Sometimes it’s a good deal and it’s a bad choice that is just luck. Good models can be beaten and lead to bad outcomes. This is one of the most important teachings of financial education.
Expected value is a tool for assessing a risky situation. It is a combination of the size of the potential gains and losses, and the probability of each event happening. It can be used when applied appropriately to give insights into trading strategies, insurance considerations, and the monetary value of gambling for entertainment purposes.
Mathematics can be presented in multiple contexts, but the intent is important. Committing capital to trade in order to gain a financial reward. When it comes to entertainment spending, you’re paying for an experience. A risk model can explain both but it does not make them equal.
What is EV really measuring?
The expected value is the average of the possible values combined with their probabilities. Statlect’s description of the math behind expected value is: multiply each outcome by its probability and then sum the products.
When making financial decisions, work out the net gains and losses, not the gross payouts:
E.V. = sum of (probability x net outcome)
Suppose you have a chance to win $150, but the odds of winning are 40% and the odds of losing are 60%.
EV = (0.40 × 
80) = $12
The model has an expected gain of $12 per attempt. It does not guarantee that the next time it will make $12 profit: It guarantees that it will gain $150 one time or lose $80 another time.
The average of many repetitions could approach the expected value, as long as the probabilities and payoff structure are the same. Someone with small capital resources may find that despite their efforts, they never earn enough to use any long run average.
How Trading Costs Affect the Calculation
It takes more effort to determine a positive EV in trading than it does to put numbers into a formula. Future probabilities must be estimated and then the market can change after the estimates.
Assume that a hypothetical strategy has a 45% probability of being a winner, a mean winning of $200 and a mean losing of $120.
EV before costs = (0.45 × $200) − (0.55 × $120) = $24
Average transaction costs: $10, expected value = $14. Those costs can be commissions, bid–ask spreads and slippage: the price difference between what is expected to be executed and the actual price achieved.
Suppose now the true winning probability is 40%:
EV after costs = (0.40 × $200) − (0.60 × $120) − 
2
A change of 5 percentage points in the error makes the result flip from positive to negative. This is just another example of how a good looking spreadsheet is not a trading edge.
Realistic costs should be taken into account in the historical testing, as should changing conditions, and the danger of being too close to past data. The SEC’s Investor.gov guidance on day trading also emphasizes that big losses can occur in short time frames.
Expected Value in Chance Based Entertainment
Similar calculations are used in chance-based entertainments, but the aim is to be understood as a form of entertainment rather than making money.
Let’s imagine a game that costs $10 to play. There is a 10% chance that it will return $50 plus the amount of the stake, and a 90% chance it will return nothing.
This means that the net results are either a $40 profit or a $10 loss:
EV = (0.10 × 
10) = −$5
This translates into a $5 per play cost. A play can still win, but a win doesn’t affect the underlying value calculation.
As users delve into casino entertainment, it is crucial to differentiate between the information about the games and the promotional material describing what is available when reading about the games online, on Miki Casino, or in other sources. The questions include the rules, payout structure and any promotional conditions. There is no evidence of positive expected value from a brand name or a good offer.
If a game sets a percent return to player, then it is the expectation of that percent return to player based on its mathematical model. It’s not a guarantee of the amount of money a player will earn during a game.
Why Variance Matters Alongside the Average
Expected value describes an average; variance describes how widely outcomes can differ from it.
Opportunity A
Possible net outcomes: 50% chance of +
10
Expected value +$10
Opportunity B
Possible net outcomes: 50% chance of +
190
Expected value +$10
The expected value of both are equal. Opportunity B offers the participant significantly greater swings.
This is important any time money is tight. The cost of two losses in B is $380, versus $20 in A. The average is not enough to indicate that the person can absorb that sequence.
Losses should therefore be taken into account along with their frequency, the timing of cash flows as well as the potential for rare outcomes not included in the model.
How can an independent source of data be correlated?How can a losing streak be overcome?
Another difference is in the relationship between the outcomes.
Previous outcomes have no impact on the next event for independent events. Losing streaks don’t make a win “due.” More spending to make up for earlier losses doesn’t alter the financial risk, it just alters the likelihood of an independent result.
The outcomes of trading can be correlated. There can be multiple jobs that react to the same announcement in the interest rate or a shock in the market or a liquidity issue. Being independent can underestimate the risk of simultaneous losses.
The lesson to be learned from this is to validate assumptions made in a model prior to relying upon the results. Arithmetic will not save incorrect probabilities or forgotten relationships.
Match the model to the purpose – activity 6.
A good risk model is more than a “What is the average return?” It also asks:
– What is the reliability of the estimates of probability?
– Do you measure gains or losses after costs?
What is the maximum possible loss?
– Is it possible for multiple losses to happen simultaneously?
– Is it money for the investment or for some leisure time?
A fixed spending budget can be used as a way to entertain without spending money on bills, savings and other obligations. When trading, exposure and leverage are what can cause the loss of capital from an incorrect model.
The expected value is a tool to understand uncertainty. Together with variance, realistic costs and financial boundaries, it allows for more informed decision making — but not to exclude the chance that the model is incorrect.
