Blackjack Hack: A very simple ?, maybe harder answer!

[Blackjack Hack]

To anyone mathmatically inclined!

Given a $100,000 bankroll and wanting a mathmatically 0% ror. How do you bet to give maximum value in the real world? Please include when to raise and lower bets. If you need a real world game:
BJA3
page 244
table 10.58
BC prac 1-2

I believe it is fair to say that the answer of continuous proportional resizing would be incomplete.

I also imagine the answer would be something between continuous proportional resizing and 1/5 fixed Kelly.

I think there are many answers, can anyone come up with the mathmatically best?

Let the mud fly!

Thank you very much anyone who responds.

[Magician]

> To anyone mathmatically inclined!

> Given a $100,000 bankroll and wanting a mathmatically
> 0% ror. How do you bet to give maximum value in the
> real world?

What do you mean by a "mathematically" 0% ROR? Mathematically, full Kelly is 0% ROR. In the real world, 0% ROR is not possible.

[Blackjack Hack]

> What do you mean by a "mathematically" 0%
> ROR? Mathematically, full Kelly is 0% ROR. In the real
> world, 0% ROR is not possible.

Specifically, I used the term "mathematically" because I have read these statements:
1/4 Kelly fixed is a practical 0% (actually .03% in the authors table) ROR. The authors did say this was "quite subjective!"
1/5 Kelly fixed is the mathmatical, absolute? (insert your term) 0% ROR. According to these authors.

Simply put - 0% ROR!

I am trying to say as little as possible to foster an open discussion. I think I provided enough framework for real answers.

Maybe look at the question this way.

A technically competent player comes to you.
He says:
I have a $100,000 bank.
The game I am playing is on page 244 of BJA3 as stated previously.
I want a 0% ROR.
I want to make as much money as possible.

If it matters to the answer when considering long run I will hesitantly add he will average 2 hours a day of play. Anyone can include or exclude this in your answer as you wish or maybe give two answers.

Try not to ask him anything else! He wants a real answer!

[Blackjack Hack]

> To anyone mathmatically inclined!

> Given a $100,000 bankroll and wanting a mathmatically
> 0% ror. How do you bet to give maximum value in the
> real world? Please include when to raise and lower
> bets. If you need a real world game:
> BJA3
> page 244
> table 10.58
> BC prac 1-2

> I believe it is fair to say that the answer of
> continuous proportional resizing would be incomplete.

> I also imagine the answer would be something between
> continuous proportional resizing and 1/5 fixed Kelly.

> I think there are many answers, can anyone come up
> with the mathmatically best?

> Let the mud fly!

> Thank you very much anyone who responds.

I offer this incomplete sacrifice!

Start at full Kelly fixed bets.

If you lose 50% of your bank reset your bets down 50%. (reset to full Kelly fixed bets).

If you win 50% of your bank reset your bets up 50%. (reset to full Kelly fixed bets).

If you need to reset your bet in half at any time because of losing half your bank and you begin to win back to the 75% level then restore to your original bet. (Don's excellent thought)

Repeat as your bankroll fluctuates.

I believe the chance of winning 50% of your bank before losing half is 75%?

I believe if you are willing to cut your bet by half several times (anyone know how many?) if you continue to lose then your ROR is 0% or very very close!

I have no idea of the long run for this, does it matter?

According to the game example given a $100,000 bank the W/100 ($) is $203. I have no idea what this betting style does to this number? Obviously if you win you keep betting up and making more and if you lose you cut your bets and make less!

If anyone wants to flesh out the questions that I don't know I would appreciate it.

Obviously I am wondering if anyone can come up with something superior.

[Don Schlesinger]

> I believe it is fair to say that the answer of
> continuous proportional resizing would be incomplete.

Why? That's the best you can do. You can't grow your log-bank any faster. You can't reach any predetermined goal in a shorter time period, with zero ROR. Anything else is just a tradeoff, for practicality. There is no one answer to your question.

> I also imagine the answer would be something between
> continuous proportional resizing and 1/5 fixed Kelly.

Whatever makes you happy. Questions like yours just can't be answered. You need 1/5? Someone else is happy with 1/4, and its three-hundredths of one percent ROR. Are you seriously saying that this is too high for you? Do you see how the answer depends on whom we are speaking to?

> I think there are many answers, can anyone come up
> with the mathematically best?

What you're asking makes no sense.

Kelly has zero ROR and grows the bank the fastest. Everything else is sub-optimal. Pick your own poison.

