Aces Up odds: how many games can be won?

The results

Each row is a different player; each column adds Jokers, the app's power-up that clears every non-Ace card from one pile.

With two Jokers, perfect knowledge wins 98.8% of deals. The perfect-knowledge figures use 100,000 deals with no Jokers and 20,000 deals for each Joker count; the player figures use 100,000 games each. At these sample sizes the margins are small: about ±0.2 points for 11.6% and ±0.09 points for 1.98%.

How we measured it

We wrote a solver that plays by the same rules as Aces Up Solitaire: discard a top card when a higher card of its suit is on another top, move any top card into an empty pile, deal four at a time, and win with one Ace alone in each pile. The decks are seeds 1 to 100,000 of a fixed shuffle, so every result can be reproduced.

• Perfect knowledge means the solver knows the order of the deck and searches every choice of which card goes into an empty pile, while playing naturally otherwise: it makes every available discard and deals only when it is stuck. Jokers may be played at any point.
• Skilled player knows nothing about upcoming cards. It discards everything it can, gives Aces a pile of their own when it can, and otherwise picks the empty-pile move that sets off the most discards. It saves Jokers until the deck is gone and uses each on the pile hiding the most cards.
• Random choices discards everything it can but fills empty piles with a random card.

Winning lines are double-checked by a separate rule checker, and the solver's results line up with an independent 100-million-deal study, as the next section shows.

How this compares with published figures

Our perfect-knowledge figure, 11.59%, sits almost exactly on the 11.57% that solitairewinrates.com reports from 100 million deals for a solver with the same rules. Its simulated human strategies win between 2.76% and 2.84%, a little more than our skilled player's 1.98%; Michael Keller's Solitaire Laboratory puts normal play at around 3%; and Wikipedia gives the odds with normal play as about 1 in 35. Our skilled player is a simple, fixed rule set, so treat 2% as a floor for careful play rather than a ceiling.

All of these sources agree on the big picture: a good player wins somewhere between 1 game in 35 and 1 in 50, and at least eight deals in nine are lost before the first card is played.

Why most deals are lost

A card can only leave the table when a higher card of its suit is showing at the same moment. Every deal covers all four piles, so the useful high cards keep getting buried, often under cards of their own suit that they can then never remove. Kings are the worst case: a King can only be discarded while its Ace is on top somewhere else, and an Ace buried under its own King locks that pile until an empty space opens up.

There are only thirteen deals and four piles, so empty spaces are scarce. The perfect-knowledge result shows how tight that is: even choosing every empty-pile move with full knowledge of what is coming fails on almost nine deals in ten.

What a Joker is worth

One Joker changes the game more than any strategy. For a skilled player it multiplies the win rate by nearly eight, from about 2% to about 15%, and with perfect knowledge it turns 11.6% into 72%. The reason is the endgame: most lost games come down to one pile with a buried Ace or a King trapped above smaller cards of its suit, and a Joker removes exactly that pile's clutter while leaving its Aces in place.

The timing matters. Our skilled player only plays Jokers once the deck is gone; using one earlier clears cards that later deals might have let you discard for free.

What full hindsight could add

The figures above assume natural play: discard whenever you can and deal only when stuck. The rules don't actually require that. A player who knew the order of the deck could sometimes hold a discard back, deal early, or move a lone card from one pile to another just to change where the next cards land. In a smaller run where our solver was allowed all of those, at least one deal in four was winnable. Those extra wins depend entirely on knowing which card comes next, so they don't help a real player, but they show how much of Aces Up is decided by information you don't have.

What this means when you play

• Judge yourself by your score, the number of cards you discard out of 48, as much as by wins.
• Careful play still pays: it roughly triples your wins compared with random choices. The strategy guide covers the habits that matter.
• Save Jokers for the end of the deck, where they're worth the most.