Flower Garden: a puzzle our solver could not fully crack
Flower Garden deals every card face up: six "flower beds" of six cards across the table, and a "bouquet" of sixteen loose cards you can pick from in any order. There is no stock and nothing hidden. It should be a straightforward game to measure, and yet it turned out to be the hardest game on our list to pin down.
Our solver took on 2,000 deals. It found a win in 43.3%, proved 5.4% impossible, and ran out of search budget on the remaining 51.4%. So the true share of winnable deals lies somewhere between 43% and 95%. That wide range is itself the finding: Flower Garden positions branch so much that even a computer searching 200,000 positions per deal often cannot reach a verdict.
At a glance: Flower Garden in numbers
| What we measured | Result | Deals | How |
|---|---|---|---|
| Deals the solver won | 43.3% (95% range 41.1–45.5%) | 2,000 | Solver, every card visible (as in the game), 200,000 positions per deal |
| Deals proven impossible | 5.4% (4.4–6.4%) | 2,000 | Same solver |
| Deals left undecided | 51.4% | 2,000 | Ran past the budget |
| 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 | Counted from the deal |
| Solved with 2 or more Aces in the bouquet | 44.2% | 747 | Same solver |
| Solved with 0 or 1 Ace in the bouquet | 42.8% | 1,253 | Same solver |
No published study has measured Flower Garden, so these are original figures.
The rules on this site
- One pack of 52 cards, all face up.
- Six tableau columns (the flower beds) of six cards each.
- The bouquet: the other 16 cards, laid out where you can see them all. Any bouquet card may be played at any time.
- On the tableau you build down regardless of suit: any 7 on any 8.
- Only one card moves at a time. Runs cannot be moved as a unit.
- Any card may fill an empty column.
- There is no stock.
- Four foundations are built up by suit from Ace to King. Get all 52 cards home to win.
What the numbers tell you
The bouquet is your real resource
With sixteen cards available in any order, the bouquet works like a large set of free cells that starts full. Every card you play out of it is one less card you have to find a home for later.
Where the Aces start barely matters
On average about 1.26 of the four Aces start in the bouquet, ready to play. You might expect those deals to be easier. They are only slightly: 44.2% solved with two or more Aces in the bouquet against 42.8% with one or none. The difference is small enough to be chance. What matters more is how the beds are stacked.
One card at a time is what makes it hard
Because you cannot move runs, every tidy sequence you build is fixed in place until you dismantle it card by card. That is why the game is so hard to search, and why it rewards thinking a few moves ahead.
Strategy for Flower Garden
Plan backwards from the buried low cards
Look at the bottom of each bed (the cards dealt first, now under five others). Low cards buried there are your main problem. Count how many cards sit on top of each Ace and 2, and start with the easiest to free.
Don't empty the bouquet too fast
It is tempting to play bouquet cards onto the beds just because they fit. A card in the bouquet is available at any moment; a card in a bed is only available when it is on top. Keep bouquet cards in reserve unless playing them achieves something.
Build runs you can take apart
Since runs cannot move as a unit, a long run sitting on a buried Ace is a problem. Try to build runs on cards you will not need for a while.
Empty a bed, then use it well
Any card can fill an empty bed, which makes an empty column very flexible. Use it to unpick a stack one card at a time rather than filling it with the first card that fits.
Undo is part of the game
With so many choices at every step, Flower Garden is a game where trying a line and stepping back is the normal way to play. Undo is unlimited here.
Playing Flower Garden here
The game is free and runs in any modern browser on a computer, tablet or phone, with no download, installation, account or email needed. The cards are large and easy to read, and a zoom control makes the table bigger. You have Hint, unlimited Undo, Restart and Auto Play, and you can drag or tap cards to move them. Wins, time and moves are tracked for the current game, and sound, fullscreen and table colour are all adjustable.
How we did the research, step by step
The free-solitaire.nz team ran this study in September 2026 to find out how winnable Flower Garden is under this site's rules.
- Read the rules from the site's code. Flower Garden has its own engine on the site: six columns of six and a 16-card bouquet, all face up; any bouquet card playable; building down regardless of suit, one card at a time; any card in a space; no stock.
- Rebuilt the game as a program and checked it follows those rules.
- Dealt 2,000 numbered games, seeds 1 to 2,000, so each one can be replayed exactly.
- Chose a solver. Nothing is hidden in Flower Garden, so the solver knows exactly what a player knows. For each deal it finds a win, proves none exists, or runs out of budget.
- Ran it with a budget of 200,000 positions per deal. The 2,000 deals took about 24 minutes.
- Looked for published figures. Blake and Gent (2026, Journal of Artificial Intelligence Research) do not cover Flower Garden, and we found no other study, so there is nothing to compare with.
- Worked out the margin of error. The solved share is 43.3% with a 95% range of 41.1–45.5%: repeat the test on fresh deals and the true figure lands there 95 times in 100.
- Stated the limits honestly. Half the deals were undecided, so we can only say the winnable share is between 43.3% and 94.7%. A bigger budget would narrow that range; we have not run one yet.
The technical side
The simulation is written in Python 3.11 using only the standard library, in its own module, flowergarden.py. The solver is a best-first search. It scores each position by the number of cards not yet home plus the number resting on a lower card, always expands the best-scoring position next, and keeps a record of positions already seen so none is explored twice. Foundation moves are made automatically only when they are provably safe; with any-suit building that means low cards, or cards whose every possible "partner" is already home. A shared runner.py spreads the work across parallel worker processes with multiprocessing, every deal comes from a numbered seed, and the 95% ranges are Wilson score intervals. An AI assistant (Claude, from Anthropic) helped write and review the code and draft this page. It produced no figures: all of them come from running the solver, and the team reviewed them before publishing.
By Admin, free-solitaire.nz. Study date: 19 September 2026.
Frequently asked questions
How many Flower Garden games can be won?
At least 43.3% of deals, and at most 94.7%, based on 2,000 deals. Our solver could not settle the other half within its budget.
Why is Flower Garden so hard to measure?
Every card is available and any card can go on any higher card, so each position has many possible moves. The number of positions grows very quickly.
Can I move a whole run at once?
No. In Flower Garden only one card moves at a time.
Can I play any bouquet card?
Yes, any of them, at any time.
What should I try next?
Try FreeCell, another game with every card visible, or Golf for something quicker.