The book is open and empty. The first entry sits on step 1, and the smallest entry in the book is the one that folds when the bell rings.
Up to ten ETH entries sit in the book, one per wallet. Each round the smallest folds and its ETH splits evenly to every entry still in. The last one left takes its own back plus every split it caught. How a book runs
no entry of yours in this book
Nine entries, the smallest 0.005 ETH. Round 1: it folds, 0.005 / 8 = 0.000625 to each of the eight left. Round 2: the next smallest, 0.008, folds, 0.008 / 7 = 0.00114 to each of seven. Eight rounds in, one entry stands and takes its own back plus all eight splits it caught.
Anyone can ring the bell once the clock has run out; the contract picks the fold, never a person. Credits are pulled with the claim button. An entry alone in a book before any fold can withdraw.