A Calcutta auction sells rights to an entrant’s tournament prizes, with auction receipts funding the pool from which those prizes are paid. When the buyer’s bid enters that pool, the bid changes both the purchase cost and the amount available for prizes.
Expected share of the prize pool
Expected pool share is the probability-weighted fraction of total pool receipts payable to the purchased interest. It combines finishing probabilities with the payout schedule.
CPGFA’s September 2026 Calcutta terms allocated 50% of the pool to first place, 30% to second and 10% to third, retaining 10%. Applicable transaction and administration costs were additional deductions from payouts. The three prize fractions therefore describe awards before those additional costs.
Take an entrant with a 20% probability of first place, 10% of second, 10% of third and 60% of an unpaid finish. Under those prize fractions, its expected gross pool share is:
q = 0.20 × 0.50 + 0.10 × 0.30 + 0.10 × 0.10 = 0.14.
The 14% expected share is neither the entrant’s 20% win probability nor the 50% award for first place. It is the average fraction payable across all finishes under the supplied probabilities.
A bid that contributes to its own payout
Let B be all other auction receipts, x the buyer’s bid, and q the expected gross pool share. Hold B and q fixed, include the entire bid in the pool, and exclude additional costs. The total pool is B + x, giving:
Expected net return = q(B + x) − x.
Setting expected net return to zero gives the break-even bid:
x = qB/(1 − q), for 0 ≤ q < 1.
Take B = $860 and q = 0.14. The break-even bid is $120.40/0.86 = $140. At that bid, the pool is $1,000 and the expected gross award is $140. Expected net return is zero.
Treating the pool as fixed at $860 would instead produce a $120.40 ceiling. That calculation omits the buyer’s contribution. Under the stated model, a $120.40 bid creates a $980.40 pool and an expected award of $137.256, leaving expected net return of $16.856 before costs.
Each extra dollar bid adds q dollars to the expected award and one dollar to the cost. At q = 0.14, the net expected cost of increasing the bid by one dollar is $0.86. The feedback reduces the marginal cost; it does not remove the bid limit.
Retention and additional charges
Retention already incorporated in the prize fractions must be counted once. The 50%, 30% and 10% awards sum to 90% of receipts. Multiplying those awards by another 90% would apply the same retained share twice.
For an additional fixed cost f, expected net return becomes q(B + x) − x − f. The break-even bid becomes (qB − f)/(1 − q). Take the same $860 of other receipts and 14% expected share, with $8.60 in additional fixed costs. The break-even bid falls to $130: the $990 pool produces an expected award of $138.60, exactly covering the bid and extra cost.
A proportional charge on every award has a different structure. A deduction rate d reduces the expected share to (1 − d)q. A cost incurred only after a particular finish belongs in that finish’s net payout. Neither charge should be inserted as an unrelated fixed fee.
Fixed assumptions and a live auction
The closed-form bid limit holds other receipts and expected share fixed. Later bids change the final pool. Changes in the purchased ownership fraction change the award the buyer receives. Uncertainty shared by the pool size and the expected payout fraction requires a joint model; multiplying their separate averages discards that dependence.
The formula prices a specified purchased interest under specified assumptions. Its break-even point is the bid at which that interest’s expected payout equals the bid and all additional costs.