Poker Estimathon

Estimate statistical properties of hidden card expressions under uncertainty.

Overview

You play 6 stages on each difficulty. Each stage deals a hand of cards from a standard 52-card deck (A–K, values 1–13). Suits are spades (black), hearts (red), diamonds (blue), and clubs (green). Choose a difficulty before starting.

Difficulties

Easy — 4 cards per stage; 3 estimation rounds (none revealed → 1st revealed → 2nd revealed); expressions use 3–4 variables with no hidden-card quota; 50s per estimate; operator weights + : − : × : ÷ = 2 : 1 : 2 : 1.
Medium — 5 cards per stage; 4 estimation rounds (same reveal pattern as Hard); expressions use 3–5 variables with no hidden-card quota; 40s per estimate; operator weights = 1.5 : 1 : 1.5 : 1.
Hard — 6 cards per stage; 4 estimation rounds; expressions use 4–6 variables and at least half must still be hidden; 30s per estimate; operators chosen uniformly.

Your profile tracks separate average ratings for Easy / Medium / Hard.

Stages & Information

Within a stage, rounds reveal cards from the left: round 1 shows none, then one more card is revealed after each round until the stage ends.
Easy has 3 rounds per stage; Medium and Hard have 4.
After the final round of a stage, all stage cards are shown, then the next stage deals new cards from the remaining deck.
The card tracker (♠, bottom-right) lights up cards that have already appeared — previous stages in full, plus any face-up cards in the current stage. Expand it to review revealed cards and factor them into your decisions.
Later stages exclude previously dealt cards from the deck — your information grows.

Each Round

A random expression is built from 4–6 of your 6 cards (x1 … x6), combined with + − × ÷ and sometimes absolute values.
At least half the cards used must still be face-down when the question is generated.
You are asked to estimate one statistic: the 10th percentile, 90th percentile, median, mean, or standard deviation of the expression's value.
Enter your estimate within 30 seconds; the system evaluates it via 100,000 Monte Carlo simulations given currently visible information.

Monte Carlo & Invalid Values

Each question is computed from all 100,000 Monte Carlo samples. Any invalid outcome (including NaN and division-by-zero situations) is recorded as 0 — never discarded.

Some Monte Carlo stats may fluctuate near 0, which creates high estimation risk. In those cases, use Skip or a strategic guess instead of a blind estimate.

Estimate with this rule in mind:

Ignore vanishingly rare pathological cases that would be invalid under almost all samples.
When a zero denominator is possible, treat those samples as contributing 0 to the distribution.
Focus on the bulk behaviour of the 100,000-sample distribution, not isolated edge cases.

Skip

Click Skip when you think the answer may swing near 0 and guessing is too risky.
The kth Skip in a game records a fixed error of k × 100% (capped at 1000%).
Example: 1st Skip = 100%, 2nd Skip = 200%, 5th Skip = 500%.
The true answer is still revealed after skipping; only scoring uses the fixed Skip penalty.

Scoring

Per-round Rating = 100 × (1 − (error/1000)²), clamped to 0–100. Your final score is the average error across all 24 rounds.

Seeds

Each game has a seed (0–2,147,483,647) determining card deals and question structure. The same seed reproduces the same game layout.