3 ms·

> # ... so they should end up with ~1.2e1000 at the end... Who has ever claimed this? Also, people end up with zero because you are doing integer division in y

by ulucs 6y ago

> # ... so they should end up with ~1.2e1000 at the end... Who has ever claimed this? Also, people end up with zero because you are doing integer division in your code (ie the simplified expected return is wrong). Here are my results with 100 bets, and 10000 bet takers. The average return is also on the upward trend, but not really close since CLT doesn't really apply to this distribution: >>> sum(balances)/1000000 24546192.840913434 >>> print(len([x for x in balances if x<=100])) 5426 >>> print(len([x for x in balances if x>=100])) 5381 >>> print(len([x for x in balances if x>100])) 4574

nullc 6y ago
Keeping it integer specifically was useful to avoid running out of precision using Python's multi-precision integers. You can show ruin without any flooring division: #!/usr/bin/sage import random balances=[Rational(100)]*100 for i in range(10000): balances=[0 if x<=0 else random.choice([x*2+2,x/2-1]) for x in balances] #Yet all or almost all are bankrupt: print(len([x for x in balances if x<=0])) The key points are that there is a state that a participant can't recover from (e.g. ending up bankrupt) and you do enough trials that are reasonably likely to eventually wander into it. One that is the case 100 bets with 10000 betters and 10000 bets with 100 betters stop being the same thing. And this is a very realistic and physical assumption because real investments have integerization, fees, overheads, etc. You can't invest a femto-cent in the market, and certainly not get the same relative returns as someone investing 100k.
- ulucs 6y ago
  But that's factored in EUT anyway: you simplify the compound lottery and it turns out you have a huge probability of hitting zero. You might ask whether people will take the bet, and that's where the utility comes in. Enough risk averseness, and noone will take a return of a million dollars with a 1% chance of happening at a price of 100%

by ulucs 6y ago

nullc 6y ago

Keeping it integer specifically was useful to avoid running out of precision using Python's multi-precision integers. You can show ruin without any flooring division: #!/usr/bin/sage import random balances=[Rational(100)]*100 for i in range(10000): balances=[0 if x<=0 else random.choice([x*2+2,x/2-1]) for x in balances] #Yet all or almost all are bankrupt: print(len([x for x in balances if x<=0])) The key points are that there is a state that a participant can't recover from (e.g. ending up bankrupt) and you do enough trials that are reasonably likely to eventually wander into it. One that is the case 100 bets with 10000 betters and 10000 bets with 100 betters stop being the same thing. And this is a very realistic and physical assumption because real investments have integerization, fees, overheads, etc. You can't invest a femto-cent in the market, and certainly not get the same relative returns as someone investing 100k.

ulucs 6y ago
But that's factored in EUT anyway: you simplify the compound lottery and it turns out you have a huge probability of hitting zero. You might ask whether people will take the bet, and that's where the utility comes in. Enough risk averseness, and noone will take a return of a million dollars with a 1% chance of happening at a price of 100%