yongkangc/matrix_lookup_logic.md

## matrix_lookup_logic.md

      
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              matrix_lookup_logic.md
            
          
    Probability Matrix Strategy - Steps 3 & 4: Signal Detection

Step 3: Query Probability Matrix

At any moment, you have:

Current market state (crypto, price, time remaining)
Probability matrix with historical win rates

Your goal: Look up the historical data for this exact situation.

3.1 Determine Matrix Cell Coordinates

Inputs:

crypto_type: BTC, ETH, or SOL (from market ticker)
current_price: Token1's current market price ($0.00-$1.00)
time_to_close_sec: Seconds remaining until market closes

Calculate:
# Time window (based on time remaining, not market duration)
if time_to_close_sec < 3600:           # Less than 1 hour
    time_window = "<1hr"
elif time_to_close_sec < 21600:        # 1-6 hours
    time_window = "1-6hr"
elif time_to_close_sec < 86400:        # 6-24 hours
    time_window = "6-24hr"
else:
    time_window = ">24hr"

# Price bucket (0-19, representing $0.05 ranges)
price_bucket = floor(current_price / 0.05)
# Bucket 0 = $0.00-$0.05
# Bucket 1 = $0.05-$0.10
# ...
# Bucket 19 = $0.95-$1.00

3.2 Look Up Historical Data

Query the matrix for:
matrix[crypto_type, time_window, price_bucket]

Returns:

token1_prob: Historical win rate for Token1 (0-1)
token2_prob: Historical win rate for Token2 (0-1)
sample_size: Number of historical trades in this cell
token1_prob_ci_lower/upper: 95% confidence interval bounds


3.3 Calculate Expected Value (EV)

For Token1:
token1_price = current_price
EV_token1 = token1_prob - token1_price
For Token2:
token2_price = 1.00 - token1_price  # Binary market: prices sum to $1
EV_token2 = token2_prob - token2_price
Interpretation:

EV > 0: Market is underpricing this token (opportunity!)
EV < 0: Market is overpricing this token (avoid)
EV ≥ $0.10: Strong edge (strategy threshold)


Step 4: Signal Qualification & Decision

Check if each token meets BOTH criteria:

EV ≥ $0.10 (minimum edge threshold)
sample_size ≥ 50 (minimum confidence)


Decision Tree

IF Token1 qualifies AND Token2 qualifies:
    → Enter "Long Both" (hedge position)
    
ELSE IF Token1 qualifies ONLY:
    → Enter "Long Token1" (directional)
    
ELSE IF Token2 qualifies ONLY:
    → Enter "Long Token2" (directional)
    
ELSE:
    → Skip market (no edge)


Example 1: 15-Minute Market

Market State:

Crypto: BTC
Market type: 15-minute
Time remaining: 8 minutes (480 seconds)
Token1 ("Up") price: $0.42
Token2 ("Down") price: $0.58

Step 3.1: Determine cell coordinates
crypto_type = "BTC"
time_window = "<1hr"         # 480 sec < 3,600 sec
price_bucket = floor(0.42 / 0.05) = 8  # Bucket 8 = $0.40-$0.45

Step 3.2: Look up historical data
Query: matrix[BTC, <1hr, 8]
Returns:
  token1_prob = 0.5500 (55%)
  token2_prob = 0.4500 (45%)
  sample_size = 35,000

Step 3.3: Calculate EV
Token1: EV = 0.55 - 0.42 = $0.13 ✓
Token2: EV = 0.45 - 0.58 = -$0.13 ✗

Step 4: Check qualification
Token1: EV=$0.13 ≥ $0.10 ✓, samples=35,000 ≥ 50 ✓ → QUALIFIES
Token2: EV=-$0.13 < $0.10 ✗ → DOES NOT QUALIFY

Decision: Enter Long Token1 only (directional bet)

Example 2: 4-Hour Market (Early)

Market State:

Crypto: ETH
Market type: 4-hour
Time remaining: 2 hours 15 minutes (8,100 seconds)
Token1 price: $0.45
Token2 price: $0.55

Step 3.1: Determine cell coordinates
crypto_type = "ETH"
time_window = "1-6hr"        # 8,100 sec is between 3,600 and 21,600
price_bucket = floor(0.45 / 0.05) = 9  # Bucket 9 = $0.45-$0.50

Step 3.2: Look up historical data
Query: matrix[ETH, 1-6hr, 9]
Returns:
  token1_prob = 0.6000 (60%)
  token2_prob = 0.4000 (40%)
  sample_size = 2,000

