How a game of chance is designed

The target comes first

A commercial game is not invented and then measured. It is specified numerically and then constructed to meet the specification. The primary figure is the proportion of everything staked that the game returns to players over its full cycle of outcomes, and the remainder is the operator's share. Every other design decision is made subject to hitting that figure.

Working backwards from a target is straightforward arithmetic once the outcome list exists. Suppose a game draws one of a hundred equally likely symbols and the designer wants a return of ninety-six per cent. The paytable must be chosen so that the sum, over all hundred outcomes, of the probability of each outcome multiplied by its payout equals 0.96. There are countless paytables satisfying that constraint, and choosing between them is where the design work happens.

The three quantities being traded

Three properties compete, and improving any one of them costs something in the others.

• Return. The proportion of stakes paid back over the full cycle. Raising it narrows the margin per unit staked.
• Hit frequency. How often a wager returns anything at all. Raising it makes the game feel responsive but consumes return on small payouts that could otherwise fund larger ones.
• Volatility. How widely results scatter, in the sense set out in the entry on variance. Concentrating the return into rare large payouts raises it; spreading it thinly lowers it.

A game with a high hit frequency and low volatility returns small amounts often, so a given bankroll survives a long time and the total staked across a session is large. A game with a low hit frequency and high volatility offers a large prize rarely, so most sessions end quickly and a few end memorably. Both can be built to identical returns, and the choice between them is a choice about what the session feels like, not about how much the game retains per unit staked.

Playing time as the real product

The entry on house edge showed that the amount retained depends on total stakes, which is the stake per wager multiplied by the number of wagers. A designer therefore has two levers on revenue, and only one of them involves the edge. Lengthening play at a constant edge raises the total retained just as surely as raising the edge does, and it does so without making the game visibly worse value.

This is why so much design attention goes to pacing: the speed of resolution, the handling of near-outcomes, the treatment of a partial return as an event in its own right. A wager that returns less than the amount staked is a net loss, but presented as a win it reads as a positive result. Nothing about that presentation changes the arithmetic; it changes how long the arithmetic is allowed to run.

Table games are designed under the same logic with different levers. Rule variations that appear minor often move the edge substantially, because they alter the payout on outcomes that occur frequently. A game advertised as offering better rules in one respect is quite often recovering the difference through a payout reduction elsewhere, and the only way to compare two versions is to work the expected value of each from the full rule set rather than from the feature being advertised.

What the designer cannot do

One constraint is absolute. A game whose expected return exceeds one is a game that loses money at scale, and no amount of design cleverness escapes the addition. The full cycle of outcomes and their payouts must sum to less than the stakes collected, and the law of large numbers guarantees that the shortfall will be realised in practice over enough wagers.

This is worth stating because it is the boundary of the whole subject. The interesting questions in game design are all about how the shortfall is distributed, how it feels while it is happening and how long it takes to arrive. The existence of the shortfall is not one of the questions. It is the premise on which the object was commissioned.