Don

[Blackjack Hack]

> Why? That's the best you can do. You can't grow your
> log-bank any faster. You can't reach any predetermined
> goal in a shorter time period, with zero ROR. Anything
> else is just a tradeoff, for practicality. There is no
> one answer to your question.

> Whatever makes you happy. Questions like yours just
> can't be answered. You need 1/5? Someone else is happy
> with 1/4, and its three-hundredths of one percent ROR.
> Are you seriously saying that this is too high for
> you? Do you see how the answer depends on whom we are
> speaking to?

> What you're asking makes no sense.

> Kelly has zero ROR and grows the bank the fastest.
> Everything else is sub-optimal. Pick your own poison.

> Don

Wow, I think they are going to try to hack up the Blackjack Hack

Gulp! into the breach!

First, I want it to be known that I am not soliciting personal advice. I am of course interested in responses and may apply some principles learned.

Under responsible posting:
I think every response should include a form of the following statement:

"0% ROR in the real world is impossible!"

I will list some reasons:
No one is perfect, mistakes can be made in counting, playing of hands and proper bet management. You can be cheated, robbed, and lose money and chips. There are also many other possibilities!

I knew this when I started this thread!

On your general thoughts. I very strongly agree and disagree! LOL I set a framework for a real world question!

Ok, yes I know there are many answers; however, I imagine there are pros and cons to each answer?

Just because there is no one answer does not mean the question cannot be answered! You made me break out the eastern philosophy on you! LOL

If it is all subjective at some point. Ok, then what are the considerations involved in picking your own poison?

Yes, continuous resizing is the fastest way to grow your log bank. Is that the only consideration? Yes, anything else is just a tradeoff, are some better then others? What are the tradeoffs? What are the pros and cons? I have read and my little subjective opinion is that continuous resizing is not practical in the real world! So it is off the table! I don't think that is unreasonable!

The floor. If 1/5 fixed Kelly is considered by many a 0% ROR then to set that as a floor is not unreasonable. If I had set the floor at 1/10 fixed Kelly then I am sure many would think that is redundant.

If 1/5 fixed Kelly is the floor then that does not mean 1/4 or 1/3 is off the table! If someone's answer is "I think it is fixed 1/4 because that is a practical 0% (actual .03%) ROR" then that is an answer, especially if they wish to give pros and cons and further flesh out their thoughts! However, how should one consider an answer that does not include a 0% ROR if that is the question?

On wanting the ROR to be 0%. I think many people in the real world would not consider a 0% or very very low ROR a foolish or timed consideration!

If we have a impractical continuous resizing theory of 0% ROR and a 1/5 fixed Kelly theory of 0% ROR then the answer for my questions incorporating 0% ROR is not unreasobable!

If applying theory to real world you are going to be off by a certain amount for whatever reasons then I would rather be incorrect trying to employ a 0% ROR then trying to emply a .03, 1, or 5% ROR. So for fudge or safety factors trying to achieve a 0% ROR is very realistic and responsible!

A thought experiement:
I bet if you tried you could come up with a not very good way to achieve a 0% ror. I will take a shot at it! The person is very wreckless with a certain portion of their bankroll! They then take the shattered remains and bet so that the global ROR is 0%, however their wrecklessness has hurt them greatly!

Another thought experiment:
Think of the top 10 people in the BJ community that you respect. I would put you in that group so you can add yourself Now lock them in separate rooms with their computers, programs, abacus, pooka beads whatever they need to come up with an answer given the stated framework of the question. Do you really think they will all have the same exact scribles on their papers? Yet I can see that each one could consider all the other answers correct in one form or another!

I think those that are more theoritically inclined will state their theories. While those with "steet cred" (playing experience) LOL would give more practical considerations to their answers.

Thank you for your response. I have locked you in a room without a bathroom break! LOL

Ding Ding
The BlackJack Hack came out swinging on that round! How do the judges score the card! LOL

[Parker]

> "0% ROR in the real world is impossible!"

It is not only possible, it is quite simple.

Here is the secret to 0% ROR:

Don't play.

[Blackjack Hack]

> It is not only possible, it is quite simple.

> Here is the secret to 0% ROR:

> Don't play.

I was wondering how long it would take for this answer! LOL.

But what about long run considerations! LOL

I am not sure but I think 1/20 fixed Kelly is superior. In my humble opinion! LOL

[black jack hack]

> I offer this incomplete sacrifice!

