The playground

Follow your curiosity.

Pick a game, try a move, and see what changes. Follow the idea as far as you like.

137 games & experiments

Heat & learning

Make four histories from one notebook

Swap heads and tails to collect different ordered histories with exactly the same notebook totals.

The history cabinet

Make four histories from one notebook

Tap a head and a tail to swap them. Find 4 distinct orderings while preserving the notebook's totals.

The notebook always reads 3 H and 3 T

Choose an H, then a T. Their positions will trade.

Your history album · 1/20 slots

HHHTTT

There are 20 compatible histories in total. Album slots are a display limit, not a limit on possible histories.

Change the notebook and count all possible histories

Notebook size

Exact log-count / trial

0.720 bits

Shannon limit / trial

1.000 bits

Ω = (\binom{n}{Y}), \log_{2} Ω / n ⟶ H_{2} (Y / n)

A Beta ledger for independent identically distributed trials retains counts, so all these orders yield the same final weights. Their tracelet order is still different. Exact finite log-count and the Shannon large-sample expression differ. An all-heads or all-tails notebook has only one history.

Follow the idea ArticleA coin, a magnet, and a learning machine