jheapsandClaude Opus 5
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"Ann - $135" is the answer to the arithmetic. The dealer's actual job at that moment
is working out that $135 is a black, a green and two reds, while four people watch
them do it.
The chip legend has known the denominations all along. It was only being used to read
chips *into* an amount -- counting a seat's stack -- and never to turn an amount back
into chips.
Final Payouts
Ann - $135
1x$100, 1x$25, 2x$5
Largest first, which is greedy and so not optimal for an arbitrary set of values. Poker
chips are not arbitrary: every real set is canonical -- each denomination divides the
next, 1/5/25/100/500 -- and greedy is exactly optimal on those. A dealer who invents a
3-and-7 chip set still gets a valid answer, possibly one chip longer than it needed to
be, which is a fair trade for not solving a knapsack in a modal.
Two cases where saying nothing is the right answer, and one where it is not.
A table with no chip legend gets the amount on its own -- it has not told us its
denominations, so there is no advice to give. But a legend that exists and cannot reach
the amount does say so: "$3 no chip covers" when the smallest chip is $5. Half a dollar
in a dollar-chip game is the dealer's problem to solve and they can only solve it if
they are told, so it is never rounded away.
12 tests (244 total): the breakdown adds up to the amount across eight amounts, cent
chips make cent amounts exactly, a jumbled legend still pays largest first, the colour
comes along for a future caller, and the two no-advice cases are told apart from the
cannot-reach one.
Driven through a real all-in hand at four sizes: $135 reads "1x$100, 1x$25, 2x$5" and
a tournament-sized $1,350 reads "2x$500, 3x$100, 2x$25", fitting without spill down to
360px. With the legend emptied the line disappears and the payout stands alone.
Contrast clean, no console errors.
Co-Authored-By: Claude Opus 5 <[email protected]>
Claude-Session: https://claude.ai/code/session_015bnp7xKUPFFSpwkYNFaPgb