Probability
Cards Expected Value Calculator
The calculator models repeated independent trials with an entered event probability, computes expected event and non-event counts, an approximate count interval, observed-rate comparison, and net expected value. The card-table visual separates probability from payoff so a favorable-looking prize is not mistaken for a favorable wager.
Entered event probability-
Expected event count-
Expected non-event count-
Binomial event-count variance-
Event-count standard deviation-
Approximate lower event-count bound-
Approximate upper event-count bound-
Expected gross value-
Expected value after fixed cost-
Observed event rate-
Expected events minus decision threshold-
Non-event probability per event probability-
Decision view
Card-event probability and payoff balance
Card-event probability and payoff balanceEvent and non-event shares are paired with their entered payoffs before fixed cost is removed to show net expected value.
Exact scenario comparisonEvent probability per trial (%) changes while all other entered assumptions remain constant.
| Event probability per trial (%) | Entered event probability | Expected event count | Expected non-event count | Binomial event-count variance | Event-count standard deviation | Approximate lower event-count bound | Approximate upper event-count bound | Expected gross value | Expected value after fixed cost | Observed event rate | Expected events minus decision threshold | Non-event probability per event probability |
|---|
Period-by-period detail
card outcome probability scenarios
How to use Cards Expected Value Calculator
- Define one event precisely, including whether draws are with replacement and whether trials are independent.
- Enter net payoff for success and failure on the same basis, including losses or stake return.
- Use the interval and expected value as model outputs, not promises about a short observed sequence.
Calculator guide
Understanding Cards Expected Value Calculator
Card-game expected value combines outcome probability, payoff when the event occurs, payoff when it does not, and any fixed entry cost.
Calculation method
How the calculation works
Combine card-event probability, trials, event and non-event payoffs, and entry cost to show expected count and value. Expected gross value equals expected events multiplied by success value plus expected non-events multiplied by failure value. Fixed cost is then subtracted. Count uncertainty uses a normal approximation to a binomial model.
Card table
Read chance and money together
The deck view shows event share and non-event share, while the payoff balance reconciles the two weighted outcomes and fixed cost.
Worked situations
Practical examples
- Drawing one ace from a full deck without replacement changes the probability of the next draw.
- A positive prize does not produce positive expected value if the loss on non-events and entry fee are larger.
- Observed events can differ materially from expectation over a small number of trials.
Better inputs
Useful tips
- Use exact combinatorics for multi-card hands rather than multiplying dependent single-card probabilities.
- Record whether success value includes return of stake.
- Separate expected value from bankroll risk and drawdown tolerance.
Before relying on the result
Limitations and common mistakes
- The core model assumes a stable event probability and independent trials.
- The normal count interval can be poor for small samples or probabilities near zero or one.
- It does not model card removal, conditional strategy, house rules, utility, bankroll ruin, taxes, or correlated outcomes.
Reference
Key terms
- Expected value
- Probability-weighted average outcome over many comparable trials.
- Event probability
- Modeled chance that the defined success event occurs on one trial.
- Failure value
- Net value assigned when the event does not occur.
- Count interval
- Approximate range around the expected number of events.
Important note
Calculated directly from the entered values using the displayed formula and rounding settings.
Frequently asked questions
Can event probability be entered from deck composition?
Yes, when one trial matches that composition and independence assumption.
Does positive expected value guarantee profit?
No.
Why is expected event count fractional?
It is a long-run average across the entered number of trials.
Can this calculate poker-hand odds?
Not reliably unless the exact hand probability is calculated separately and entered.