Flower Garden Solitaire: a ceiling somewhere between 43% and 95%
Flower Garden is an open game. Every card is face up from the start: six "flower beds" of six cards each, and a "bouquet" of sixteen loose cards you can use at any time. There is no stock and nothing hidden. Whatever happens, you could see it coming.
That makes it a fair test for a solver, and also a surprisingly hard one. On 2,000 deals, our solver found a winning line for 43.3% and proved 5.4% impossible. More than half, 51.4%, were still undecided when it reached its search limit. So the most we can honestly say is that somewhere between 43.3% and 94.7% of Flower Garden deals can be won.
That is a wide range, and we would rather show it than pretend to a precision we do not have. Play it here for free, with nothing to install.
The ceiling at a glance
| Result | Value | Deals | How |
|---|---|---|---|
| Solved | 43.3% (95% range 41.1–45.5%) | 2,000 | Solver, up to 200,000 positions per deal |
| Proven impossible | 5.4% (95% range 4.5–6.4%) | 2,000 | Same solver |
| Undecided at the search limit | 51.4% | 2,000 | Same solver |
| Winnable share, best estimate | between 43.3% and 94.7% | 2,000 | Solved, up to solved plus undecided |
| Aces that start in the bouquet (of 4) | 1.26 on average | 2,000 | Deal inspection |
| Solved when 2+ Aces start in the bouquet | 44.2% | 747 | Same solver |
| Solved when 0–1 Aces start in the bouquet | 42.8% | 1,253 | Same solver |
We found no published winnability figure for Flower Garden, so there is no outside number to compare against.
Why so many deals stayed undecided
Flower Garden has an unusual mix of freedom and restriction. The bouquet gives you sixteen cards you can play at any time, which multiplies the possible move orders. But you can move only one card at a time in the beds, which makes each line of play long. Together, that creates a huge number of positions to search. Half the deals needed more than the 200,000 positions we allowed.
What we can say with confidence: at least 43.3% are winnable, and at most 94.7% are, since 5.4% are proven impossible. The true figure lies in between.
The rules as this site plays them
Beds and bouquet
- Six beds (columns) of six cards each, all face up. That uses 36 cards.
- The bouquet: the other 16 cards, face up and all available.
- Four foundations, built up by suit from Ace to King.
What you may move
- Any bouquet card can be played at any time, onto a bed or a foundation.
- In the beds, build down regardless of suit: any 6 goes on any 7.
- Only one card moves at a time.
- Any card can go into an empty bed.
Finishing the garden
All 52 cards on the foundations.
What the numbers suggest about playing well
The bouquet is a reserve, not a to-do list
You can play bouquet cards whenever you like, so there is no rush. Keep them as options for the moment a bed needs exactly that card.
Do not count on Aces in the bouquet
On average 1.26 of the four Aces start in the bouquet, where they are free to go straight home. You might expect that to help a lot. It barely did: 44.2% of deals were solved with two or more Aces in the bouquet, against 42.8% with none or one. The order of the cards in the six beds counts for more.
An empty bed takes any card
Any card can go into an empty bed. That is your most powerful tool for untangling a stack, since you can move only one card at a time.
Plan the order of each bed
Because single cards are all you can move, the order cards sit in a bed matters. Look for the bed that buries the most low cards and work on it first.
Working through a Flower Garden deal
With every card visible, the first few minutes of Flower Garden are best spent looking rather than moving. A practical order of work:
- Send home any Aces you can. Aces in the bouquet can go straight up. Aces at the bottom of a bed can too.
- Find the bed that hides the most low cards. A bed with an Ace or 2 buried near the top of the pile, under several cards, is your first project.
- Count what that bed needs. Each card on top of the buried one must go somewhere: onto a card one rank higher in another bed, or into an empty bed. Check that there is a home for each before you start.
- Use the bouquet to fill gaps. If a bed card needs a landing spot one rank higher, a bouquet card of that rank can often be placed first to create one.
- Keep building the foundations evenly. Since any suit can go on any card in the beds, low cards of every suit are useful landing spots. Sending all the 3s up too early can leave you with nowhere to put the 2s you still need to move.
This is slower than simply making the first available move, but Flower Garden rewards it. One careless move can bury a key card under a pile you can only take apart one card at a time.
Inside the test, one step at a time
The solitaire-online.us team tested Flower Garden in September 2026.
- Reading the rules from our game code. Six beds of six, a 16-card bouquet, all face up, any bouquet card playable, building down in any suit, one card at a time and any card into an empty bed.
- Rebuilding the game. We wrote Flower Garden as a Python program with those rules.
- Dealing the cards. 2,000 deals, each from a numbered seed.
- Choosing the player. A solver. Every card is face up, so it knows exactly what you know.
- Running it. Up to 200,000 positions per deal: solved, proven impossible or undecided.
- Checking against published research. We found no published figure for Flower Garden, so there was nothing to check against.
- Working out the margin of error. A 95% range means the true value would fall inside it in 19 of 20 repeats. Deals solved: 41.1–45.5%.
- What the numbers cannot tell you. With half the deals undecided, our range is wide. A bigger search budget would narrow it.
The code behind the ceiling
The study is written in Python 3.11 using only the standard library. Flower Garden has its own module, flowergarden.py, and a shared runner spreads the deals across processor cores with Python's multiprocessing.
The solver is a best-first search that always explores the most promising position next and keeps track of positions already seen. It sends a card home automatically only when no other card could ever need to sit on it: low cards, or when every foundation has already reached the rank just below. For the 95% ranges we use the Wilson score interval, which behaves well near 0% and 100%.
Our team worked with Claude, an AI assistant from Anthropic, on the solver code and the first draft of this page. It did not produce any of the numbers. They all come from running the solver.
By Admin, solitaire-online.us (Solitairen OOD). Study date: September 19, 2026.
Ceiling questions from players
What share of Flower Garden deals is winnable?
Between 43.3% and 94.7%, based on 2,000 deals. We cannot narrow it further without a bigger search.
Can I play any bouquet card at any time?
Yes. That is what makes the bouquet special.
Can a stack of cards move together?
No. Flower Garden moves one card at a time.
Does it matter what suit I build on?
Not in the beds. Any card can go on any card one rank higher.
Other open-layout games?
Baker's Solitaire and FreeCell are also fully open games. For more, see our games page.