Solitaire Draw 3: when a perfect player still loses
Imagine a player who can see through every face-down card and already knows the order of the stock. Surely that player wins every deal? Not in Draw 3. When we gave 1,000 numbered deals to a computer solver with exactly that power, it proved that 9.5% of them (95% range 7.8%–11.5%) cannot be won by any sequence of moves at all. With one-card draws, on the same 1,000 deals, only 2.1% (1.4%–3.2%) were proven lost.
This page is the same game as our home page: Klondike, stock turned three cards at a time, only the top card of each three playable, unlimited trips through the stock. The home page shows what three-card draws do to an ordinary player. Here we look at the other end: what they do to the best play there is, and why some deals close for good.
At a glance: the ceiling in Draw 3
| Outcome for the all-seeing solver | Draw 3 | Draw 1 (comparison) | Deals |
|---|---|---|---|
| Found a winning line | 66.2% (63.2–69.1%) | 76.6% (73.9–79.1%) | 1,000 each |
| Proved no winning line exists | 9.5% (7.8–11.5%) | 2.1% (1.4–3.2%) | 1,000 each |
| Undecided: search limit of 150,000 positions reached | 24.3% (21.7–27.1%) | 21.3% (18.9–24.0%) | 1,000 each |
| So the winnable share lies between | 66.2% and 90.5% | 76.6% and 97.9% | |
| Published winnable share (Blake and Gent, 2026) | 81.95% (±0.08) | 90.48% (±0.12) | their sample |
Our ranges contain both published values, so the two studies agree. The published figures are tighter because their solver ran far longer; ours leaves about a quarter of Draw 3 deals undecided, and we report them as undecided rather than guess.
Why a three-card draw can lock a deal
In Draw 1, every stock card reaches the top of the waste sooner or later, so a perfect player can always get at the card they need. In Draw 3 you only ever see every third card of the pile. The others become reachable only when you play something off the waste and the groups shift. If the card you need sits in the middle of a group, and nothing from the waste can go anywhere to shift it, it stays out of reach no matter how many times you go round.
That is the mechanism behind the gap between 2.1% and 9.5% proven lost. Our solver models exactly which positions the three-card deal can reach, so these proofs are about the draw rule, not about bad luck in the tableau. The deals themselves are the same in both columns of the table.
And for a player who cannot see the cards?
The ceiling is one side. The floor is a simple program that sees only what you see, plays by a fixed priority list and never undoes a move. On 10,000 deals it won 10.6% in Draw 3 (10.0%–11.2%) and 42.3% in Draw 1 (41.3%–43.3%). The distance from 10.6% up to the 66.2% the solver found is room that planning, memory and Undo can claim. Nobody will reach the ceiling, because nobody can see the face-down cards.
We have no figure for how real people do in Draw 3. The only real-player number we cite, 44.8% over 913,106 games on solitairex.io, is for draw-one Klondike.
What the undecided quarter means
For 24.3% of Draw 3 deals the solver hit its limit before it could either find a win or prove there was none. Those deals are not lost; they are simply unsettled. That is why we give the winnable share as a range, 66.2% to 90.5%, and not as one number.
Draw 3 rules on this site
- Deck: one 52-card deck.
- Tableau: seven columns of 1 to 7 cards, top card face up, 21 face down.
- Stock: 24 cards, turned three at a time; only the top waste card plays.
- Redeals: unlimited. We did not measure a pass limit for Klondike, so we cannot say what one would cost.
- Building: down in alternating colors; any face-up run may move.
- Empty columns: Kings only.
- Foundations: Ace to King by suit; one card may be taken back down.
Keeping a deal open
Leave the waste movable
A waste card you can play is your only lever for shifting the groups. Before you fill the last spot a waste card could have gone, ask whether you will need to shift the stock later.
Take cards back from the foundation
The site lets one foundation card come back down. A 4 returned to the tableau can give a waste 3 somewhere to land, and that single play reshuffles every later group.
Remember the groups
After one lap you know which cards are stuck in the middle. Plan the play that frees them rather than cycling and hoping.
Use Undo when a lap goes nowhere
If a whole lap produced no play, the stock will repeat itself exactly. Step back and change something in the tableau first.
Playing on solitaire-turn-3.com
Draw 3 is free in any current browser on computer, tablet or phone, with no account. You get Hint, unlimited Undo, Restart and Auto Play, drag or tap moves, zoom and fullscreen, sound and table-color settings, and a Draw 1 / Draw 3 toggle that takes you to Klondike Turn 1. Klondike Turn 3 is this same game with a practical guide to the stock.
How the figures were made
- Rules: read from this site's own Klondike code; Draw 3 and Draw 1 share every rule except the number of cards turned.
- Solver: a depth-first search over every legal move, seeing hidden cards and the stock, modeling the exact positions a three-card draw can reach, with a limit of 150,000 positions per deal. An exhausted search counts as a proof.
- Deals: seeds 1–1,000 for the solver and 1–10,000 for the program, the same in both modes.
- Ranges: Wilson score 95% intervals. Published figures from Blake and Gent (2026).
Claude, an AI assistant by Anthropic, helped write the code and draft this page. Every figure comes from running the code or from the linked study, and the team checked them.
Draw 3 questions
Was my lost game impossible?
Maybe, but probably not: about one deal in ten is proven lost for a perfect player, and at least two in three were won by the solver.
Is Draw 1 always easier?
On our evidence, yes: higher at both floor and ceiling, on identical deals.
Where next?
See all games on the games page and longer articles on the blog.
By Admin, solitaire-turn-3.com (Forty Media). Research run September 2026.