How to Play Craps Smart: Understanding the Math Behind Every Bet

🎲 CardsChat Casino Learning Series​

Craps – Part 4 of 4 - How to Play Craps Smart: Understanding the Math Behind Every Bet​

After inundating you with all that crazy math explaining Pass and Come bets, let’s dig into the rest of the numbers behind craps — and I promise you, this part is much simpler to follow than the last lesson!

By the end of this article, you’ll have a solid foundation on:

• How the remaining bets work
• The math behind them
• Which bets give you the best value
• Which bets to avoid

Let’s get into it.

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🔍 Quick Refresher: Dice Probabilities​

All calculations below assume a $10 wager.

These probabilities drive every bet on the table.

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💥 The Rest of the Bets (And the Math Behind Them)​

🎯 Field Bet​

What it is:
Betting that the next roll is 2, 3, 4, 9, 10, 11, or 12.

Payout:

• 2 or 12 → 2:1
• All others → Even money

Math Breakdown:

• 2 & 12 → 5.56% chance → Win $20
• 3, 4, 9, 10, 11 → 38.89% chance → Win $10
• 5, 6, 7, 8 → 55.56% chance → Lose $10

Expected Value: -$0.56 per $10 bet
👉 Fun short-term bet. Not a long-term winner.

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🎲 Free Odds (Best Bet on the Table)​

What it is:
An additional bet placed behind your Pass or Come bet that the point will be made before a 7.

You can:

• Increase it
• Decrease it
• Remove it before resolution

(Some casinos allow 3x, 5x, 10x, 20x — even 100x odds!)

Payouts (True Odds):

• 4 or 10 → 2:1
• 5 or 9 → 3:2
• 6 or 8 → 6:5

Expected Value: $0.00

This is the only bet on the table paid at true mathematical odds.
It doesn’t overcome the house edge on your Pass/Come bet — but it lowers your overall house edge significantly.
👉 Always take free odds.

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🎲 Big 6 / Big 8​

What it is:
Betting that a 6 or 8 rolls before a 7.

Payout: Even money
True Odds: 6:5
Expected Value: -$0.27
This is basically a worse version of a Place 6 or 8 bet.
👉 Skip it and place the number instead.

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🎯 Place Bets​

What it is:
Betting a specific number (4, 5, 6, 8, 9, 10) will roll before a 7.
You choose the number — unlike Free Odds, which is tied to the point.
Payouts:

• 6 or 8 → 7:6
• 5 or 9 → 7:5
• 4 or 10 → 9:5

Expected Value:
Ranges from -$0.05 to -$0.17 per $10

These are among the better bets on the table outside of Free Odds.
👉 Strong option, especially 6 and 8.

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💎 Hardways​

Hard 4 / Hard 10​

What it is:
Betting on doubles (2-2 or 5-5) before:

• A 7
• The “easy” version (1-3, 3-1 or 4-6, 6-4)

Payout: 7:1
Expected Value: -$0.28

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Hard 6 / Hard 8​

What it is:
Betting on 3-3 or 4-4 before:

• A 7
• An easy 6 or 8

Payout: 9:1
Expected Value: -$0.28
👉 Fun sweat bets. Not strong mathematically.

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⚠️ Proposition Bets (High House Edge)​

Any 7​

What it is:
Betting the next roll is a 7.
Payout: 4:1
True Odds: 5:1
Expected Value: -$1.67

This is the worst bet on the table.
👉 Avoid completely.

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Any 11​

Payout: 15:1
True Odds: 17:1
Expected Value: -$1.11

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Any Craps (2, 3, 12)​

Payout: 7:1
True Odds: 8:1
Expected Value: -$1.11

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Horn Bet​

A four-number combo bet on 2, 3, 11, 12 — evenly split.
Payouts:

• 2 or 12 → 30:1
• 3 or 11 → 15:1

Only one quarter of your total bet wins.
Expected Value: -$1.25
👉 Flashy. Exciting. Drains bankroll fast.

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💥 Best Bets to Take​

Now that math class is over…

🥇 1. Free Odds​

The best bet in the casino. Zero house edge.

🥈 2. Place 6 & 8​

Solid payouts and frequent hitters.

🥉 3. Place 5 & 9​

Still respectable.
Big 6/8? Just place them instead.

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🚫 Bets to Avoid​

If we’re being purely mathematical:

1. Any 7 – Biggest long-term loss
2. Horn Bets – Complicated and expensive
3. Any 11 / Any Craps – Poor payout vs. true odds

The center of the table is designed to look exciting — and it is — but it’s where the casino makes the most money.

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🎯 Overall Summary​

Craps is one of the wildest, loudest, most action-packed games in the casino. The number of bets is overwhelming at first. A 7 can be your best friend… and one roll later your worst enemy.
But when you break it down? It’s all probability.

Once you understand:

• Which bets pay true odds
• Which ones carry higher house edges
• How expected value works

You’re no longer gambling blindly — you’re gambling informed. And that’s how you stretch your bankroll and maximize the fun.

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💬 What Did You Learn?​

What surprised you the most?
Do you stick to the “smart bets,” or do you like mixing in some action plays?

Drop your favorite craps strategies in the comments — and let’s keep the loudest game in the casino rolling.

CRStals said:

Do you stick to the “smart bets,” or do you like mixing in some action plays?

Drop your favorite craps strategies in the comments — and let’s keep the loudest game in the casino rolling.

Click to expand...

I'm not an expert, but sticking to the smart bets sounds the best way to go, though I'd mix it up a little by making some small bets on the least probable outcomes.
Strategy: Free odds and Place 6 & 8 all day with small bets on Hardways and Proposition bets.

An interesting, fairly complex and very dynamic game. But thanks to such detailed explanations, everything becomes much clearer. It is important to try everything out step by step in practice in order to understand and master how it all works. I am a fan of smart betting, this approach is closer to me

Yeah i think as soon as we know the true odds when playing a game like craps, everything will become more easy and comfortable. And with the knowledge about expected value we might even beat the house! (I know i know. On some occasions only).

Obviously, a player who is good at calculating and assessing chances has an advantage over those who play solely on intuition. Luck is certainly more important, but combining luck with mathematics definitely makes the game more promising.

Played a lot of craps when I was younger and like poker can really hook you, I understand what your saying about the safer bets but what I found in reality is when your playing this game luck IS everything,I found not playing every roll and watching and waiting for hot rollers and just following along with the shooters you can make a decent profit,when a shooter is hot you play along with them ,if they roll let say a 6 ,I am betting for a hard 3-3 ,and same thing if you got a shooter coming in that never seems to roll their number or craps out everytime they roll I m betting on the Do not pass line and for them to crap out,it really is a fun game!

This game is especially fun to play with a team of friends. Where everyone can essentially perform their own specific function, and if you think carefully about budget management and bet insurance, you can get a very real profit.