> Start at full Kelly fixed bets.

> If you lose 50% of your bank reset your bets down 50%.
> (reset to full Kelly fixed bets).

> If you win 50% of your bank reset your bets up 50%.
> (reset to full Kelly fixed bets).

> If you need to reset your bet in half at any time
> because of losing half your bank and you begin to win
> back to the 75% level then restore to your original
> bet. (Don's excellent thought)

> Repeat as your bankroll fluctuates.

> I believe the chance of winning 50% of your bank
> before losing half is 75%?

> I believe if you are willing to cut your bet by half
> several times (anyone know how many?) if you continue
> to lose then your ROR is 0% or very very close!

> I have no idea of the long run for this, does it
> matter?

> According to the game example given a $100,000 bank
> the W/100 ($) is $203. I have no idea what this
> betting style does to this number? Obviously if you
> win you keep betting up and making more and if you
> lose you cut your bets and make less!

> If anyone wants to flesh out the questions that I
> don't know I would appreciate it.

> Obviously I am wondering if anyone can come up with
> something superior.

If my math is correct?

Fixed Kelly ROR compared to resizing at half stakes ROR.

Fixed Kelly:

Each level is fixed. You continue to bet the same amount.

Fixed Kelly = 13.53%

1/2 Fixed Kelly = 1.83%

1/3 Fixed Kelly = .24%
(1 in 416 chance of going broke)

1/4 Fixed Kelly = .03%
1/4 subjectively considered 0% ROR (1 in 3333)

1/5 Fixed Kelly = .004%

Now resizing at half stakes:

You resize at every 50% loss level. Every time you lose half your bank you resize your bets by half. You have about a 75% chance of winning 50% of your bank before losing 50% of it.

Cut in half one time = 4.97% ROR

1.5 times = .67% (You cut your bank in half only once, after that you would resize to Kelly if needed)

2 times = .24% (1 in 416 chance of going broke)

2.5 times = .03% (1 in 3333)

3 times = .012

3.5 times = .001%

Notice that the two following ROR's are the same:

1) If you cut to half stakes twice compared to fixed 1/3 Kelly both have a ROR of .24%. Any thoughts on which is superior?

2) If you cut to half stakes 2.5 times compared to fixed 1/4 Kelly both have a ROR of .03 (practical 0% ROR). Any thoughts on which is superior?

In the literature I have read I come across what appears to be 2 extremes:
1) Resizing constantly
2) Fixed

I am trying to foster thoughts and discussion on what is in between.

I am expanding on (maybe to the point of lunacy LOL) a simple paragraph in BJA3 pg. 115, 2nd paragraph.

I believe pros and cons of each system when establishing a similar ROR are:
A pro of the 50% system. You are making large bets in relation to your total bankroll, you may be able to bet and earn at higher rates.
The con is longer time horizon to any certainty level of winning.
or simply said!
The potential for big SD swings and big earnings or losses.

A pro of the fixed system is shorter time horizon for a certinty level of winning.
A con of the fixed system is because of smaller bets in relation to your bankroll your earnings may be lower.
or simply said!
The potential for small swings and smaller earnings or losses.

Any thoughts or comments on long run considerations?
I understand the more frequent you resize the faster your log growth of bank but the longer you must play to achieve any certain level of winning.

Effects of hourly expectation when cutting stakes?

Real world applications?
One is if your bankroll is small it may be difficult to cut your stakes several times and be able to continue to play due to table minimums. However, just cutting it more then once or twice if needed should be sufficient.

Another is both are easy to employ whether you never resize or resize at 50% intervals.

Remember: In the real world probably quite impossible to have 0% ROR. Only bet what you can afford to lose!

[Don Schlesinger]

I don't have to the energy to answer all of your questions, but I continue to be baffled by one statement that you keep making, which is obviously false:

"I understand the more frequent[ly] you resize the faster your log growth of bank but the longer you must play to achieve any certain level of winning."

What sense does that make? If your bankroll grows faster using "pure" Kelly, how could the above be true? Here is what Ed Thorp writes, in "The Mathematics of Gambling," p. 127:

"The thrid desirable property of the Kelly system is that you tend to reach a specified level of winnings in the least average time. For example, suppose you are a winning card counter at blackjack, and you want to run your $400 bankroll up to $40,000. The number of hands you'll have to play on average to do this will, using the Kelly system, be very close to the minimum possible using any system of money management."

