Simple Simon Solitaire: our result, the published one, and a gap we haven't explained
Simple Simon is a one-pack cousin of Spider. Every card is dealt face up in a staircase of ten columns, you build down regardless of suit, and you win by assembling each suit from King to Ace so that it clears away. With nothing hidden, it is a natural game to measure with a solver.
Over 3,000 deals our solver won 86.5%, proved 5.2% impossible and left 8.3% undecided, which puts the winnable share somewhere between 86.5% and 94.8%. The peer-reviewed study from the University of St Andrews puts it at 97.450%. Those two results do not agree, and we have not yet found out why. This page sets out both honestly, together with what we have checked so far.
The two results side by side
| Source | Solved / winnable | Proven impossible | Undecided | Deals |
|---|---|---|---|---|
| Our solver, this site's rules | 86.5% (95% range 85.3–87.7%) | 5.2% (95% range 4.4–6.0%) | 8.3% | 3,000 |
| St Andrews study (Blake and Gent) | 97.450% winnable (±0.034%) | at most about 2.55% | – | – |
Where the disagreement lies
If 97.45% of deals are winnable, then no more than about 2.55% can be impossible. Our solver proved 5.2% impossible, and even the lower end of our margin of error, 4.4%, is above that ceiling. So this is not a matter of our sample being small or unlucky: at least one of the two studies must be looking at a slightly different game.
What we have checked
- A second, independent check. We took six of the deals our solver called impossible and ran them through a completely separate brute-force search. It agreed on all six.
- A deal with no moves at all. One of our deals (seed 81) has no legal move in its opening position, so it is certainly lost. That shows impossible Simple Simon deals exist under the rules we coded.
- The rules. We read the rules from this site's game code, and they appear to match the rule table in the published study. We have not found the difference.
What we are not claiming
We are not saying the published figure is wrong. It comes from a careful, peer-reviewed study. The most likely explanation is a rule detail that we read differently. Until that is resolved, please treat our Simple Simon figure with caution: it describes the game as coded on this site, as best we understand it.
More from the deals
- On average, a deal starts with 0.76 same-suit links already in place — places where a card sits directly on the next higher card of its own suit.
- Some deals, such as seed 81, give you no legal first move at all.
How Simple Simon is played here
The layout
All 52 cards are dealt face up into ten columns in a staircase: the first three columns have eight cards, then seven, six, five, four, three, two and one. There is no stock.
Building and moving
- Any card may go on a card one rank higher, of any suit: the 4 of hearts on the 5 of clubs.
- Only a run in a single suit can be moved as a group, and on this site there is no limit to its length.
- Any card, or same-suit run, may go into an empty column.
Winning
When a column holds a complete suit in order from King down to Ace, it is removed automatically. Clear all four suits to win.
Strategy tips
Build in suit whenever you can
You are allowed to build in any suit, but only same-suit runs move together. A mixed run is stuck unless you break it card by card.
Empty columns first
The short columns on the right are quick to clear. An empty column takes any card, and it is your best tool for untangling mixed runs.
Check the opening
Look for the same-suit pairs already in place (fewer than one per deal on average) and build on them.
Recognise a dead deal
If there is no legal move at the start, the deal cannot be won. Deal again.
Simple Simon on solitaire-free.uk
It is free and plays in any modern browser, on computer, tablet or phone, with nothing to install and no account. Cards are big and easy to read, with a zoom control for ten columns. There is Hint, unlimited Undo, Restart and Auto Play; you can drag or tap to move; and wins, time and moves are kept for the current game. You can switch sound off, go fullscreen and change the table colour.
How we ran the research, step by step
- Rules from the game code. Ten face-up columns of 8, 8, 8, 7, 6, 5, 4, 3, 2 and 1 cards; building down in any suit; same-suit runs of any length move; any card into a space; completed King-to-Ace suits removed automatically.
- Rebuilding the game. We wrote Simple Simon in Python, sharing code with our Scorpion program, and built a solver.
- Numbered deals. 3,000 deals (seeds 1 to 3,000), each shuffled from a numbered seed so any deal, including seed 81, can be dealt again.
- The solver. Nothing is hidden, so the solver sees what you see. It searched up to 200,000 positions per deal and reported each deal as solved, proven impossible or undecided.
- Cross-checking the "impossible" verdicts. Six of them were re-checked with a separate brute-force search, which agreed each time.
- Comparing with St Andrews. Blake and Gent (Journal of Artificial Intelligence Research, 2026) report 97.450%. Our proven-impossible share is too high to fit that, and we have not found the reason.
- Margin of error. Our 86.5% solved has a 95% range of 85.3% to 87.7%; the 5.2% proven impossible has a range of 4.4% to 6.0%.
- Limits. 8.3% of deals were undecided. And until the gap with the published study is explained, our figure should be read as provisional.
Behind the numbers: the code
The solver is in spiderlike.py, written in Python 3.11 with only the standard library; the same module handles Scorpion. It is a best-first search that always explores the most promising position next and keeps a set of positions already seen so it never searches one twice. The separate cross-check is verify_simplesimon_bruteforce.py. Deals were spread over the cores of one machine with Python's multiprocessing, and the 95% ranges are Wilson score intervals. We used Claude, an AI assistant from Anthropic, to help write and review the code and draft this page. The AI did not supply any figure: all of them come from running the solver.
Frequently asked questions
How many Simple Simon deals can be won?
By our count, between 86.5% and 94.8% under this site's rules. The published study says 97.45%. We explain the gap above.
Why don't your figures match the research?
We don't know yet. Six of our impossible deals were confirmed by a second method, and one has no legal first move. Most likely, a rule is being read differently somewhere.
Can any card go into an empty column?
Yes, any card or same-suit run.
Can I move a run of mixed suits?
No. Only single-suit runs move together.
What should I try next?
The two-pack Spider Solitaire builds suits the same way; Scorpion is a much harder one-pack relative. See every game on the games page.
By Admin, solitaire-free.uk. Study date: 19 September 2026.