[Ganchrow]

Originally Posted by abacus30

Your biggest play ever should still never exceed what % of your bankroll?

If you're look for an overly technical yet essentially meaningless answer rife with extended HTML character codes that may look impressive to the untrained eye, try this out for size:

For bets with win probabilities < 100% your biggest play as a fraction of bankroll should never exceed:

1-ε (where ε ∈ ℜ⁺ is defined such that ∀ δ ∈ ℜ⁺, ε < δ)

Putting it in equivalent terms, for bets not 100% guaranteed to win, you should always wager less than your entire bankroll.

While this might like a silly statement you really can't say any more than this given the information provided (and given highly atypical preferences, even that weak statement might be too strong a generalization).

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I think it fair to say that someone will eventually respond to this thread and unilaterally declare that one should never, ever, never wager more than 2% or 5% or 10% of bankroll. But make no mistake about it -- these number are completely meaningless and are based on the underlying realities of neither economics nor mathematics. (Of course precious few will ever proclaim that a bettor shouldn't ever wager more than (π² / e)% of bankroll, which would of course be no less arbitrary than any other similarly conceived precise all-purpose figure.)

No, to meaningfully answer a question like this you really need to know at least these 4 pieces of information:

1. the bettor's risk/return/etc. preferences,
2. the probability of the bet winning/losing/pushing,
3. the payout odds on the bet,
4. the details and cross-correlations of all the player's other bets and financial obligations

Still, for advantage players I think the simplest reasonable advice I could give would just be to treat a bet's Kelly stake as the upper, upper limit for that bet.

For recreational players, I could just recommend that under no circumstances should one ever, ever, ever bet more than (π⁴ / 17.83354)%, except on Tuesdays and the third Friday of every odd-numbered month, when that fraction can occasionally be bumped up to (π⁷ / 173,175.9)%.

But instead, if you're a recreational player, probably the best bet-sizing axiom is this: never ever never wager any more than you'd reasonably feel comfortable losing.

But a single catch-all number? That would either be disingenuous or plain foolish ... or perhaps some combination of both.