So, why do you keep saying just the opposite? Am I misunderstanding your point?

Don

[Wolverine]

> I am not sure but I think 1/20 fixed Kelly is
> superior. In my humble opinion! LOL

My worthless opinion: **IF** you have enough bankroll (thousands of dollars) to play at a high limit table and have an expectation of $100 per hour (betting blacks, and with 'acceptable' ROR%), why would you cut the risk to 0% but only manage to (possibly) make $5 per hour (in the long run) by playing reds? I see 0% risk in finding a minimum wage job, collecting over $5 per hour, **AND** managing to stash my bankroll in an investment that will return 5% (or more) over the long run. I have yet to find an employer that asks for their paycheck back, once they have given it to you. Not so in the fluxuations of blackjack. You want 0% risk? Then collect a paycheck, or park your bankroll in an FDIC insured savings account.

RISK=REWARD in ANY endeavor.

[Black Jack Hack]

> I don't have to the energy to answer all of your
> questions, but I continue to be baffled by one
> statement that you keep making, which is obviously
> false:

> "I understand the more frequent[ly] you resize
> the faster your log growth of bank but the longer you
> must play to achieve any certain level of
> winning."

> What sense does that make? If your bankroll grows
> faster using "pure" Kelly, how could the
> above be true? Here is what Ed Thorp writes, in
> "The Mathematics of Gambling," p. 127:

> "The thrid desirable property of the Kelly system
> is that you tend to reach a specified level of
> winnings in the least average time. For example,
> suppose you are a winning card counter at blackjack,
> and you want to run your $400 bankroll up to $40,000.
> The number of hands you'll have to play on average to
> do this will, using the Kelly system, be very close to
> the minimum possible using any system of money
> management."

> So, why do you keep saying just the opposite? Am I
> misunderstanding your point?

> Don

Wow, I must have you frustrated to take the time to look up a quote, though you may have it memorized! LOL

Belive me I am probably more frustrated with myself then you are with me.

I am sure it's obvious your formal math training far exceeds mine. So I do realize I am the pupil in this discussion. You have corrected me on terminology more then once when I have tried to convey a concept.

I agree 100% with the above quote.

Perhaps this will help me either figure out where I am mistaken or to help clarify my thoughts.

BJA3
page 21
table 2.2
Probably of Being Ahead after N Hours of Play

I belive this table is considering fixed bets?

You mention the table assumes you have enough money to continue to play?

So can we assume 1/4 or 1/5 fixed Kelly (0% ROR, or close)?

If the above is true then if you changed the betting style to continuous resizing would the number of hours go up or down?

or if the table is already considering continous resizing then how would fixed resizing affect it?

Thanks for your near exhausted patience!

[Don Schlesinger]

> Wow, I must have you frustrated to take the time to
> look up a quote, though you may have it memorized! LOL

I have it memorized, I know what page it's on in Thorp's book, and I can usually find it in about ten seconds. :-)

> Belive me I am probably more frustrated with myself
> then you are with me.

Difficult to conceive. :-)

> I agree 100% with the above quote.

Thorp will be pleased. :-)

> Perhaps this will help me either figure out where I am
> mistaken or to help clarify my thoughts.

> BJA3
> page 21
> table 2.2
> Probably of Being Ahead after N Hours of Play

> I belive this table is considering fixed bets?

It considers a style of play (whatever it may be) that yields the specified win rate and standard deviation. The latter two are the only variables to plug into the equation to determine the probability of being ahead after n hours of play. The style(s) of play that created those e.v.s and s.d.s doesn't matter.

> You mention the table assumes you have enough money to
> continue to play?

Right. You have to play the specified number of hours, and you can't do that if you run out of money.

> So can we assume 1/4 or 1/5 fixed Kelly (0% ROR, or
> close)?

No, not at all. You assume whatever style of play created those e.v.s and s.d.s. In my case, it was probably full Kelly stakes at the start, with no resizing. If we ran out of money, somneone leant us some more. The concept has nothing to do with ROR; we were simply trying to find out if we'd be ahead after n hours. It was a given that we had enough money to complete the experiment.

> If the above is true then if you changed the betting
> style to continuous resizing would the number of hours
> go up or down?

I imagine it would go down, if I'm understanding Thorp correctly, but, frankly, I've never given it any thought, because no one ever plays that way.

> or if the table is already considering continous
> resizing then how would fixed resizing affect it?

See above.

> Thanks for your near exhausted patience!

I'm trying.

Don