Simple Simon Solitaire: a high ceiling, and a result we are still checking

Simple Simon is Spider with one deck and no secrets. All 52 cards are dealt face up into ten columns shaped like a staircase, from eight cards down to one. You can build on any suit, but only runs of the same suit move together, and your goal is to assemble four complete suits, King down to Ace.

Because every card is visible, a solver knows exactly what you know. On 3,000 deals ours found a winning line for 86.5%, proved 5.2% impossible and left 8.3% undecided at its search limit. So between 86.5% and 94.8% of Simple Simon deals on this site can be won.

We want to be upfront about one thing: our result does not match the best published figure, and we have not yet found out why. Details are below. Play the game here for free, with nothing to download.

The ceiling at a glance

Where our result and the published one differ

Blake & Gent (2026) report that 97.450% of Simple Simon deals are winnable, which means at most about 2.55% are impossible. We proved 5.2% impossible, with a 95% range of 4.4–6.0%. Those two results cannot both be right for the same game.

Here is what we have checked so far:

• A second program agrees with ours. We re-checked 6 of our "impossible" deals with a completely separate brute-force search. It confirmed all 6.
• Some deals have no move at all. In one of our test deals, not a single legal move exists from the opening position. That deal is clearly lost.
• The rules seem to match. As far as we can tell, the rules we read from this site's game code are the same as those in the paper's rule table.

We have not found the cause of the gap. Until we do, please treat our Simple Simon figures with caution. The top line, that most deals are winnable, holds either way.

The rules as this site plays them

The staircase layout

One deck, all 52 cards face up, in ten columns of 8, 8, 8, 7, 6, 5, 4, 3, 2 and 1 cards. There is no stock.

Mixed-suit building, single-suit moving

• You may place a card on the next-higher rank whatever its suit, mixed suits allowed.
• A run moves as a unit only if it is all one suit. A matching-suit run of any length can travel in one move.
• Any card, or same-suit run, can go into an empty column.

Four suits and done

Build a full suit, King down to Ace, in a column and it is removed automatically. Remove all four suits to win.

Playing close to the ceiling

Prefer the matching suit

Any suit is allowed, but only same-suit runs can move later. A mixed-suit stack is easy to make and hard to undo.

Use the short columns

The columns of one, two and three cards are the easiest to empty. An empty column lets you park a run while you rearrange everything else.

Start with what the deal gives you

On average a deal starts with fewer than one same-suit link already in place (0.76). You will be building almost everything yourself, so plan the order.

Look for the tallest same-suit run you can make

Long same-suit runs move as a unit, and once a run reaches from King to Ace it leaves the table. Keep your eye on which suit is closest to completion.

Use Undo

Every card is visible, so any dead end is visible too. Back up and try the other move.

A sample opening

Simple Simon's staircase layout gives you a natural place to start: the right-hand side, where the columns hold only one, two or three cards.

1. Look at the single card on the far right. If it can go on any card one rank higher, move it. That empties a column straight away.
2. Use the empty column as a workbench. Move a short run or a lone card there so a card underneath can join its own suit elsewhere.
3. Join same-suit cards whenever you can. A 6 of hearts on a 7 of hearts is worth more than a 6 of hearts on a 7 of clubs, because only the first can move later as a group.
4. Clear the next short column. Each empty column makes the one after it easier to clear.
5. Work toward one complete suit. Once a full suit from King to Ace is together, it leaves the table, and there is more room for everything else.

You will not always get a free move from the far-right card, and some deals open slowly. Our solver even found a deal with no legal move at all at the start. Most deals, though, give you a first move or two in those short columns, and a good opening there sets up the rest of the game.

Inside the test, one step at a time

The solitaire-online.us team tested Simple Simon in September 2026.

1. Reading the rules from our game code. Ten face-up columns of 8, 8, 8, 7 down to 1, building down in any suit, same-suit runs that move together with no length limit, any card into a space, and finished suits removed automatically.
2. Rebuilding the game. We wrote Simple Simon as a Python program with those rules.
3. Dealing the cards. 3,000 deals, each from a numbered seed.
4. Choosing the player. A solver. With every card face up, it knows exactly what a player knows.
5. Running it. Up to 200,000 positions per deal: solved, proven impossible or undecided.
6. Checking against published research. Our proven-impossible share is higher than the published figure allows. A separate brute-force program confirmed 6 of our impossible verdicts, and we have not yet found the reason for the difference.
7. Working out the margin of error. A 95% range means the true value would fall inside it in 19 of 20 repeats. Deals solved: 85.3–87.7%.
8. What the numbers cannot tell you. Until the gap with the published figure is explained, we cannot be sure our impossible share is right. It could be too high.

The code behind the ceiling

The study is written in Python 3.11 using only the standard library. Simple Simon shares the module spiderlike.py with Scorpion, and a shared runner spreads the deals across processor cores with Python's multiprocessing. The separate cross-check is verify_simplesimon_bruteforce.py.

The solver is a best-first search: it always expands the position that looks closest to a win, and keeps track of positions it has already seen. We report 95% ranges using the Wilson score interval.

Claude, an Anthropic AI assistant, worked with us on the code, its review and this page's first draft. The AI did not produce the figures. They all come from running the programs, and it was our own comparison with the published research that exposed the gap we describe above.

By Admin, solitaire-online.us (Solitairen OOD). Study date: September 19, 2026.

Ceiling questions from players

What share of Simple Simon deals has a solution?

Most of them. We solved 86.5% of 3,000 deals and estimate between 86.5% and 94.8%. Published research puts it at 97.45%.

Why do your numbers differ from the published ones?

We do not know yet. Our impossible deals were confirmed by a second program, and the rules appear to match. We are still looking.

Can I build on any suit?

Yes, but only same-suit runs move as a group.

Is there a stock?

No. All 52 cards are on the table from the start.

Games in the same family?

Spider Solitaire uses the same idea with two decks and hidden cards. Scorpion Solitaire also removes finished suits, but is far harder.