If I, 24 years old living in the US, believe in a risky investment, say identifying a severely undervalued stock or going long on a put option, is there a rule of thumb for how much I should be investing in this? Perhaps X percentage of my liquid holdings? The reward is large because of the risk, which would be the full X percentage of the total. Is there a rule of thumb for this sort of thing, in the way that there are rules of thumb for car and house purchases or spend/savings splits?
There are all kinds of rules about asset allocation and they involve time horizon and risk tolerance.
If you're young, your time horizon is long and you can invest more aggressively. It's based on your age which everyone knows :->)
Risk tolerance is more subjective because it's a personal decision. If you're young, your time horizon suggests that you can be more aggressive but you may not feel comfortable doing so. The rule of thumb is that you risk as much as you can tolerate losing. That number is different for everyone.
I think this is too personal of a question, since only you know how much you are comfortable losing.
I would first validate whether I have an adequate Rainy Day fund, am funding my 401(k) at 12%+, saving for a house, and have reserve funds for auto replacement, vacation, insurance deductibles, etc.
After all that, ask yourself how much you could throw in a bonfire without impacting your life.