Cornering capital

• The average cost of a card is $latex (5+10+15+20+25+30+35+40) / 8 = \$22.5$.
• The average cost of a set of 7 auctioned cards is $157.50
• The average turn-to-turn-ROI of a card is 29% (52/180)
• In each set of 7 auctioned cards an average of (22.5*7) = $157.50 will be spent in card cost across the players (assuming no rounds in which everyone passes and assuming no duplicate card values in the set)
• If only one card is purchased per round at face value (likely to be one or two), then a minimum of $12 was spent in bid reservations, giving an average total expenditure per round of $169.50
• Assuming that bidding pressure forces an average over-cost payment of 30% per card, that means the total per-round expenditure is $220.35
• An average player will spend 1/N of that (N is number of players) in acquiring cards.
• Mapping out the turns:
• if a player spends $X on cards in a given round
  • At the end of the round they will earn 29% of $X
• if the player spends $X on the second round
  • Their starting capital will need to have been at least 171% of $X
  • They will earn 58% of $X in revenue
• If they spend $X on the third round
  • Their starting capital will need to have been at least 213% of $X
  • They will earn 87% of $X
• If they again spend $X on the fourth round
  • Their starting capital will need to have been at least 226% of $X
  • They will earn 116% of $X
  • They are now profitable; their per-round expenditures of $X are exceeded by their revenue income
• Thus the total capital required among the players at the start of the game is $latex (4*220.35 * 2.26) = \$1,991.96$

The above doesn’t account for the probabilities of multiple cards of the same value in a lot, thus increasing over-payment, or the potential of players passing and thus driving prices down. It also ignores the fact that cards pay out 6 times per game, thus making the big cards even more valuable than they already are. And there are some other nice fat holes in the logic. Still, $500 per player in a 4 player game seems a reasonable sum.

Hurm.

An idle thought to enliven the mix:

• When passing a player may instead tap some or all their cards for cash and receive Q% (50%?) of their revenue in cash. Such tapped cards do not pay again at the end of the round.