Flower Garden Solitaire: an open game with an honestly wide answer
Flower Garden is one of the prettiest patience layouts: six "flower beds" of six cards each, and a "bouquet" of sixteen more cards that you can pick from in any order. Every card is face up from the start, so there is no luck of the draw once the cards are dealt. That makes it a natural game to test with a solver — and a humbling one, because it turned out to be very hard to search.
Over 2,000 deals, our solver won 43.3%, proved 5.4% impossible, and ran out of search on the remaining 51.4%. So the honest answer to "how many Flower Garden deals can be won?" is: somewhere between 43% and 95%. The University of St Andrews study, which we compare our work with elsewhere on this site, does not include Flower Garden, so there is no published figure to narrow it down.
What we measured
| Measure | Result | Deals |
|---|---|---|
| Solved | 43.3% (95% range 41.1–45.5%) | 2,000 |
| Proven impossible | 5.4% (95% range 4.4–6.4%) | 2,000 |
| Undecided when the search limit was reached | 51.4% | 2,000 |
| Winnable share, as best we can pin it | between 43.3% and 94.7% | 2,000 |
| Aces that start in the bouquet | 1.26 of 4 on average | 2,000 |
| Published figure (St Andrews study) | None: game not covered | – |
Why the range is so wide
Every card is visible, so in principle a computer could settle every deal. In practice the bouquet makes the search enormous: any of up to sixteen cards can be played at almost any moment, and because building ignores suit, many cards have several possible homes. Our solver looked at up to 200,000 positions per deal and still could not reach a verdict on half of them.
We would rather tell you that than round it into a tidy number. What the result does show is that at least 43% of deals can definitely be won, and at least 5% definitely cannot.
Do Aces in the bouquet help?
You might expect a deal with Aces sitting in the bouquet — where you can play them at once — to be easier. Our results barely support that. Deals with two or more Aces in the bouquet were solved 44.2% of the time (747 deals); deals with none or one were solved 42.8% of the time (1,253 deals). That gap is well within the margin of error, so a lucky-looking bouquet is no guarantee.
The rules in this site's game
The layout
One pack of 52 cards. Thirty-six are dealt face up into six columns of six (the flower beds). The other sixteen form the bouquet, spread face up.
Playing
- Any card in the bouquet may be played at any time, onto a foundation or onto a column.
- In the columns, build down regardless of suit: any 7 may go on any 8.
- Only one card moves at a time.
- Any card may go into an empty column.
- There is no stock and no redeal.
Winning
Build all four suits from Ace to King on the foundations.
Advice that follows from the numbers
The bouquet is your toolbox, not a to-do list
Because you can play any bouquet card whenever you like, there is no rush to empty it. Keep cards there until they have a useful place to go.
Mind the suits even though building ignores them
You can put any 6 on any 7, but the foundations are strictly by suit. A long column of mixed suits can bury the very card you need next.
Empty a flower bed
Since any card can go into an empty column, and only one card moves at a time, an empty column is the most useful space you can make for rearranging the beds.
Don't be fooled by a good-looking bouquet
Our results show Aces in the bouquet made little difference. Look at how deeply the low cards are buried in the beds instead.
Flower Garden on solitaire-free.uk
Play for free in any modern browser on a desktop, tablet or phone, with no download or sign-up. Large clear cards and a zoom control make the bouquet easy to read. Hint, unlimited Undo, Restart and Auto Play are always available, cards can be dragged or tapped, and wins, time and moves are tracked for the current game. You can turn off the sound, play fullscreen and pick a table colour.
How we ran the research, step by step
- Reading the rules. From the site's Flower Garden code: six columns of six, a sixteen-card bouquet with any card playable, all cards face up, building down regardless of suit one card at a time, any card into a space, no stock.
- Rebuilding the game. We wrote Flower Garden in Python with a solver for it.
- Numbered deals. 2,000 deals (seeds 1 to 2,000), each shuffled from a numbered seed.
- The solver. Nothing is hidden, so the solver sees exactly what you see. It searched up to 200,000 positions per deal.
- Splitting the deals. We also grouped the deals by how many Aces began in the bouquet and compared the solve rates.
- Checking against published research. The St Andrews study (Blake and Gent, Journal of Artificial Intelligence Research, 2026) does not cover Flower Garden, so there is no outside figure to test ours against.
- Margin of error. Our 43.3% solved has a 95% range of 41.1% to 45.5%.
- What we can't tell you. With half the deals undecided, we can't say how winnable Flower Garden really is beyond "at least 43%, at most about 95%". A bigger search budget would narrow it.
Behind the numbers: the code
The solver lives in flowergarden.py, written in Python 3.11 with only the standard library. It is a best-first search, always examining the most promising position next (judged by how many cards are not yet home and how many rest on a lower card), with a record of positions already seen and automatic foundation moves only where they are provably safe. The deals were spread over the cores of one machine using Python's multiprocessing, and the run took about 24 minutes. Ranges are Wilson score intervals. Claude, an AI assistant made by Anthropic, helped us write and review the code and draft this page. No figure came from the AI: they all come from running the solver.
Frequently asked questions
Can every Flower Garden deal be won?
No. Our solver proved about 5% of deals impossible.
So what share can be won?
Between about 43% and 95%. Half our deals were too complex for the solver to settle.
Can I play any card from the bouquet?
Yes, any of them, at any time.
Can I move a sequence of cards at once?
No, only one card at a time on this site, which is why empty columns are so valuable.
What is similar?
Try FreeCell or Eight Off, also dealt face up, or Baker's Solitaire. Every game is on the games page.
By Admin, solitaire-free.uk. Study date: 19 September 2026.