2026 Calcutta — Portfolio P&L Monte-Carlo

50,000-draw forward simulation of Wednesday's auction. If we ran it thousands of times, what is our profit/loss distribution — and how much should we risk?

+28%

Best feasible slate E[ROI]
(fav5, sharp probs)

−4 to −14%

E[ROI] if probabilities are uniform (no edge)

~$1,500

Recommended stake (~60% of $2,500 budget)

121%

Budget used by the rec6 slate — over budget

Executive summary / verdict

A positive-EV slate exists — but only if the model's sharp probabilities are roughly right, and only at a sane bet size. Sharp p_win: every slate +18% to +37% E[ROI]. Shrunk: +8% to +19%. Uniform 1/6: every slate loses (−4% to −14%).
The recommended 6-team slate does not fit the $2,500 budget. Half-back cost ~$3,021 (121%); adverse selection ~$4,293 (172%). rec5/rec8 also over. Feasible attractive slates: sand3, cheap5, fav5.
Recommended: a small value/favourite-tilted 3–5 team slate, ~$1,300–$1,900 (50–75% of budget), holding dry powder. fav5 = best single slate; sand3 = top ROI but feast-or-famine; cheap5 = lowest downside (VaR ~$630).
Risk of ruin is non-trivial: P(lose >50% of staked capital) is 15–25% (sharp/shrunk), 25–44% (uniform). Size it like a high-variance bet.

Bottom line: No slate is positive-EV under the pessimistic (uniform) probabilities. If the model is even partly sharp, a 3–5 team value slate at ~$1,500 (~60% of budget) is the risk-adjusted sweet spot: positive expected P&L, lowest dollar downside, and budget held in reserve in case the model is wrong.

P&L distribution by probability scenario

P&L distribution by scenario — rec6 slate. The sharp distribution (navy) sits clearly right of zero; shrinking the probabilities pulls the mean toward zero; under uniform (red) the mean goes negative.

Headline results — naive buyback, est-price

E[ROI] is on capital actually deployed. VaR$ = 5th-percentile P&L (95% one-sided VaR). ⚠ = mean capital deployed exceeds the $2,500 budget.

Slate	Scenario	E[ROI]	E[P&L]	P(profit)	Median	VaR$ (5th)	P(lose >½ stk)	Stake	%budget
sand3 n=3	sharp	+36.5%	$+496	51%	$+27	$-1,411	25%	$1,360	54%
	shrunk	+19.3%	$+262	45%	$-80	$-1,433	32%	$1,360	54%
	uniform	-5.9%	$-80	35%	$-302	$-1,459	44%	$1,360	54%
cheap5 n=5	sharp	+17.8%	$+116	56%	$+74	$-629	17%	$655	26%
	shrunk	+9.0%	$+59	51%	$+17	$-648	22%	$655	26%
	uniform	-4.5%	$-30	44%	$-77	$-664	29%	$655	26%
fav5 n=5	sharp	+27.6%	$+514	59%	$+400	$-1,697	16%	$1,863	75%
	shrunk	+10.9%	$+203	51%	$+42	$-1,816	22%	$1,863	75%
	uniform	-13.9%	$-258	37%	$-468	$-1,898	34%	$1,863	75%
rec5 n=5	sharp	+21.6%	$+490	59%	$+397	$-2,178	16%	$2,267	91%
	shrunk	+8.8%	$+199	52%	$+57	$-2,245	21%	$2,267	91%
	uniform	-10.2%	$-231	41%	$-424	$-2,302	30%	$2,267	91%
rec6 n=6	sharp	+21.8%	$+660	59%	$+504	$-2,467	16%	$3,021	121% ⚠
	shrunk	+9.5%	$+286	52%	$+81	$-2,832	20%	$3,021	121% ⚠
	uniform	-8.6%	$-261	41%	$-478	$-2,999	29%	$3,021	121% ⚠
rec8 n=8	sharp	+19.6%	$+672	59%	$+518	$-2,513	13%	$3,425	137% ⚠
	shrunk	+8.3%	$+283	52%	$+105	$-2,789	18%	$3,425	137% ⚠
	uniform	-8.3%	$-283	41%	$-474	$-3,105	26%	$3,425	137% ⚠

Slate comparison

Buyback model: naive vs adverse selection

Buyback effect — Adverse selection (owners buy back the strong teams, we keep the losers) **raises total dollars** but **lowers ROI** and pushes capital deployed from $3,021 to $4,293 — it makes the big slates budget-infeasible. The honest metric is ROI, which falls.

Optimal number of teams & bet sizing

ROI vs slate size — More teams cut variance but E[ROI] drifts down as the slate grows. Beyond ~5 teams you also blow the budget. Sweet spot: 3–5 teams.

More teams → lower variance (P(lose >½ stake) 25% → 13% sharp) but E[ROI] erodes (+36% → +20%), and you exceed budget past ~5 teams.
fav5 — best balance: +28% E[ROI] sharp, 59% P(profit), 75% of budget. The recommended single slate.
cheap5 — lowest variance and smallest dollar VaR (~$630); a base-hit portfolio.
sand3 — highest E[ROI] (+37%) but only 3 bets, so feast-or-famine (lowest P(profit)).
Sizing rule: stake ~60% of budget (~$1,500) on a 4–5 team slate; hold ~40% reserve.

Caveat on EV

Under the uniform scenario every slate is negative-EV (favorites hit −39% in a backtest year). If Wednesday's room prices efficiently, reality sits near uniform. All the positive EV above is contingent on our probability edge being real — the biggest risk, bigger than buyback or price noise, and the reason to bet small and keep powder dry. Also note: if we win every bidding war (pay recommended_max_bid), rec6 E[ROI] collapses from +21.8% to +9.1% — discipline at the auction matters as much as slate choice.

Assumptions

Budget	$2,500 partnership stake.
Payout	Within each flight, winner 70% / runner-up 30% of the payout pool; 10% of the pot directed to the shootout. Ties split.
Buyback (naive)	Every won team half bought back → cost = hammer/2, own 50%.
Buyback (adverse)	P(buyback)=logistic(−0.62 + 12·(p_win−1/6)); favourites ~55–70%, average ~35%. We keep full ownership of losers (adverse selection). Tunable.
Probabilities	Sharp `p_win`/`p_2nd`, shrunk-to-uniform versions, and uniform 1/6 (pessimistic). We do not know which is right.
Prices	`est` ~ est_price ±12% noise; `maxbid` = recommended_max_bid (we win every bidding war).
Outcomes	Winner ~ p_win; runner-up ~ p_2nd over non-winners. Buyback decided pre-outcome (independent). Flights independent.

50,000 draws/cell, seed 20260610, common random numbers across scenarios. Engine: mc_portfolio.py. Data: valuation/bid_sheet_enriched.csv, valuation/team_values.csv. Times US Eastern.