The Gambler's Ruin Problem: Is Betting Mathematically Impossible Without Infinite Bankroll?

[Klaus]

Question for serious discussion: Gambler's Ruin problem.

Mathematical theorem states: even with positive edge, bettor with finite bankroll betting against infinite bankroll (house) will eventually reach ruin with probability approaching 100%.

Does this mean sports betting mathematically impossible long-term regardless of skill?

Interested in community thoughts on this probability theory application.

 

[SharpEddie47]

This is a great question Klaus and one that kept me up at night when I first learned about it.

The short answer: yes, gambler's ruin is real. But Kelly Criterion provides the solution.

If you bet a fixed percentage of bankroll (never fixed dollar amounts), your bankroll can't reach zero. It approaches zero but never gets there mathematically.

That's why percentage-based betting is crucial.

 

[ThePuntingProf]

This is an excellent topic that goes to the heart of sustainable betting methodology and I must say Klaus has identified the central paradox that all serious bettors must confront, the gambler's ruin theorem mathematically proves that a bettor with finite resources betting against an opponent with infinite resources will inevitably reach bankruptcy even when possessing a positive edge, this seems to suggest that sports betting is ultimately futile regardless of skill level, however the Kelly Criterion which was developed by John Kelly at Bell Labs in 1956 provides an elegant solution to this problem, Kelly demonstrated that by betting a fraction of one's bankroll proportional to one's edge rather than fixed amounts one can optimize growth while theoretically avoiding ruin, the formula is quite simple, optimal bet fraction equals edge divided by odds, so if you have a five percent edge on even money bet you should wager 2.5 percent of your bankroll, the mathematical beauty of Kelly betting is that because you always bet a percentage you never quite reach zero, half of something is never nothing, Margaret and I used Kelly Criterion for twenty years and while we experienced significant drawdowns we never approached actual ruin, the key is strict discipline in recalculating bet size as bankroll fluctuates which most bettors find psychologically difficult when variance goes against them.

 

[TaffyTipster]

Prof wrote a proper essay there.

Good one though.

So basically bet a percentage not a fixed amount and you can't go broke?

 

[SharpEddie47]

That's the theory Taffy, yes.

In practice you need discipline to actually reduce bet size when you're down, which is when most bettors want to increase stakes to get even.

 

[oli_sussex]

Kelly Criterion mathematically optimal. Maximizes long-term growth, minimizes ruin risk.

Most bettors don't follow it. Ego and impatience override math.

 

[ParlayPrincess_88]

Wait I'm confused. What's the Gambler's Ruin thing?

Can someone explain in simple terms?

 

[CoachTony_Bets]

Princess imagine you flip a coin against a casino.

You have $100. Casino has $1,000,000.

Even if it's a fair coin (50/50), you'll eventually lose all your money before the casino loses theirs.

That's gambler's ruin - limited money versus unlimited money, you always lose eventually.

 

[ParlayPrincess_88]

Ohhh that makes sense! So we're all gonna go broke eventually?

That's depressing!

 

[Klaus]

Not if betting strategy accounts for ruin probability.

Kelly Criterion solution: bet size as percentage of current bankroll.

If bankroll = $1000, bet 2%.
If bankroll drops to $500, bet 2% of $500.

Never reach absolute zero mathematically.