Key Insights
Quick Answer
You can model casino outcomes with simple formulas by combining RTP or house edge with your bet size and number of bets. Expected loss estimates long-run cost, while volatility range depends on how swingy the game is and how many bets you make. These models guide planning, not prediction.
Best Way To Use This Article
Choose your game, set your base bet, estimate how many bets you will make, then calculate expected loss. Use that number to adjust stake size and session length before you play.
Biggest Advantage
You stop guessing. You can estimate the price of a session and decide whether the entertainment cost fits your budget.
Common Mistake
Using one short session as proof a game is “good” or “bad.” Averages need volume. A single session is noise.
Pro Tip
The simplest model is enough: expected loss per session. If you know the long-run cost, you can set limits that keep your play enjoyable.
The Core Inputs You Need
To model outcomes, you need only a few inputs.
Bet Size
This is how much you wager each trial.
Number Of Bets
This is how many trials you will make.
A trial can be:
- a spin
- a hand
- a resolved wager
House Edge Or RTP
House edge is the long-run percentage cost of a wager.
RTP is the long-run percentage return.
These are connected.
- House edge is roughly 100% minus RTP
Pace
Pace is bets per hour.
This turns expected loss into a time-based cost estimate.
Formula 1: Expected Loss Per Bet
Expected loss per bet is:
Expected Loss Per Bet = Bet Size × House Edge
If your bet is $10 and the house edge is 5%, the expected loss per bet is:
- $10 × 0.05 = $0.50
That does not mean you lose fifty cents every bet.
It means the long-run average drift is about fifty cents per bet.
Formula 2: Expected Loss Per Session
Expected loss per session is:
Expected Loss Per Session = Bet Size × Number Of Bets × House Edge
This is the single most useful model for most players.
It tells you the long-run price of your session.
Example:
- Bet size: $5
- Number of bets: 200
- House edge: 4%
Expected loss:
- $5 × 200 × 0.04 = $40
That $40 is not a guarantee.
It is the long-run average cost if you repeated that session pattern many times.
If $40 feels too expensive for entertainment, you can adjust:
- bet size
- session length
- game choice
- add-ons
Formula 3: Expected Return Using RTP
If you have RTP instead of house edge, you can estimate expected return.
Expected Return = Bet Size × Number Of Bets × RTP
Example:
- Bet size: $5
- Bets: 200
- RTP: 96%
Expected return:
- $5 × 200 × 0.96 = $960 returned from $1,000 wagered
The expected loss is the difference:
- $1,000 wagered minus $960 expected return = $40 expected loss
Same result.
Different framing.
Formula 4: Expected Loss Per Hour
To model cost per hour, you need pace.
Expected Loss Per Hour = Bet Size × Bets Per Hour × House Edge
Example:
- Bet: $2
- Pace: 500 spins per hour
- House edge: 4%
Expected loss per hour:
- $2 × 500 × 0.04 = $40 per hour
This is why fast play matters.
A small house edge can still become expensive when pace is high.
If you want cheaper entertainment:
- slow down
- size down
- or both
Where Players Go Wrong With These Models
Expected loss is simple, but players misapply it.
Mistake 1: Forgetting Total Amount Wagered
Players think:
I only brought $200.
But the model uses total wagered volume.
You can wager thousands in a session if the pace is fast, even with a small bankroll.
That is why bankroll can disappear quickly.
Mistake 2: Ignoring Add-Ons
Side bets and feature buys increase:
- amount wagered
- volatility
- often house edge
If you model only the main bet and ignore add-ons, your expected loss estimate can be too low.
Mistake 3: Treating Expected Loss As A Prediction
Expected loss is not a forecast of your exact result.
Variance can put you far above or below the expected number.
The model is a planning tool, not a promise.
Modelling Volatility Without Complex Maths
Variance and standard deviation can get technical.
But you can still model volatility in a simple way.
The Practical Volatility Rule
The bigger the bet and the fewer the trials, the wider your results can spread.
As trials increase, outcomes tend to average out.
So a simple way to plan for volatility is:
- high volatility + short session = wide outcome range
- low volatility + longer session = narrower outcome range
That is not a number.
But it is actionable.
It tells you why a short, high-stake session is the worst combination for emotional stability.
A Simple “Range” Mindset
Instead of expecting one outcome, assume a range.
For example:
- expected loss might be $40
- actual outcomes could be anywhere from a profit to a larger loss in a single session
Your job is not to predict the outcome.
Your job is to size the session so the downside is acceptable.
If the downside is not acceptable, the plan is wrong.
A Simple Session Planning Template
Here is a step-by-step model you can use before you play.
Step 1: Pick Your Session Bankroll
This is the maximum you are willing to lose.
Step 2: Pick A Base Bet
Choose a bet size that creates enough units.
If your bankroll is $200, a $10 bet gives only 20 units.
That is fragile in many games.
A $2 bet gives 100 units, which is more survivable.
Step 3: Estimate Bets Per Hour
You do not need an exact number.
You just need a rough sense:
- fast games create high volume
- slow games create lower volume
Step 4: Estimate Expected Loss Per Hour
Use the formula:
Bet × Pace × House Edge
If the number feels too high, change something before you start.
Step 5: Cap Add-Ons
If you add side bets, include them in your total wager estimate.
If you cannot estimate their cost, assume they increase your exposure and reduce them.
Step 6: Set Stop Rules
Expected loss is long-run. Stop rules protect the short run.
Use:
- stop-loss
- stop-time
- no chasing
Why These Models Help You Play Smarter
These models do not beat the casino.
They do something more realistic.
They help you:
- understand the cost of entertainment
- avoid accidental overexposure
- choose bet sizes that match your bankroll
- reduce the emotional chaos that leads to chasing
When you treat gambling as entertainment with pricing, you avoid the biggest traps.
FAQs About Modelling Casino Outcomes
Can These Formulas Predict My Exact Result
No. They estimate long-run averages. Short sessions can vary widely because of variance.
What If I Do Not Know The House Edge Or RTP
Treat the value as unknown. Assume higher cost, reduce bet size, shorten session length, and avoid add-ons until you have better information.
Why Does Speed Matter So Much
Because expected loss scales with total amount wagered. Fast play increases volume, which increases cost per hour even when house edge is unchanged.
Do Side Bets Change The Model
Yes. Side bets increase total wagered amount and usually increase house edge and volatility. If you add them, your expected loss and swing range both increase.
What Is The Most Useful Formula For Most Players
Expected loss per session: bet size × number of bets × house edge. It gives you a simple “price tag” for the session.
Where To Go Next
Now that you can model casino outcomes using simple formulas, the next step is learning how odds awareness helps you choose smarter games and bets, so you can reduce long-run cost without relying on luck.
Next Article: How To Use Odds Awareness To Choose Smarter Games
Next Steps
If you want the full foundation that ties probability, odds, house edge, EV, variance, and value evaluation together, go back to The Complete Guide To Casino Game Odds And House Edge.
If your goal is to play smarter from the very first session, use The Ultimate Player Checklist for Evaluating Game Odds & House Edge.
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