RivalPip Cycle

RivalPip Cycle is a hands-on nontransitive-dice construction and pairwise-dominance studio for math-club coaches, middle- and high-school probability teachers, puzzle designers, and recreational mathematicians. Lock face-number maps where A beats B, B beats C, and C beats A, prove win rates exactly, and hand students printable nets—all in one dedicated offline studio instead of scattered PDFs. Open a seeded classic set (Efron, Miwin, Grime, Oskar, or starter pairs) or a blank cube pack. Edit face pips on interactive nets, run exact pairwise outcome matrices and directed cycle graphs, drill beat-this-die classroom challenges, and export worksheet PDFs. Full offline seed libraries and interactive engines power every step. CLASSIC SEEDED GALLERY Browse Efron’s four-die set, Miwin dice, Grime dice, Oskar dice, and two-die starter pairs with illustrated cycle previews, teaching blurbs, and one-tap open—no empty states. DOMINANCE-CYCLE CANVAS Directed arrows show which die beats which, with exact win, tie, and loss percentages on every edge. Tap any die to inspect its faces. INTERACTIVE FACE NETS Edit individual cube faces on an unfolded net with optional 3D-tilt preview. Assign pip counts from 0–9, lock or unlock faces, and instantly recompute cycle strength as numbers change. EXACT PAIRWISE MATRICES Run the full face×face sample space for any two dice. Charts display win/tie/loss bars, with an optional Monte Carlo cross-check strip for classroom demonstration. SEEDED CHALLENGES Solve prompts such as “craft a die that beats Die A but loses to Die B” or “restore a broken Efron cycle,” with automatic validation, progressive hints, and solution reveal after attempts. PRINT-READY WORKSHEETS Generate and preview PDF handouts: labeled face nets, blank student dice, win-rate tables, and a one-page nontransitivity primer suitable for class. COMPARE, REMIX, SAVE Overlay any custom die’s face histogram against a fair d6 or another custom die. Duplicate any seed into a remixable set, rename it, and save progress locally so originals stay intact for teaching. OFFLINE PRIMER & WIDGET Read illustrated definitions of nontransitivity, historical sets, facilitation tips, and common student misconceptions—fully browsable without a network. Pin a medium home-screen widget that rotates a seeded pair of the day with a local win-rate teaser (no push notifications). Built for real probability classes and puzzle nights with SwiftUI, SwiftData, Charts, PDFKit, WidgetKit, and Accessibility. RivalPip Cycle is a mathematics utility—not a multiplayer parlor, not a polyhedral QC tool, not a backgammon coach, and not a generic probability sheet. Build, prove, and teach nontransitive dice with exact engines so your club finally has a dedicated studio.