The mathematics
of ruin
One percent sounds like nothing. Charged on every bet, compounding over a playing career, it decides the outcome before you sit down. Duel published a table making that case. We reran all fifteen cells to check it.
The setup
A player with a million-dollar bankroll betting ten thousand a hand on even-money propositions. The question is how often they end up half a million down, and how often half a million up, as total turnover grows.
Turnover is the axis that matters, not time. A hundred million wagered sounds absurd until you notice it is ten thousand bets — which a serious player reaches inside a year.
The results
| Wagered | Bets | 3% edge | 1% edge | 0% edge |
|---|---|---|---|---|
| $5M | 500 | −6.4% / +0.2% | −2.5% / +0.8% | −1.4% / +1.4% |
| $10M | 1,000 | −27.5% / +0.6% | −10.6% / +3.1% | −6.1% / +6.1% |
| $20M | 2,000 | −59.6% / +0.7% | −25.9% / +6.1% | −13.6% / +13.6% |
| $50M | 5,000 | −92.3% / +0.3% | −50.8% / +8.0% | −24.5% / +24.3% |
| $100M | 10,000 | −99.4% / +0.0% | −69.6% / +6.8% | −31.2% / +31.2% |
Read each cell as: chance of finishing $500K or more down / chance of finishing $500K or more up.
What the table says
At 3%, volume is fatal. By a hundred million wagered the chance of a heavy loss is 99.4% and the chance of a heavy win is effectively zero. There is no strategy inside the game that touches this. It is not bad luck, it is arithmetic arriving on schedule.
At 1%, it takes longer and ends the same way. Nearly 70% chance of a heavy loss against under 7% of a heavy win. A one percent edge feels almost fair per bet and is a ten-to-one proposition against you by the end.
At 0%, the columns are symmetrical. 31.2% against 31.2%. Same at every level of turnover, forever. That symmetry is the whole product: the outcome stops drifting anywhere.
Look down the 3% column: 6, 28, 60, 92, 99. That is not a cost that scales, it is a clock running out. Every additional bet moves the distribution further from where you want it, and no individual result changes the direction.
Duel's figures, checked
Duel published its own version of this table. We ran ours independently with 200,000 simulated players per cell and compared every value.
All fifteen cells agree, with our numbers a fraction of a percentage point more pessimistic in the loss column — a difference explained by rounding, not by method. We could not find a cell where their table flattered them.
That is worth stating plainly because it is rare. A casino published a table showing gambling maths in an unflattering light, and the table is correct.
What zero edge does not fix
Symmetry is not safety. At 0% edge, 31% of players still finish half a million down at that volume — the same share that finish half a million up. A fair game is still a game, and variance at these stakes is brutal in both directions.
What disappears is the certainty. At 3% the result is decided in advance; at 0% it is genuinely open. Those are different situations, and only one of them is gambling in any meaningful sense.
The inversion at the end
Here is the part that explains why zero edge barely exists anywhere. A casino with an edge and sensible limits expects to profit over time. A casino with no edge expects to go bankrupt over time — regardless of what limits it sets.
Same random walk, seen from the other chair. Without drift in its favour, the operator is subject to exactly the symmetry above, and one of the directions is insolvency. Which is why zero-edge games come with caps, and why the caps are the offer working rather than a catch. That reasoning is worked through in why zero edge needs a ceiling.
Methodology
200,000 independent players per cell. Flat 10,000 stakes on an even-money proposition paying 2×, win probability set to (1 − edge) ÷ 2. No ruin barrier applied, so a player may go arbitrarily negative — adding one would make the loss figures worse, not better. Real games have skewed payout distributions that push the median further down still.
Related: 99% versus 99.9% RTP, and how the same maths sets the multipliers in Mines.
The edge is the only number
Everything else about a casino is presentation. This is what decides the outcome.
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