My naive attempt to reverse distribution of "second guessers" based on result from Thaler guessing game

thaler.py

#!/usr/bin/env python3

"""
Thaler guessing game
---------------------

https://en.wikipedia.org/wiki/Guess_2/3_of_the_average

Guessing how much people guess ahead?

> When performed among ordinary people it is usually found that the winner
> guess is much higher than 0, e.g., 21.6 was the winning value in a large
> internet-based competition organized by the Danish newspaper Politiken.
> This included 19,196 people and with a prize of 5000 Danish kroner

Result
-----

* 26% ppl think 1 step ahead
* 35% ppl think 2 step ahead
* 24% ppl think 3 step ahead
* 10% ppl think 4 step ahead


Detail log
-----------

```
# 10% migration
Avg: 22.46337448559671 Seq: [316, 347, 207, 90, 40]
Avg: 21.69012345679012 Seq: [285, 341, 220, 103, 51]
Avg: 20.949382716049378 Seq: [257, 333, 231, 116, 63]
Final Avg: 20.949382716049378 Seq: [257, 333, 231, 116, 63]
```

```
# 5% migration
Avg: 22.235390946502054 Seq: [298, 355, 221, 94, 32]
Avg: 21.87572016460905 Seq: [284, 351, 228, 100, 37]
Avg: 21.511111111111106 Seq: [270, 347, 234, 107, 42]
Final Avg: 21.511111111111106 Seq: [270, 347, 234, 107, 42]
```

```
# 2% migration
Avg: 21.686831275720163 Seq: [271, 352, 243, 106, 28]
Avg: 21.548148148148147 Seq: [266, 350, 245, 109, 30]
Final Avg: 21.548148148148147 Seq: [266, 350, 245, 109, 30]
```
"""

import math

RATIO = 2/3
TOP_GUESS = 5
GUESTS = 1000
TARGET_AVG = 21.6
STEP = 0.02

SEQ = [50 * math.pow(RATIO, i) for i in range(1, TOP_GUESS+1)]

def cal_avg_for_order(number_of_guesses_for_each_step):
    # assuming that there are more intelligent guests than non-intelligent
    assert len(number_of_guesses_for_each_step) == TOP_GUESS
    sum_of_guesses = 0
    for o,s in zip(number_of_guesses_for_each_step, SEQ):
        sum_of_guesses += o*s
    return (sum_of_guesses / GUESTS)

def make_smarter(seq):
    for i in reversed(range(len(seq)-1)):
        diff = math.floor(seq[i] * STEP)
        seq[i] -= diff
        seq[i+1] += diff
    return seq

if __name__=='__main__':
    print("Sequence: {}".format(SEQ))

    # Test the average
    current_sequence = [1000,0,0,0,0]
    current_avg = cal_avg_for_order(current_sequence)
    print("Start avg - assuming 1 degree cleverness: {}".format(current_avg))
    assert 33 < current_avg < 34

    while current_avg >= TARGET_AVG:
        current_sequence = make_smarter(current_sequence)
        current_avg = cal_avg_for_order(current_sequence)
        print("Avg: {} Seq: {}".format(current_avg, current_sequence))

    print("Final Avg: {} Seq: {}".format(current_avg, current_sequence))