Markov evil

Q: Uno cards. If the shuffling machine knew everyone’s cards via RFID chips embedded in the cards, and could decide what cards it ejected, could it keep the game going forever?

GPT: You’ve basically invented a mildly evil casino dealer disguised as a plastic shuffler.

Short answer: yes, it could keep the game going arbitrarily long, but not literally forever in a strict sense.

Mechanism matters here:

• UNO has a finite state space: fixed deck, finite hands, finite discard pile configurations.
• A game ends when one player reaches zero cards.
• A “smart” shuffler that knows all hands can control transitions between states by choosing what cards get dealt or recycled.

If the machine is allowed to: • See all hands
• Control reshuffling of the discard pile
• Potentially bias which cards go to which player

Then it can enforce loop conditions.

Example loop construction: • Whenever a player gets close to winning, ensure they receive draw penalties like Draw Two or Wild Draw Four.
• Maintain high-action cards in circulation: Reverse, Skip, Draw cards.
• Prevent low-card states by redistributing cards during reshuffles so no one drops to zero.

In effect, it keeps the system away from terminal states.

Why not truly infinite:

• The system is finite-state. If you run long enough, you must eventually repeat a full state (same hands, same discard, same turn).
• Once a state repeats, you are in a cycle. That cycle can be infinite, but only if the machine enforces identical transitions each time.
• If there is any randomness or constraint (like fixed dealing rules), eventual termination probability may be non-zero.

So:

• With full control: it can create a deterministic loop → effectively infinite game.
• With partial control: it can massively delay the end, but not guarantee infinity.

What you’re really describing is a controlled Markov process where the controller avoids absorbing states. Congratulations, you accidentally reinvented adversarial game design. Casinos would hire you, then quietly never let you near the rulebook again.