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Questions and Answers / Re: Structured posts
« Last post by heatmap on Today at 01:20:35 AM »
@mickyp did you just assume my gender!? Jk I am not <- that <- type of person
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Roulette Strategy Discussion / Re: A Mathematican Speaks About Gambling
« Last post by Reyth on Today at 01:12:22 AM »
Here is a quote from Leonard C. MacLean† , Edward O. Thorp‡ , Yonggan Zhao§and William T. Ziemba¶:

But how do full Kelly and fractional Kelly strategies that blend with cash actually preform in practice?

To investigate this we revisit three simple investment situations and simulate the behavior of these strategies over medium term horizons using a large number of scenarios. These examples are from Bicksler and Thorp (1973) and Ziemba and Hausch (1986) and we consider many more scenarios and strategies.

The results show:

1. the great superiority of full Kelly and close to full Kelly strategies over longer horizons with very large gains a large fraction of the time;

2. that the short term performance of Kelly and high fractional Kelly strategies is very risky;

3. that there is a consistent tradeoff of growth versus security as a function of the bet size determined by the various strategies;

4. that no matter how favorable the investment opportunities are or how long the finite horizon is, a sequence of bad scenarios can lead to very poor final wealth outcomes, with a loss of most of the investor’s initial capital.

Hence, in practice, financial engineering is important to deal with the short term volatility and long run situations with a sequence of bad scenarios. But properly used, the strategy has much to commend it, especially in trading with many repeated investments.


Found here:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.225.4036&rep=rep1&type=pdf

An interesting strategy that has just occurred to me while reading this excellent paper, is to earn a "Kelly Bankroll" from profit and then attempt to use it to achieve "Kelly WealthTM", and then go back to regular betting and repeat. O_o

Maybe this is what they mean by "financial engineering"?

I definitely am a fan of the full Kelly because the divergence from the fractional Kelly's in total profit is truly immense!

Another excellent paper by some of the same authors:

http://onlinelibrary.wiley.com/doi/10.1002/9781119206095.app1/pdf

This quote is gold:

Logs abound in information theory and Kelly argued that maximizing the expected log of final wealth was a good idea. The idea of using log as a utility function was not new to Kelly and dates at least to Daniel Bernoulli in 1732. But Kelly, in an ad hoc math way, showed that it had good properties. Later Breiman (1960, 1961) cleaned up the math and showed the great long run properties:

1. Maximizing E log maximizes the rate of asset growth asymptotically, and
2. it minimizes the time to reach arbitrarily large goals.

This means that a log bettor, who is in competition with another bettor who bets differently infinitely often, will have arbitrarily more money than the other bettor as time goes to infinity.

So the longer you play, the better log is, but we know from Chapter 4 that in the short run, log betting is extremely risky. Indeed the Ziemba-Hausch (1986) example discussed in Chapter 2 shows that you can make 700 bets on assets with a 14 % advantage, all independent, all with chance of winning of 0.19 to 0.57 and turn $ 1000 into $ 18.

This is part of the Merton, Samuelson critique. Even if you play a long time and have a good advantage on every bet, you can still lose a lot.

But, Kelly advocates like I am point to the great gains most of the time and the corrective action that you can take should you have a sequence of bad scenarios and the fact that in practice trading is financial engineering not pure financial economics.


So my version of "financial engineering" is to obtain 3x one's table bank and then use 2 full table banks for Full Kelly. 

This will allow me to start doubling my bets much earlier and then allow me to incrementally raise my bets as by "Kelly BankrollTM" grows. :D

I currently already double & triple my bets (and even higher) but none of my betting is based on bankroll.
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Roulette Strategy Discussion / Re: A Mathematican Speaks About Gambling
« Last post by kav on Today at 12:37:20 AM »
About the Kelly Criterion I strongly suggest this book:
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Roulette Strategy Discussion / Re: A Mathematican Speaks About Gambling
« Last post by Reyth on Today at 12:10:08 AM »
Ya, I guess it went viral and since we are profiled by YT as roulette players, guess what shows up in the sidebar? XD
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Roulette Strategy Discussion / Re: Are Some Bets Worse Than Others?
« Last post by Reyth on Yesterday at 11:58:27 PM »
I wish it were that easy for me! :D

I know there are many people that do this easily, but I am unable. :'(

I have found that every selection will become hot at one point or another as part of its natural cycle and I have not found a way to look at these cycles with a short-term view and be able to tell the difference between a short-term cycle and one that will extend for 100's or even 1000's of spins; in other words, I don't know how to track the most recent spins reliably.

I have a certain "weakness" in roulette where I don't do well with existing losses on the books on a regular basis and I am not good at thinking-acting creatively. :(
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Roulette Strategy Discussion / Re: Are Some Bets Worse Than Others?
« Last post by Scarface on Yesterday at 11:30:28 PM »

The important thing to realize though, is that these hot selections do not always remain the hottest; roulette will EVENTUALLY correct the disparity.  But how does it do it?  With ANOTHER hottest selection!

Exactly!  Always stay with the most recent hottest.  Hot numbers can change, so you got to change with them.  Sometimes, if playing 4 or 5 numbers, at least 1 of these will stay hot for 200 spins or more.
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Roulette Strategy Discussion / Re: A Mathematican Speaks About Gambling
« Last post by Scarface on Yesterday at 11:25:34 PM »
That's crazy you posted this.  I watched this video 2 days ago.  Smart guy!
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Roulette Strategy Discussion / Re: A Mathematican Speaks About Gambling
« Last post by Reyth on Yesterday at 11:06:19 PM »
He was quoting a physicist from the 1950's, John Kelly:

https://en.wikipedia.org/wiki/John_Larry_Kelly_Jr.

Quote
John Kelly was a remarkable character. Apart from being a physicist he embodied certain stereotypical Texan character attributes being a tough guy, recreational gunslinger and a daredevil pilot all at the same time. He was also an associate of Claude Shannon at Bell Labs. Together they developed a Game theory type method based on the principles of information theory developed by Shannon.[6] It is reported that Shannon and his wife Betty went to Las Vegas with M.I.T. mathematician Ed Thorp, and made very successful forays in roulette and blackjack using this method, later called the Kelly criterion, making a fortune as detailed in the book Fortune's Formula by William Poundstone[7]

This Kelly Criterion type betting is what Real & Mr. Perfect do.

Here is Real's formula:

edge/expectancy x confidence level = percentage of bankroll

Mr. Perfect does this:

Quote from: Mr. Perfect
3 pound(number)  bet - 36 return, 30 pound bet -  360 return, 300 bet - 3600 return - go home. 3 bets placed...  15 min job, 3663 profit. 

I've lost so much, so many times, I can't think straight because I'm always scared to death! >.<
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Roulette Strategy Discussion / Re: A Mathematican Speaks About Gambling
« Last post by kav on Yesterday at 10:45:39 PM »
He obviously know his math.
But I get the idea he has never placed a bet (or traded) in his whole life q-)
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Roulette Strategy Discussion / A Mathematican Speaks About Gambling
« Last post by Reyth on Yesterday at 10:16:51 PM »
https://www.youtube.com/watch?v=658xlubwnDc

Wow.  Does:

Odds*Pwin-Plose
---------------
Odds

actually work??
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