Pyramid and TriPeaks: How Many Deals Are Solvable?
Pyramid and TriPeaks both clear 28 cards from a layout with help from a stock, yet they behave very differently when you ask how many deals can be won. Here are the figures from our own solver, the settings they depend on, and what they do not tell you.
What our solver found
| Game | Deals tested | Proved winnable | Share |
|---|---|---|---|
| Pyramid | 4,000 | 2,321 | 58.0% |
| TriPeaks | 2,000 | 1,827 | 91.3% |
Each winning line was replayed move by move to confirm it wins. The search had a fixed budget, so the numbers are lower bounds: an unproven deal is not shown to be unwinnable.
Why the two games differ
In Pyramid you must remove cards in pairs that add up to 13, and each value has exactly one partner, so a deal can run out of partners. The stock can be turned over twice, so you see it up to three times in total. In TriPeaks any card one rank above or below the waste card can be played, so there are usually several choices, and Ace and King count as neighbours. That wider choice is a plausible reason for the higher figure, but we have not tested it in isolation.
The numbers depend on the rules
The figures hold for the settings the solver used: two turn-overs of the stock in Pyramid, and Ace-King wrapping in TriPeaks. Changing either setting would change which deals are winnable, and the library would have to be rebuilt. Solitaire Play deals new games and the Daily Challenge only from the proved library for both games.
Winnable is not easy
The solver sees every hidden card and you do not, so a proved deal can still be hard. See the strategy guides for Pyramid and TriPeaks, then try Pyramid or TriPeaks.
Frequently asked questions
Can every Pyramid deal be won?
No. In our run of 4,000 deals the solver proved 58.0% winnable. Solitaire Play deals only from that proved set.
Can every TriPeaks deal be won?
Not every one. In our run of 2,000 deals the solver proved 91.3% winnable, and the game deals only from that proved set.
Why is TriPeaks more winnable than Pyramid?
In our sample it is: 91.3% against 58.0%. TriPeaks gives more choices per move; Pyramid needs exact pairs that add up to 13. We have not isolated the cause.
Do the numbers include redeals?
Pyramid figures assume the stock can be turned over twice, as in the game. TriPeaks has no redeal.