More volatility, more risk

I changed the session distribution for more realism.

I selected the binomial distribution for the simulation at first, then I changed it to Poisson.

For a simple and statistical reason: iGaming isn’t a coin flip. It’s a wild ride.

Main Goals of the day:

Replace binomial distribution with Poisson for session count per player
Explain the main reason why Poisson fits better than the Binomial one
Validate that session durations follow an exponential distribution (long tail), suitable for the gaming sessions

Step by Step

📍 Step 1: Removed np.random.binomial() — too rigid, not dynamic
📍 Step 2: Used np.random.poisson(lam=8.33) — natural for “events over time”
📍 Step 3: Confirmed session duration: np.random.exponential(30) → 30 min avg, but long tails (some sessions > 90 min)

Challenges / Insights

The logic of the 2 probability distributions is simple:

📊 Binomial distribution = “Each player plays exactly 8 sessions.”
❌ False.

📊 Poisson distribution = “On average, 8 sessions — but a guy can play 1-2 sessions, someone else 20 or more.”
✅ More realistic.

In other words, trying to model human behavior.

In iGaming (sources: Italian Market):

80% of players play 1–5 sessions
15% play 6–15
5% play 15+ → they’re your VIPs

Poisson captures that.
Binomial? Simple, but not reliable.

Code Snippet Final

session_counts = np.random.poisson(lam=avg_session, size=n_players)
session_counts = np.clip(session_counts, 1, 30)  # no one plays 100 sessions in a week

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Next Step

👉 Now that I have realistic session counts → time to add real metrics: Return-To-Payment, Gross Gaming Revenue, Net Gaming Revenue.