[FRIAM] The Gambler and the Academic

Tue Sep 1 18:25:56 EDT 2020

I'm pretty sure what's being talked about is "Gambler's Ruin"
(https://en.wikipedia.org/wiki/Gambler's_ruin) a paradoxical result
where infinite wealth will always win out, even when the odds are
stacked against. I see from the Wikipedia article, that this has been
known about since Blaise Pascal's time. I remember it being discussed
in my undergraduate stats course, so the "Academic" in this piece
seems remarkably ill-informed.

Cheers

On Tue, Sep 01, 2020 at 12:17:57PM -0700, uǝlƃ ↙↙↙ wrote:
> 
> >From the most recent Reasoner (http://www.thereasoner.org/). I didn't cutnpaste the code. My edited code is attached. If you run it, you see that most of them gain back their losses within 100 bets. It would be fun to run some sweeps looking for edge cases. For non-programmers, the code is super easy to read and try out: https://ideone.com/UjvIej
> 
> > Gambler: I find my self in a bit of a hole. I’ve lost 1,000 units.
> > Academic: Well that’s a shame. Stop gambling!
> > Gambler: On the contrary, I will keep gambling and dig myself out of this hole!
> > Academic: That’s not how it works.  Bets have a negative expected value.  That means that you will simply fly off to negative infinity as you bet more and more.
> > Gambler: You clearly haven’t spent much time around gam-blers.  Every gambler always gets out of the hole, unless they run out of money first.
> > Academic: You are an odd creature, O Gambler. What you say cannot be true.
> > Gambler: Record my loss as -1,000.  I will bet 55% of (the absolute value of) my bankroll to win 50%, as that is how gambling works. You bet 110 to win 100, or multiples thereof. Thus my first bet will be to either lose 550 units or win 500units.  That brings my bankroll to -1550 or -500.  I’ll keep betting 55% of my bankroll to win 50%, and get out of debt.
> > Academic: You are a fool. You will lose ever more if you persist in your plan.
> > Gambler: Very well then.  Let us imagine 1,000 gamblers in my position, each planning to undertake 1,000 bets.  You believe that most gamblers will wind up with less than -1,000 units after 1,000 bets?
> > Academic: I do. Starting at -1,000 and losing means that most gamblers will wind up at less than -1,000.
> > Gambler: I have run the experiment!  Every single one of the 1,000 gamblers ended up making over 99.9% of the 1,000 unit debt.  Every single gambler got out of debt by making almost all of the 1,000 units, even though every single bet had a negative expected value.
> > Academic: That cannot be correct.
> > Gambler: It is. As yours is a common reaction, I will share Python code so you can run the experiment yourself.  You, O Academic, for 350 years have focused on the long run average effects of a single, repeated bet. You have not paid much attention to path dependent sequences of bets.  You also have not spent much time around gamblers, who bet more whenthey lose because they are rational and know, on some level, that it will get them out of debt.
> > Academic: I believe none of this.
> > Gambler: Very well. Let me leave you, O Academic, with two items. The first is a paper by Ole Peters (2019: The
> > ErgodicityProblem in Economics, Nature Physics, 1216-1221). In it, hepoints out that sequences of positive expected value coin flips can have bad outcomes for almost everyone (see, in particular,Figure 2).  A flip around 0 to the negative numbers gets you to good outcomes in negative expected value environments. The second item I will leave you with is the code that I promised you.  It prints out the outcomes of each Gambler’s 1,000 bets. Note that a move from -1,000 to 0 is a gain of 1,000 units. On almost every run every gambler gets out of debt, that is, thecode prints "0" 1000 times.
> > Academic: I will study these, wise Gambler.
> > Gambler: Very well.  A final thought.  It is not hard to realize that if money can be made in a negative expected value environment by gamblers in debt, then money can be made in a negative expected value environment by anyone.  Perhaps an enterprising person or two moves from the betting world to a setting where money can be sloshed around (in an intelligent, path dependent manner) with less vigorish.
> > Academic: I do not follow. Come to think of it, I am also having trouble seeing how your points, Gambler, differ from the paper cited above.
> > Gambler: If you do not see the difference between losing money (in a positive expected value environment) and gaining money (in a negative expected value environment), then I gain confidence that I am talking to a true Academic! The following is Python code that simulates 1,000 Gam-blers each running 1,000 Bets.  Each bet either loses 55% (which is multiplying a negative number, the Bankroll, times 1.55) or wins 50% (which is multiplying the Bankroll times 0.5).
> > 
> > Jeremy Gwiazda
> 
> 
> -- 
> ↙↙↙ uǝlƃ

> import random
> Gamblers=100
> Bets=100
> Bankrolls=[]
> for i in range( Gamblers ) :
>     Bankroll = []
>     x = -1000
>     Bankroll.append(x)
>     for j in range( Bets ) :
>         CoinToss = random.randint ( 0 , 1 )
>         if ( CoinToss == 0 ) : # a  l o s s
>             x *= ( 1.55 )
>         elif ( CoinToss == 1 ) : # a win
>             x *= ( 0.5 )
>         Bankroll.append(int(x))
>     Bankrolls.append(Bankroll)
> 
> for row in Bankrolls:
>     for col in range(0,len(row),10):
>         print(format(row[col], "7d"),end=', ')
>     print()

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