games: the buy-in and the rake each player sees are their own, not the table's

The two-browser pass found it: at a table two humans share, the felt quoted
each of them the pair's total. "Bought in for 200" to a player who put in 100,
and a session-rake line that climbed on a pot the other one won.

Both were table totals the view read straight off the engine — correct while a
table had one human, wrong the moment it had two. Fixed along the border it
already draws: bought_in is border accounting, so it comes from the viewer's own
game_seats.staked; session rake is a within-table event, so it rides a new
per-seat Seat.Paid beside the audit's table-total s.Paid.

And top-up never grew game_seats.staked, so the storage invariant drifted by
every top-up and the felt under-reported the buy-in — it does now.

Claude-Session: https://claude.ai/code/session_013M5nD7PgUboJXoDcYHzpuJ

internal/games/holdem/eval.go

@@ -187,7 +187,12 @@ func (s *State) payPot(pot Pot, live []ranked, evs *[]Event) {
 			// climbed while every human folded would be telling them it had.
 			for _, w := range winners {
 				if !s.Seats[w.seat].Bot {
+					// The table total (for the audit's delta) and the winner's own
+					// running tally (for the ledger line the felt shows them). At a
+					// table with two humans these are different numbers: each player is
+					// only ever quoted the rake that came out of a pot they won.
 					s.Paid += rake / int64(len(winners))
+					s.Seats[w.seat].Paid += rake / int64(len(winners))
 				}
 			}
 			*evs = append(*evs, Event{Kind: "rake", Seat: -1, Amount: rake})