Hold YES contracts on a basket of World Cup teams. If any one of your teams wins, the basket pays out. Below are four strategies — switch between them and plug in your own estimates to see how each mode changes cost, net return, and ROI.
Change the Defaults to Quantify Your Estimates
Tap the card that matches how you’d trade; switch anytime. The comparison panel below shows which path wins and changes as you adjust your teams and probabilities.
Simple basket: n upfront YES, no fillers for the eliminated teams (default n=8)
Eight upfront YES, with fillers for the eliminated teams at quarter-finals
n upfront YES now, 8−n planned adds at quarter-finals, with fillers for the eliminated teams at quarter-finals
Four upfront YES, with fillers for the eliminated teams at semi-finals
Fillers are extra YES contracts bought at the round you target to top up your basket to the required slot count. Mode A has no fillers (just your chosen n upfront teams). In Mode B they cover whoever missed quarter-finals from your upfront eight. In Mode C they cover those misses plus your planned 8−n quarter-final adds. In Mode D they cover the four semi-finalist slots. Price is estimated using the adjustable λ blend and filler multiplier right under Section 1. Check the Math reference section for more details.
Mode Comparison Panel (select K per mode)
Dial in your three inputs below —scenario probabilities, risk-free rate, and lifetime N— and the six cards below update automatically. Top row: expected dollar return on one deployment, Sharpe ratio per opportunity, and the Kelly fraction (the theoretically optimal stake — treat it as a ceiling). Bottom row: long-run wealth compounding if you play this N times at half-Kelly, and how often you’d expect a total wipeout in N bets. Your probabilities drive everything. Change them and watch everything move.
Equality blend (λ): When buying filler YES contracts at the target round (quarter-finals in Modes B and C, semi-finals in Mode D), you need to decide how many shares of each to buy to maintain the payoff target. The proportional approach buys shares in proportion to each team's implied win probability (i.e. how much the market thinks they'll win). The flat approach gives each filler slot an equal share of the $1 payoff pool regardless of odds — that's 1 / N_slots, so 12.5¢ for 8-slot quarter-final fields (Modes B and C) and 25¢ for 4-slot semi-final fields (Mode D). λ blends the two: filler_share_i = λ × (ask_i / Σ asks) + (1 − λ) × (1 / N_slots). At λ=1, you track the market exactly. At λ=0, you split the payoff equally across all slots. Intermediate values let you underweight expensive favorites and overweight cheap longshots among your fillers.
Filler price multiplier: The multiplier applies a premium over the proportional baseline cost estimate — e.g. 1.85× means fillers are modeled to cost 85% more per share than a purely proportional pre-tournament price would suggest. This is a conservatism assumption for scenario cost modeling, not applied to your upfront holdings. Default 1.85× for Mode D keeps the semi-final premium conservative without over-penalizing plausible survivor paths.
Variables: k = scenario row index; K in row labels = count of upfront picks that miss the target round where relevant (K = 0..8 in Mode B with eight upfront picks; K = 0..n in Mode C with n upfront picks; K = 0..4 in Mode D with four upfront picks). Mode A is binary (basket wins vs not). Also p_k = probability of scenario k, PL_k = dollar profit/loss in scenario k, S = initial spend, r_k = PL_k / S = return per opportunity under scenario k, rf = annual risk-free rate, N = estimated number of similar opportunities in your life. Filler dollar spend uses ask-implied weights blended by λ and scaled by the filler multiplier m (see below).
Expected value (dollars): EV_$ = Σ p_k · PL_k. This is the probability-weighted average dollar P/L for one modeled cycle.
Expected return (percent): EV_% = EV_$ / S. Same expectation, scaled by upfront deployment S.
Sharpe ratio (per opportunity): Sharpe_bet = (E − rf / T) / σ where E = Σ p_k · r_k, σ = √(Σ p_k · (r_k − E)^2), d = calendar days to final resolution, and T = 365 / d.
Kelly fraction: f* = argmax_f Σ p_k · ln(1 + f · r_k). This is the capital fraction that maximizes expected log growth over scenarios (textbook optimum, not prescriptive). If any active scenario has r_k = -100%, full deployment f=1 is invalid and the UI caps Kelly at 99.99%. If every active scenario has r_k ≥ 0 and at least one has r_k > 0, that objective has no finite maximizer (leverage can always increase expected log growth in this toy model); the UI shows ∞ for f*.
Expected log growth per opportunity: μ_log = Σ p_k · ln(1 + (f*/2) · r_k). This is an expectation (probability-weighted average) over scenarios at half Kelly sizing (only finite when f* is finite).
Lifetime wealth multiple (half Kelly, geometric/log scale): Let one-opportunity multiplier be M_t = 1 + (f*/2) · r_{k_t}. Over N opportunities, total compounding is a product: M_total = Π_t M_t. Taking logs turns product into sum: ln(M_total) = Σ_t ln(M_t). Over N opportunities, expected total log growth is N · μ_log, and converting back gives LifetimeMultiple = exp(N · μ_log). This is geometric/log compounding, not arithmetic expected multiplier math like (Σ p_k · M_k)^N.
Lifetime wipeout probabilities: Let p be per-bet wipeout probability (p = p_abandon). Then P(0) = (1 − p)^N, P(1) = Np(1 − p)^{N−1}, and P(≥2) = 1 − P(0) − P(1). The cards below list P(1) then P(≥2).