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House edge and return to player

Every casino game reduces to the same sum: probability times payout, added up. The shortfall from your stake is the entire business model.

The sum, worked through

Take a bet that wins one time in ten and pays 9×. Ten stakes of one unit cost ten and return nine, so the shortfall is one in ten — a 10% margin. Take a bet that wins one time in ten and pays 9.8× and the margin is 2%.

That is the whole calculation. Return to player is the same figure from the other side: a 2% margin is a 98% return. Neither is a prediction about your session; both are statements about a long run of identical bets.

How the house edge appears in a payout tableWhere the margin actually sitsTen stakes of one unit on a bet that wins one time in ten. What comes back:Staked: 10 unitsPays 9×Returns 9 units10% edgePays 9.8×Returns 9.8 units2% edgeSame probability, same game, different payout table. Nothing about how the stakeswere chosen moves either bar.
The house edge is the gap between the true odds and the paid odds, and it lives entirely in the payout table. Two games with identical probabilities can differ fivefold.

Why a margin is a rate, not an outcome

A 2% edge on 3,000 USDT of turnover has an expected cost of 60 USDT. Your actual result will almost never be minus 60 — it will be a number drawn from a distribution centred near it, and the spread of that distribution is volatility.

The two quantities do different jobs. The margin tells you what the activity costs per unit staked. Volatility tells you how wild the ride around that cost will be. Confusing them is how a lucky evening becomes a theory.

Where the edge lives in each kind of game

In roulette, in the gap between 37 pockets and a 35-to-1 payout. In blackjack, in the table rules and in how correctly the hand is played. In a slot, in a paytable certified by the studio. In a crypto original, in the multiplier table set by the operator.

Only the last of those is the casino's own choice, which is why the originals are the part of the floor where operators genuinely differ. The games section derives it where the rules allow.

What no staking system changes

The expected value of a sum is the sum of the expected values, regardless of how the stakes were chosen. Martingale, Fibonacci and every variant reshape the distribution of results — more small wins and a rarer catastrophic loss, or the reverse.

The centre of that distribution does not move. A system that wins 95% of sessions and loses everything in the other 5% is the same expected loss, reorganised into a shape that feels better until it does not.

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