A board of 4 face-up cards is dealt. A question about the next card from the remaining deck is announced. You receive 2 private cards giving extra info about what's left.
Bet YES or NO on whether the hidden card satisfies the property. Choose your confidence: 1:1, 2:1, or 3:1.
| Result | Payout |
|---|---|
| Correct at 1:1 | +0.95× ante |
| Correct at 2:1 | +1.90× ante |
| Correct at 3:1 | +2.85× ante |
| Incorrect | -odds × ante |
ACTIONS
PEEK: Pay 1× ante to reveal one extra card (max 2). BURN: Pay 1× ante to remove a board card and replace it (once per round).
SIDE BETS
| Bet | Condition | Pay |
|---|---|---|
| BAYES | True prob differs >20pp from public | 4:1 |
| SYMM | True probability is 50% (±1%) | 3:1 |
| EXACT | Declared exact count correct | 5:1 |
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How many of the remaining cards satisfy the property?