Collatz_Conjecture_Analysis_The_Odds_Against_The_Odds_Arata Okabe

This paper examines the mechanism by which any positive integer n eventually converges to 1 in the Collatz conjecture (3n + 1 problem), focusing on the asymmetry of the frequency of even and odd numbers within the sequence. Due to the characteristics of the Collatz map, the transition "Odd to Even" is mandatory, whereas the transition "Even to Even" remains possible. This study demonstrates that due to this structural property, the probability of the reduction operation exceeds that of the growth operation, causing the sequence to contract toward zero in terms of the geometric mean.