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Insidious Casino

Cards are revealed in pairs. A red–red pair goes to you, a black–black pair goes to the dealer, and a mixed pair is discarded. Can your final pile ever be larger?

Probability of winning
0%
The final piles always tie.

Try a random deck

52 cards remaining.
YOU
♥ Red–red pairs
0
cards collected
CURRENT PAIR
?
?
DEALER
♠ Black–black pairs
0
cards collected
Red cards seen0 / 26
Black cards seen0 / 26
Mixed pairs discarded0

Every mixed pair removes exactly 1 red + 1 black.

Recent pairs RR → you · BB → dealer · RB → discard
No cards revealed yet.

Why you can never win

1
The deck starts balanced.

There are 26 red cards and 26 black cards.

2
Mixed pairs remove colors symmetrically.

If there are p mixed pairs, then exactly p red and p black cards are discarded.

3
The same number of each color remains.
red remaining = black remaining = 26 − p
4
Those remaining cards must belong to same-color pairs.

All remaining reds are yours; all remaining blacks are the dealer’s. Therefore both piles have exactly the same size.

Invariant RED LEFT 26 − p BLACK LEFT 26 − p The shuffle cannot break this equality.
You win only if your pile is larger, but the two piles are always equal. Therefore the casino's offer is insidious because winning is impossible.