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() > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC http://friam-comic.blogspot.com/ -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders hpco...@hpcoders.com.au http://www.hpcoders.com.au ---------------------------------------------------------------------------- - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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