>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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