Step 3.3: Calculate EV
Token1: EV = 0.60 - 0.45 = $0.15 ✓
Token2: EV = 0.40 - 0.55 = -$0.15 ✗

Step 4: Check qualification
Token1: EV=$0.15 ≥ $0.10 ✓, samples=2,000 ≥ 50 ✓ → QUALIFIES
Token2: EV=-$0.15 < $0.10 ✗ → DOES NOT QUALIFY

Decision: Enter Long Token1 only

Example 3: 4-Hour Market (Late) - "Long Both"

Market State:

Crypto: SOL
Market type: 4-hour
Time remaining: 40 minutes (2,400 seconds)
Token1 price: $0.40
Token2 price: $0.60

Step 3.1: Determine cell coordinates
crypto_type = "SOL"
time_window = "<1hr"         # 2,400 sec < 3,600 sec
price_bucket = floor(0.40 / 0.05) = 8  # Bucket 8 = $0.40-$0.45

Step 3.2: Look up historical data
Query: matrix[SOL, <1hr, 8]
Returns:
  token1_prob = 0.5200 (52%)
  token2_prob = 0.4800 (48%)
  sample_size = 8,000

Step 3.3: Calculate EV
Token1: EV = 0.52 - 0.40 = $0.12 ✓
Token2: EV = 0.48 - 0.60 = -$0.12 ✗

Wait, Token2 doesn't qualify! Let me recalculate Token2's price:
Actually, if Token1 = $0.40, then Token2 must be trading separately.
Let me redo this with a proper "Long Both" scenario:
Corrected Market State:

Token1 price: $0.42
Token2 price: $0.35
Combined cost: $0.77

Step 3.3: Calculate EV (corrected)
Token1: EV = 0.52 - 0.42 = $0.10 ✓
Token2: EV = 0.48 - 0.35 = $0.13 ✓

Step 4: Check qualification
Token1: EV=$0.10 ≥ $0.10 ✓, samples=8,000 ≥ 50 ✓ → QUALIFIES
Token2: EV=$0.13 ≥ $0.10 ✓, samples=8,000 ≥ 50 ✓ → QUALIFIES

Decision: Enter Long Both (hedge position)

Buy Token1 at $0.42
Buy Token2 at $0.35
Combined cost = $0.77 → Guaranteed profit of $0.23 (29.9% ROI)


Example 4: No Edge (Skip Market)

Market State:

Crypto: BTC
Time remaining: 5 minutes
Token1 price: $0.48
Token2 price: $0.52

Step 3: Query matrix
matrix[BTC, <1hr, 9]
Returns:
  token1_prob = 0.5023 (50.23%)
  token2_prob = 0.4977 (49.77%)
  sample_size = 39,482

Calculate EV:
Token1: EV = 0.5023 - 0.48 = $0.0223 ✗ (below threshold)
Token2: EV = 0.4977 - 0.52 = -$0.0223 ✗ (negative)

Decision: Skip market (no edge)

Key Insights

Time Window Behavior

15-minute markets:

Always fall in <1hr bucket (max 15 mins remaining)
Matrix cell: [crypto, <1hr, price_bucket]

4-hour markets:

First 3 hours: 1-6hr bucket (240-60 mins remaining)
Final hour: <1hr bucket (60-0 mins remaining)
Matrix cells: [crypto, 1-6hr, bucket] OR [crypto, <1hr, bucket]

This explains why:

<1hr window has 47 cells (mix of 15-min + 4-hour final hour)
1-6hr window has 50 cells (4-hour early life only)
6-24hr window has 16 cells (if daily markets exist)

Why Token Prices Don't Always Sum to $1

In a binary prediction market, theoretically:
token1_price + token2_price = $1.00

But in practice on Polymarket:

Orderbook spreads create gaps
Token1 best ask = $0.42, Token2 best ask = $0.60
Sum = $1.02 (market maker profit = $0.02)

This is why "Long Both" opportunities exist:

When combined_cost < $1.00, guaranteed arbitrage
When both tokens have EV ≥ $0.10, strong statistical edge


Summary

Step 3: Look up historical win rates for current (crypto, time_window, price_bucket)
Step 4: Check if EV ≥ $0.10 and samples ≥ 50 for each token

Both qualify → Long Both (hedge)
One qualifies → Directional bet
Neither qualifies → Skip

Critical: Time windows are based on time remaining, not market type:

15-min markets → always <1hr
4-hour markets → 1-6hr early, <1hr late
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