Not sure I understand the question. Consider a bet that looks like this:

Start with 100 EUR

At each period, toss a fair coin. Heads => your money goes up 50%. Tails => your money goes down 40%.

Averaging over a large number of people playing the bet N
times, the value of this bet is the (traditional) expected value of its payoff, i.e. 100 x (1. 0.05)^N
. Your wealth grows exponentially at a 5% rate.

Averaging over a long time, the value of this bet is 100: you lose all your wealth.
Peters uses it to explain loss aversion, currently thought to be a deviation from perfect rationality.
I have cobbled up some Python code to try it. The range of 1000, of course, can be replaced with anything. If you want a biased coin, you can enter the odds you want as an argument of the coinToss()
function.
import random
def coinToss(odds=0.5):
'''
(float ) => bool
returns True with probability equal to odds
'''
flip = random.random()
if flip > odds:
return True
else:
return False
wealth = 100
for i in range(1000):
toss = coinToss()
if toss == True:
wealth += wealth * .5
else:
wealth = wealth * .4
print wealth
An interesting question is which trend is stronger. What happens when you average a large population, each member of which averages over a long time? Increasing the size of the population makes the average payoff go up; increasing the time duration of the bet makes each individual payoff go down. Which of the two trends is stronger?
I played with incorporating this code into various loops. In the end, a totally nonscientific, backoftheenvelope test was this:
 Take 10 populations of 10,000 people starting with a wealth of 1.
 Make everyone play the Peters bet for N periods.
 At the end of each N, count the number of people that ended up with more than 1, i.e. more than their initial endowment.
 Let the model run for
N = 100
, then N = 1,000
, then N = 10,000
.
Results:
number of time periods: 100
Average of average outcomes across all populations: 42.161242451
Average number of people who increased their wealth across all
populations, normalized for population size: 0.1349
Expected value of the bet: 131.501257846
***********************
number of time periods: 1000
Average of average outcomes across all populations: 2.76743582216
Average number of people who increased their wealth across all
populations, normalized for population size: 0.00015
Expected value of the bet: 1.54631892073e+21
**********
number of time periods: 10000
Average of average outcomes across all populations: 2.42586953452e149
Average number of people who increased their wealth across all
populations, normalized for population size: 0.0
Expected value of the bet: 7.81611065843e+211