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Author Topic: A Mathematican Speaks About Gambling  (Read 240 times)

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Reyth

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A Mathematican Speaks About Gambling
« on: November 18, 2017, 10:16:51 PM »
https://www.youtube.com/watch?v=658xlubwnDc

Wow.  Does:

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

actually work??
« Last Edit: November 18, 2017, 10:27:27 PM by Reyth »


 
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kav

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Re: A Mathematican Speaks About Gambling
« Reply #1 on: November 18, 2017, 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-)
« Last Edit: November 18, 2017, 10:51:21 PM by kav »
 
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Reyth

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Re: A Mathematican Speaks About Gambling
« Reply #2 on: November 18, 2017, 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! >.<
« Last Edit: November 19, 2017, 12:26:48 AM by Reyth »
 

Scarface

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Re: A Mathematican Speaks About Gambling
« Reply #3 on: November 18, 2017, 11:25:34 PM »
That's crazy you posted this.  I watched this video 2 days ago.  Smart guy!
 
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Reyth

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Re: A Mathematican Speaks About Gambling
« Reply #4 on: November 19, 2017, 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
 

kav

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Re: A Mathematican Speaks About Gambling
« Reply #5 on: November 19, 2017, 12:37:20 AM »
About the Kelly Criterion I strongly suggest this book:
 
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Reyth

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Re: A Mathematican Speaks About Gambling
« Reply #6 on: November 19, 2017, 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.
« Last Edit: November 19, 2017, 02:18:00 AM by Reyth »
 
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vitorwally

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Re: A Mathematican Speaks About Gambling
« Reply #7 on: November 19, 2017, 09:51:54 AM »
I already seen this video in the past too. If correctly applied the Kelly Criterion can be used in all kinds of gambling, not only roulette. That's why I have it in my bookmarks for whenever I want to apply it. But I'll have to agree with Kav. One thing is tossing coins, which should have no "adulteration" or some kind of house edge like roulette, another is playing a game with a stated house edge. By the way, the Q&A is also a good watch as well. It led me to some laughs because first I took some seconds to read the comments and they're indeed good spoilers of the funny moments of the video.
 
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MrPerfect.

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Re: A Mathematican Speaks About Gambling
« Reply #8 on: November 19, 2017, 01:27:47 PM »
Kelly is very agressive betting criteria.  People can vomit while using it. Big swings of bank up and down require balls to endure. It's " Russian hills" multiplied by 10!!!
   Besides everything it require very precise edge estimation, as both up and down swings are maximised ( comparing with flat bet ), user may encounter situation where he enter the game when down swing is expected....  proper math is your friend.
    To smooth it out a bit, additional ratio " confidence" ( expressed as %) can be used.
    As with everything,  common sense is due, playing with 10% advantage require very different money management as playing with 40%. Higher the edge, less risky it become, less time is needed to arrive where your edge dominate possible math fluctuations.  That's why looking for a higher edge is mandatory for a serious player.
 
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