## The Relationships Between Market Types
The 1X2 (match result), Asian Handicap, and over/under markets for the same match are mathematically related. A consistent probability model should produce consistent prices across all three.
## From 1X2 to AH0 (Draw No Bet)
AH0 removes the draw. The implied probabilities for home and away wins must be scaled to remove the draw weight.
AH0 Home price = 1 / (P_home / (P_home + P_away))
Where P_home and P_away are the de-vigged probabilities from the 1X2 market.
**Example:**
De-vigged: Home 45%, Draw 28%, Away 27%
AH0 Home: 1 / (0.45 / (0.45 + 0.27)) = 1 / 0.625 = 1.60
AH0 Away: 1 / (0.27 / (0.45 + 0.27)) = 1 / 0.375 = 2.67
Check: 1/1.60 + 1/2.67 = 0.625 + 0.375 = 1.00 ✓
## From Expected Goals to AH Line Selection
Your expected goals model gives: Home xG 1.8, Away xG 1.1.
Using Poisson simulation, you calculate the probability distribution of goal margins. The AH line that gives 50/50 probability is the "correct" line for fair pricing.
At 1.8 vs 1.1: roughly AH−0.5 to AH−0.75 for the home team is near-50/50.
If Pinnacle offers AH−0.75 at 1.95 home and your model says the home team has 52% probability of winning this AH: edge exists.
## Cross-Market Consistency Check
After converting 1X2 to AH using this method, compare to the actual AH offered. Large discrepancies between your converted AH and the live AH suggest either your 1X2 model is wrong or the markets are inconsistently priced — a potential cross-market edge.
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