Pricing Framework Fundamental

Expected Value (EV)

The foundation of all betting pricing. EV tells you the average profit or loss per bet over the long run. Users should have negative EV; the house should have positive EV.

💰 The EV Formula

EV = P(win) × Payout − P(loss) × Stake

Or equivalently: EV = P(win) × Payout − 1 (unit stake)

Interpretation: If EV is positive, you profit on average. If negative, the house profits. The magnitude tells you how much per dollar wagered.

Bet Parameters

0.3 0.7

1.1x 3x

📊 EV Analysis

Expected Value $-47.01

ROI per Bet -47.01%

Implied Probability 52.6%

Your Edge -0.6%

House Edge 4.6%

🎯 What This Means

-EV Bet. The house profits $47.01 per $100 you wager. This is how sportsbooks make money.

Long-Run Profit/Loss (1000 bets)

Blue shows actual random results; gold shows expected value line. Over time, results converge to the EV line.

EV Sensitivity to Win Probability

At current payout of 1.9x, you break even at 52.6% win probability.

📋 Common Payout Structures

Bet Type	Payout	Implied Prob	Breakeven	House Edge @ 50%
Standard Over/Under	1.91x	52.4%	52.4%	2.4%
Power Play (3-leg)	2.25x	44.4%	44.4%	-5.6%
Flex Play (2-leg)	3x	33.3%	33.3%	-16.7%
Demon Mode (5-leg)	10x	10.0%	10.0%	-40.0%
Fair Odds (coin flip)	2x	50.0%	50.0%	0.0%

🏦 The House Perspective

Pricing Strategy

1. Estimate True Probability: Use models to predict actual over/under probability
2. Add House Edge: Set payout so implied prob > true prob (from house's perspective)
3. Balance Book: Adjust to avoid one-sided liability
4. Monitor Sharp Action: Re-price if sophisticated bettors find edge

EV in Product Design

Higher Payouts: Attract users, increase volume. Risk: thin margins.

Lower Payouts: Higher margin, lower volume. Risk: users leave.

Optimal Point: Maximize revenue = price elasticity × margin

R Code Equivalent

# Expected Value Calculator
calculate_ev <- function(win_prob, payout, stake = 1) { 
  win_prob * (payout * stake) - (1 - win_prob) * stake
}

# Implied probability from payout
implied_prob <- function(payout) 1 / payout

# House edge calculation
house_edge <- function(true_prob, payout) { 
  implied <- implied_prob(payout)
  implied - true_prob  # Positive = house wins
}

# Example
ev <- calculate_ev(win_prob = 0.52, payout = 1.9, stake = 100)
cat(sprintf("EV: $%.2f\n", ev))
cat(sprintf("ROI: %.2f%%\n", (ev / 100) * 100))
cat(sprintf("House edge: %.2f%%\n", house_edge(0.52, 1.9) * 100))

✅ Key Takeaways

• EV = probability × payout − 1 (per unit stake)
• House always sets negative EV for bettors
• Implied probability = 1/payout tells you breakeven

• Long-run results converge to EV line
• Edge = True Prob − Implied Prob
• All pricing decisions stem from EV math