TriPeaks Solitaire
Play TriPeaks solitaire, plus solved proof of what the king-to-ace wrap rule is worth: it removes 89% of the impossible deals.
Click any uncovered card that is one rank above or below the face-up card, and it becomes the new face-up card. A card is uncovered once both cards resting on it have gone. Stuck? Turn a card from the stock. Clear all 28 to win. Flip the wrap setting to feel the difference the table below measures. Everything runs in your browser; nothing is uploaded.
The wrap rule removes nine impossible deals in ten
TriPeaks is played two ways. In one, a king wraps round to an ace so that K–A–2 is a run; in the other a king only ever meets a queen. It reads like a footnote on a rule sheet. It is closer to being a different game. Every deal below was solved — the search either finds a way to clear all 28 cards or proves that none exists.
| Rule | Deals | Winnable | Share | Impossible | Undecided |
|---|---|---|---|---|---|
| No wrap | 2,000 | 1,450 | 72.5% | 550 | 0 |
| King wraps to ace | 2,000 | 1,941 | 97.0% | 59 | 0 |
The impossible column falls from 550 to 59 — 89% of the dead deals stop being dead. Put the other way round: without the wrap you are handed an unwinnable deal about once every four games, and with it about once every 34.
Both rows use the same 2,000 shuffles, so they can be subtracted. 491 deals are winnable with the wrap and not without it — 25.3% of everything the wrap version wins. That is the measure of how often the rule is load-bearing rather than decorative: in a quarter of your victories it was doing real work.
Which is why "TriPeaks is a game you almost always win" is a claim about a rule rather than about the game. Under the wrap it is right, at 97.0%. Said of the version without it, it is wrong — better than one deal in four cannot be cleared at all.
Every deal was decided
None of the 4,000 deals hit the search budget, so the "impossible" column is a proof rather than a timeout. That distinction is the whole difference between a measurement and a guess: a bounded search that counts everything it failed to crack as unwinnable would inflate exactly the number this page is about. The button above reports three outcomes and will say it could not decide rather than pretend.
TriPeaks is much cheaper to solve than most solitaires, and for a specific reason: the only things that can matter are which tableau cards have gone, how far into the stock you are, and the rank of the face-up card. The waste is never drawn from again, so its history can be thrown away entirely.
And 59 deals resist both versions — 2.9% that no rule variant here rescues. Those were lost at the shuffle.
The table is frozen, because solving 4,000 deals takes over a minute. So that it cannot go quietly stale, 40 fresh deals from a different stretch of the shuffle are solved under both rules every time this page is built: 65% without the wrap against 95% with it.
How to use
- Click any uncovered card one rank above or below the face-up card to take it.
- A card is uncovered once both cards resting on it have gone.
- Turn a stock card when nothing is playable; there is no redeal.
- Clear all 28 tableau cards to win.
- Switch the wrap setting to play the harder version where a king only meets a queen.
Frequently asked questions
What is the king-to-ace wrap rule?
In one version of TriPeaks a king wraps round to an ace, so K-A-2 counts as a run and you can play an ace onto a king. In the other a king only ever meets a queen. Both versions are played and neither is more official, which matters more than it sounds.
How much does the wrap rule actually change?
A great deal. Solving 2,000 shuffles under each rule: without the wrap 72.5 per cent of deals are winnable, with it 97.0 per cent. The number of impossible deals falls from 550 to 59, so 89 per cent of dead deals stop being dead. Without the wrap you meet an unwinnable deal roughly every fourth game; with it, about every thirty-fourth.
How often does the wrap actually matter in a game you win?
Both figures come from the same 2,000 shuffles, so they subtract cleanly: 491 deals are winnable with the wrap and not without it, which is 25.3 per cent of everything the wrap version wins. In about a quarter of your victories the rule was load-bearing rather than decorative.
Are these win rates from playing or from solving?
From solving. Each deal is either shown to be clearable or proved impossible, so the figures describe the deals rather than anyone’s skill. None of the 4,000 searches hit its budget, so the impossible column is a proof and not a timeout — the solver reports "could not decide" as a separate outcome precisely so it can never be mistaken for "impossible".
Why is TriPeaks so much easier to solve than other solitaires?
Because almost nothing about the position needs remembering. Only three things can matter: which tableau cards have gone, how far into the stock you are, and the rank of the face-up card. The waste is never drawn from again, so its entire history can be discarded, which collapses the search enormously.
Does this send anything anywhere?
No. Deals are shuffled and solved entirely in your browser and nothing is uploaded.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.