📊 What Is the Law of Large Numbers?

 

The Law of Large Numbers states that as the number of trials (or bets) increases, the actual outcomes will get closer to the expected statistical averages.

In plain English:

The more times you roll the dice, the closer your results will match the true probabilities.

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🎲 How It Applies to Craps

Every roll of the dice in craps has fixed mathematical odds:

• Rolling a 7: 6 out of 36 combinations (≈16.67%)
• Rolling a 6 or 8: 5 out of 36 combinations each (≈13.89%)
• Rolling boxcars (12): 1 out of 36 (≈2.78%)

🔁 Short-Term vs. Long-Term:

• In the short run, you might see unusual streaks (e.g., five 11s in a row).
• Over hundreds or thousands of rolls, those results begin to “settle” into predictable patterns. You’ll see more 7s than 2s or 12s, just as the math predicts.

This is why the house edge always wins over time—because the probabilities assert themselves with more trials.

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🧠 Law of Large Numbers in Craps Strategy

✅ Why It Matters for Players:

Low House Edge Wins in the Long Run
If you always bet Pass Line with odds (≈0.85% combined edge), over time, your results will reflect this small disadvantage. You won’t “beat” the house, but you’ll lose more slowly, which is critical for long-term play.

High-Variance Bets Will Hurt You
Prop bets like “Any 7” (house edge ≈16.67%) might occasionally hit, but over time, they will drain your bankroll. The Law of Large Numbers guarantees that the house edge catches up.

Flat Betting + Consistency Protects You
Systems like the 4D Craps Method, which avoid high-edge bets and stick to flat betting with selective positioning, use this law to their advantage. You’re giving the math time to work in your favor (or at least, against the house less aggressively).

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⚖️ Misunderstanding the Law

Some players confuse it with the Gambler’s Fallacy. Remember:

• The Law of Large Numbers tells us what happens over thousands of rolls, not what happens next.
• It doesn’t mean a 7 is “due.” It means that over time, 7s will appear about 1 in every 6 rolls, regardless of streaks.

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📌 Bottom Line

The Law of Large Numbers reinforces this key idea:

The more you play, the more your results will match the math—so choose bets where the math is on your side.

That’s why disciplined, flat-bet strategies and low-edge wagers are not just conservative—they’re mathematically sound. You’re not trying to win the lottery in one roll. You’re trying to survive the game long enough for the probabilities to work in your favor.