100 case.

It is only "relevant" because the worst case scenario breaks the bank. 0-100 could have 3.85E-50000000 possibility and it would have the same effect.

[tomcowley]

Yes, it's relevant because it's so bad. If you changed the probability to your E-50000000 number, then your growth would be virtually indistinguishable from your fantasyland growth, not from your actual expected growth. Its effect is a product (literally) of how rare it is and how bad it is.

As to your other argument, how any outcome that bad "means you're busto anyway, so you may as well ignore it", that should make you more risk AVERSE than Kelly suggests, not more risk tolerant.

[BigCap]

Yes, it's relevant because it's so bad. If you changed the probability to your E-50000000 number, then your growth would be virtually indistinguishable from your fantasyland growth, not from your actual expected growth. Its effect is a product (literally) of how rare it is and how bad it is.

Not true. If you consider 0-100 event, maximum expected growth reaches a limit not exceeding 2.51%, regardless of how small a probability you assign. If you properly rule out 0-100 potential outcome, expected growth (not "fantasy" growth) goes up to 2.55%. So no, the actual probability of 0-100 event is not relevant for this reason, so long as it can be reasonably ruled out from any real world event. I'm sure you don't believe me, so perhaps you should plug in the numbers and find out.

As to your other argument, how any outcome that bad "means you're busto anyway, so you may as well ignore it", that should make you more risk AVERSE than Kelly suggests, not more risk tolerant.

If it won't happen, why worry about it? Would you think 3.75E-500000 would happen in this scenario? Would you ever consider it a possibility? Would you arbitrarily choose to lower you expected growth from 2.55% to 2.51% because you think it would actually happen? I don't think you would...

[tomcowley]

Oh, because you're magically simultaneously wagering more than your bankroll on uncorrelated bets, but not actually risking more than your bankroll? LOL.

[BigCap]

Oh, because you're magically simultaneously wagering more than your bankroll on uncorrelated bets, but not actually risking more than your bankroll? LOL.

Wow, you get to pick and choose what is reality and what is fantasy? 0-100 outcome is indeed fantasy, and not much else.

So, I guess this is your way of recognizing that 2.51% != 2.55%?

So no books take bets on credit with next day settling? Now that you've read post #1, how about a reality check reading #10, #14, #37, #59, #84, #89, #101, #181, #191, #194, and #198.

[tomcowley]

Lol. Ignoring things that can happen is the fantasy, obviously. And you're putting yourself in a situation where you're risking more than you can settle and just praying it doesn't happen. Nice plan.

[BigCap]

Lol. Ignoring things that can happen is the fantasy, obviously. And you're putting yourself in a situation where you're risking more than you can settle and just praying it doesn't happen. Nice plan.

You really believe that 3.75E-32 is an outcome worth considering? Now that is fantasy:

Fantasy (defined): a mental image, esp. when unreal or fantastic; vision: a nightmare fantasy.

Did you consider the risk that the books with which you are betting will shut down and stiff you? Did you consider changes in the law that will prohibit you from getting your money? Did you consider that you might get hit by a comet when going to the mailbox to pick up your withdrawal check? All are orders of magnitude higher probability than 3.75E-32.

[tomcowley]

The math can account for all of those outcomes (and when arbing sketchy books, it actually does matter, and comes up indirectly on these forums from time to time). When you intend to gamble more than your bankroll (lol, whatever that means) and stiff the bookie when you don't run well enough, the standard expected growth math doesn't apply when figuring out how much to bet, because it requires a positive bankroll at all times (if you can't pay and will never pay either way if you lose, betting $100,000 and stiffing is clearly better than betting $50,000 and stiffing since it's just a freeroll). You can make up whatever utility function you want for how bad stiffing a bookie is going to be, but it has nothing to do with a player who can and will settle all losing wagers.

[BigCap]

The math can account for all of those outcomes (and when arbing sketchy books, it actually does matter, and comes up indirectly on these forums from time to time).

Indeed. So what is the risk of getting hit by a comet, or all books stiffing you? And how did the "math" account for these outcomes? Or, how about losing so many consecutive bets that your bankroll is in fact beyond recovery?

When you intend to gamble more than your bankroll (lol, whatever that means)...

This goes on every day in investing. A really simple concept.

...and stiff the bookie when you don't run well enough, the standard expected growth math doesn't apply when figuring out how much to bet, because it requires a positive bankroll at all times

Expected growth only requires a set of potential outcomes to be considered, including (a)the probabilities of each, and (b)the returns on each.

... (if you can't pay and will never pay either way if you lose, betting $100,000 and stiffing is clearly better than betting $50,000 and stiffing since it's just a freeroll). You can make up whatever utility function you want for how bad stiffing a bookie is going to be, but it has nothing to do with a player who can and will settle all losing wagers.

Again, if you deduce that the 0-100 event will NOT occur, then this does not need to be considered, right? I don't think "praying" is required on an event with probability 3.75E-32.

I really don't want to get involved again with this discussion in betting on margin, or in which theory misapplied contradicts reality. The point is simple: if one can deduce that 0-100 event will not happen, then there is no requirement to include it in one's expected growth calculation. If one insists that 3.75E-32 event should be considered, then that person would put that outcome in the calculation. However, we all know that 3.75E-32 event will NOT happen in this example.

[tomcowley]

You can't deduce that it won't occur any more than you can deduce that any of the other 2^100 - 1 outcomes won't occur. (well, slightly, but if these were coinflips at +106 instead, they would all be identical, instead of just being close). The odds of LLLLLLLLLLLLLLLLLLLLLLLLLLLLLL (in ROT# order) would be no different than the odds of WLLWLWWLWLWWLWLWLWLLWWWLLWLWLWL (in ROT# order). Any justification for excluding the LLLL... configuration applies equally to excluding any other particualr configuration as well- in other words, it's complete nonsense.

As far as investing goes, if you gamble "more than your bankroll" on margin and lose it all, you are not completely broke, due to bankruptcy laws. You still have some small amount of assets and the potential for future earnings- a positive bankroll- so by definition you haven't actually wagered more than your bankroll because you cannot lose more than your bankroll. The entity that extended the margin credit takes a laydown. Applied to gambling, if you could legally stiff with relatively small future consequences, but be sure you'd get paid if you won, then you would massively overbet your "bankroll" in a lot of situations. Of course, it would take a moron to be on the other side of those bets.

[BigCap]

You can't deduce that it won't occur any more than you can deduce that any of the other 2^100 - 1 outcomes won't occur. (well, slightly, but if these were coinflips at +106 instead, they would all be identical, instead of just being close). The odds of LLLLLLLLLLLLLLLLLLLLLLLLLLLLLL (in ROT# order) would be no different than the odds of WLLWLWWLWLWWLWLWLWLLWWWLLWLWLWL (in ROT# order). Any justification for excluding the LLLL... configuration applies equally to excluding any other particualr configuration as well- in other words, it's complete nonsense.

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.

As far as investing goes, if you gamble "more than your bankroll" on margin and lose it all, you are not completely broke, due to bankruptcy laws. You still have some small amount of assets and the potential for future earnings- a positive bankroll- so by definition you haven't actually wagered more than your bankroll because you cannot lose more than your bankroll. The entity that extended the margin credit takes a laydown. Applied to gambling, if you could legally stiff with relatively small future consequences, but be sure you'd get paid if you won, then you would massively overbet your "bankroll" in a lot of situations. Of course, it would take a moron to be on the other side of those bets.

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.

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.