The Volatility Tax:
Sequence Risk & Ergodicity Breaking
Why "Average Returns" are a mathematical lie in High-Frequency Algorithmic Greyhound Markets.
Abstract
This interactive report defines the conflict between Ensemble Average (the market's theoretical return) and Time Average (a single trader's realized return). In "Non-Ergodic" systems like betting markets, a strategy can be profitable on average across 1,000 parallel universes, yet bankrupt a single trader in reality due to Sequence of Returns Risk.
1. The Ergodicity Conflict
In an Ergodic system, the average outcome of a group (Ensemble) is the same as the outcome of an individual over time. Betting markets are Non-Ergodic.
Explore the difference below. The Grey Lines represent the "Ensemble" (many traders). The Black Line is YOU. Notice how you can go bust even if the "average" trader survives.
Key Concept
Ensemble Average:
$\frac{1}{N} \sum x_i$
(Snapshot of everyone)
Time Average:
$\lim_{t \to \infty} \frac{1}{t} \sum x(t)$
(Your actual bankroll)
Simulated coin flips. 50% Win (+50%), 50% Loss (-40%). Expected Value is Positive (+5%), but Time Average is Negative (-10%).
2. The Volatility Tax (Gravity Well)
Losses are not linear; they are geometric. A 50% loss requires a 100% gain just to break even. This asymmetry creates a "Volatility Tax" that drags down compounded returns. In algorithmic betting, this is the Absorbing Barrier.
?? The Ruin Calculator
Required Recovery Gain
3. Sequence Risk in High-Velocity Markets
In Greyhound Lay Betting, races occur every 10 minutes. This high velocity compresses Sequence Risk. A traditional stock trader faces a bad year; an algo-bettor faces a "bad afternoon" that contains the same statistical variance.
- The Early Luck Paradox: A bad sequence at the start of an algorithm's life is 5x more destructive to capital than the same sequence occurring after 1,000 bets.
- Capital Sensitivity: If you lose 30% of your bankroll on Day 1, your stake size (and profit potential) shrinks immediately.
The 'Martingale' Trap
Many lay bettors attempt to fix Sequence Risk by "Chasing Losses" (Martingale). This creates Negative Skew.
*In a non-ergodic world, the market can remain irrational longer than you can remain solvent.
4. Strategy Comparison Engine
Test the defenses. Run a simulation of 100 bets using different staking methods. Observe how they handle a randomized sequence of wins and losses.