What "Dominant Strategy" Actually Means
In game theory, a dominant strategy is one that produces the best outcome for a player no matter what the other player does. It does not depend on prediction, on reading your opponent, or on luck. If a strategy is dominant, you should play it every time, regardless of circumstances. It is unconditionally optimal.
The classic example is the Prisoner's Dilemma, where defecting dominates cooperating because it yields a better payoff no matter what the other prisoner chooses. You do not need to know their decision. The maths resolves it for you.
Now apply that framework to a casino. What is the casino's strategy? It is fixed. The house edge is encoded into the game rules, the payout tables, the RTP. The casino does not adapt to you. It does not change its strategy based on whether you are winning or losing. It plays the same move every single time: maintain the edge.
This is an unusual game-theoretic situation. Your opponent's strategy is not just known — it is constant. And when your opponent's strategy is fixed, finding your dominant strategy becomes much simpler. The question reduces to: given a permanent, unchanging house edge, what is the one variable you can control?
The Only Variable You Control
You cannot change the house edge. It is built into the game. You cannot change the RTP. You cannot change the odds of roulette or the paytable of a slot machine. The expected value of each individual bet is fixed before you place it.
What you can control is exposure: the total amount of money you put through the house edge. Exposure is a function of two things — bet size and number of bets. That is it. Those are your strategic variables. Everything else is locked.
Your total expected loss for any session is:
Expected Loss = Bet Size × Number of Bets × House Edge
A $1 bet on a 4% house edge game costs you 4 cents in expectation. Repeat that 600 times in an hour and you have paid $24. Play for four hours and you have paid $96. The house edge per bet is tiny. The cumulative exposure is not. Duration is the multiplier.
Prof. Boston says
Casino floor layouts are not designed for navigation. They are designed for retention. No clocks. No windows. Circuitous paths to exits. Restaurants and toilets positioned to route you past more machines. The physical architecture is optimised around a single metric: time on device. That should tell you everything about which variable the casino considers most important to its revenue. It is not your bet size. It is your session length. Every minute you stay is another minute of exposure, and the house edge converts exposure into revenue with mathematical certainty.
Optimal Stopping: A Strategy, Not a Surrender
In decision theory, optimal stopping is the problem of choosing when to take an action — when to stop searching, stop waiting, stop playing — to maximise an expected payoff. It is a rich area of maths with applications in hiring decisions, house-hunting, and financial markets. The key insight is that the decision to stop is itself a strategic choice, not an absence of strategy.
In casino terms: every moment you continue playing, you are making an active decision to expose more money to the house edge. Continuing is not a neutral default. It is a bet — a bet that the entertainment value of the next hour exceeds the expected cost of the next hour. Sometimes that bet is worth making. Often, it is not. And loss aversion makes it extremely difficult to evaluate honestly in the moment.
This is why the decision to walk away must be made before the session begins. In the moment, your brain is operating under the influence of variable reward schedules, near-miss reinforcement, and the sunk cost fallacy. These are not minor biases. They are powerful, well-documented cognitive distortions that reliably prevent people from stopping when stopping is optimal.
Pre-commitment is the counter. It moves the stopping decision out of the emotional environment and into the rational one.
Building Decision Architecture: Stop-Loss and Stop-Win
The bankroll calculator produces two numbers: a stop-loss limit and a stop-win target. These are not arbitrary. They are decision architecture — pre-committed boundaries that replace in-session judgement with pre-session analysis.
The stop-loss
Your stop-loss is the maximum you are willing to lose in a session. Set it before you play, based on what you can afford, not what you hope to recover. When you hit it, you leave. No exceptions, no renegotiation, no "just ten more spins." The purpose is to cap your exposure at a level you chose when your thinking was clear.
The stop-win
Your stop-win is the profit level at which you leave. This one is counterintuitive — why stop when you are winning? — but the game theory is clear. Every additional bet after your stop-win has the same negative expected value as every bet before it. The house edge does not shrink because you are ahead. Your winnings are not "house money." They are your money, and every additional spin exposes them to the same edge that produced your losses.
A worked example
You sit down with a $200 bankroll to play a 96% RTP slot at $0.50 per spin. Your pre-session plan: stop-loss at $60 (30% of bankroll), stop-win at $80 (40% profit). At 600 spins per hour, your expected loss rate is $12/hour. Your stop-loss gives you roughly five hours of play in expectation before you hit the floor. Your stop-win means that if variance swings in your favour, you lock in the gain rather than feeding it back.
Neither boundary guarantees a good outcome. What they guarantee is that your worst-case exposure is capped and your best-case gains are preserved. Over many sessions, this discipline reduces total losses compared to unstructured play. The maths is unambiguous on this point.
Key Point
Stop-loss and stop-win targets are pre-commitment devices — they work precisely because they are set before the session starts, when your decision-making is not compromised by arousal, loss aversion, or reinforcement schedules. The targets do not need to be optimal. They need to exist. Any pre-committed boundary outperforms no boundary at all.
The Dominant Strategy, Stated Plainly
Against a fixed house edge, the dominant strategy is to minimise unnecessary exposure. Play games with higher RTP. Bet at levels your bankroll supports. Set session boundaries before you start. And when those boundaries are reached, stop — not because you have given up, but because continuing is a dominated strategy. You are choosing the option that produces a worse expected outcome regardless of what happens next.
Walking away is not quitting. It is the game-theoretically correct action when your opponent's strategy is fixed and every additional round increases your expected loss. The casino has unlimited time and unlimited bankroll. You have neither. Duration favours the house. The only way to counteract that is to control how long you play.
Prof. Boston says
In my game theory seminar, I run a live auction where students can bid real money. The auction has a known negative-EV structure — I tell them the maths upfront. Every semester, the bidding exceeds the rational ceiling within 90 seconds. Afterwards, I ask what happened. The answer is always the same: "I knew I should stop, but it felt like I was about to win." That sentence is the entire casino business model. The feeling of being about to win is not a signal. It is the product. And the only reliable defence is a number you wrote down before the feeling started.
The expected value framework tells you the cost per bet. This page tells you that the total cost is a function of how many bets you make — and that controlling that number is the single most impactful decision available to you. The psychology articles explain why controlling that number is so difficult. And the tools give you the pre-commitment architecture to actually do it.
Maths, systems, then awareness. That is the order. And it starts with knowing when to stop.