Really solid breakdown on the NPV of future income reframing Kelly. The paycheck example maks alot of sense when you think about it. I remeber when I was first starting out trading, I was way too conservative with position sizing because I only looked at my current balance, not the fact that I had a salary coming in every two weeks. The counterpoint worth mentionng tho is that most young people dont actually have stable income streams, especially in this job market. If the paychecks arent guaranteed or if theres a layoff risk, then the whole premise kinda falls apart and Kelly becomes way more relevant again.
yeah and also realistically you probably don't want to truly go to zero even if the check was guaranteed, but maybe more like some small amount such that you can cover rent, groceries, etc.
When your current bankroll represents no more than 4% of your total expected lifetime capital — equivalent to having at least 25 future re-ups — the Kelly criterion, applied to your full human capital, prescribes betting exactly 100% of the liquid stack.
As originally framed in the "52/48 coin flip" problem (even-money bet with p=0.52 probability of winning), the issue reduces precisely to treating your wealth as n consecutive stacks (or "re-ups") rather than a single closed bankroll.This follows directly from the Kelly formula for even-money bets:
f^ = 2p - 1 = 0.04* (with p = 0.52),
so the optimal bet is f^ × (n × K) = 0.04n × K*,
where K is the current liquid stack.The threshold is reached exactly when n ≥ 1 / f^ = 25*: the optimal bet becomes K (100% of the current stack).
For n > 25, the formula would prescribe more than 100%, but you are constrained to betting at most K — thus remaining at full commitment.
Betting any less in this regime is no longer prudent conservation; it is under-betting Kelly, quietly sacrificing long-term geometric growth
.The true risk lies not in exhausting a single stack, but in failing to swing boldly enough when the mathematics demands maximum leverage — especially since the probability of total ruin (losing all n stacks consecutively) decays exponentially as (0.48)^n, becoming astronomically low beyond n=20.
Really solid breakdown on the NPV of future income reframing Kelly. The paycheck example maks alot of sense when you think about it. I remeber when I was first starting out trading, I was way too conservative with position sizing because I only looked at my current balance, not the fact that I had a salary coming in every two weeks. The counterpoint worth mentionng tho is that most young people dont actually have stable income streams, especially in this job market. If the paychecks arent guaranteed or if theres a layoff risk, then the whole premise kinda falls apart and Kelly becomes way more relevant again.
yeah and also realistically you probably don't want to truly go to zero even if the check was guaranteed, but maybe more like some small amount such that you can cover rent, groceries, etc.
When your current bankroll represents no more than 4% of your total expected lifetime capital — equivalent to having at least 25 future re-ups — the Kelly criterion, applied to your full human capital, prescribes betting exactly 100% of the liquid stack.
As originally framed in the "52/48 coin flip" problem (even-money bet with p=0.52 probability of winning), the issue reduces precisely to treating your wealth as n consecutive stacks (or "re-ups") rather than a single closed bankroll.This follows directly from the Kelly formula for even-money bets:
f^ = 2p - 1 = 0.04* (with p = 0.52),
so the optimal bet is f^ × (n × K) = 0.04n × K*,
where K is the current liquid stack.The threshold is reached exactly when n ≥ 1 / f^ = 25*: the optimal bet becomes K (100% of the current stack).
For n > 25, the formula would prescribe more than 100%, but you are constrained to betting at most K — thus remaining at full commitment.
Betting any less in this regime is no longer prudent conservation; it is under-betting Kelly, quietly sacrificing long-term geometric growth
.The true risk lies not in exhausting a single stack, but in failing to swing boldly enough when the mathematics demands maximum leverage — especially since the probability of total ruin (losing all n stacks consecutively) decays exponentially as (0.48)^n, becoming astronomically low beyond n=20.