Poker Outs Rule of 2 and 4
Compare 2/4 outs approximation with exact without-replacement at-least-one clean-out probability for one/two cards; caller clean outs may not guarantee winning and overlap/dirty outs are not inferred.
Description
An outs model counts drawing at least one favorable card without replacement.
An outs model counts drawing at least one favorable card without replacement. Common 2%/4% rules are approximations.1
Enter unseen cards 1–52, integer outs 0–unseen and one or two draws no greater than unseen count. Return exact probability, capped rule-of-thumb percent and their percentage-point difference.
When to use Poker Outs Rule of 2 and 4
Use Poker Outs Rule of 2 and 4 when you need to evaluate the supplied records under the calculation and evidence rules below. Outs are assumed distinct and genuinely favorable; opponent redraws and shared-card ambiguity are excluded.
Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
How to use Poker Outs Rule of 2 and 4 and understand its results
- Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
- Enter cleanOutCount, unseenCardCount, cardsToCome using the field table and calculation rules, then run the tool.
- Read ruleOfTwoOrFourApproxPercent, exactAtLeastOneCleanOutPercent, signedApproximationErrorPercentagePoints. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| cleanOutCount | Clean out count | number | Required |
| unseenCardCount | Unseen card count | number | Required |
| cardsToCome | Cards to come | number | Required |
Enter unseen cards 1–52, integer outs 0–unseen and one or two draws no greater than unseen count. Return exact probability, capped rule-of-thumb percent and their percentage-point difference.
exact=1−product((unseen−outs−drawIndex)/(unseen−drawIndex)) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| ruleOfTwoOrFourApproxPercent | Rule of two or four approx percent | number |
| exactAtLeastOneCleanOutPercent | Exact at least one clean out percent | number |
| signedApproximationErrorPercentagePoints | Signed approximation error percentage points | number |
{
"input": {
"cleanOutCount": 9,
"unseenCardCount": 47,
"cardsToCome": 2
},
"output": {
"ruleOfTwoOrFourApproxPercent": 36,
"exactAtLeastOneCleanOutPercent": 34.96762257169288,
"signedApproximationErrorPercentagePoints": 1.0323774283071216
}
}Limitations and assumptions
Outs are assumed distinct and genuinely favorable; opponent redraws and shared-card ambiguity are excluded.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Pot Odds Percent Calculator: Calling a poker bet adds the call amount to the final pot. Break-even equity compares that cost with the resulting pot. For a complementary task, use Call EV Positive Checker: A call EV compares expected returned pot share with the call cost. A tie contributes half of the declared distributable pot.
References
-
Poker Outs Rule of 2 and 4 — tool.io
Similar or alternative tools
- Pot Odds Percent Calculator
Calling a poker bet adds the call amount to the final pot. Break-even equity compares that cost with the resulting pot.
- Call EV Positive Checker
A call EV compares expected returned pot share with the call cost. A tie contributes half of the declared distributable pot.