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Place Your Bets
Blackjack
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Player
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Your Hand
Texas Hold'em
Community Cards
You
Opponent
Pot: 0 coins
Omaha Poker
Community Cards
You
Opponent
Pot: 0 coins
Craps Mathematics
In craps, the house has a 1.41% edge on pass line bets. This means for every $100 you bet, you'll lose about $1.41 on average over time.
| Bet Type | House Edge | Win Probability |
|---|---|---|
| Pass Line | 1.41% | 49.29% |
| Don't Pass | 1.36% | 49.86% |
| Field Bets | 5.56% | 44.44% |
Key Probabilities
- Come-out 7 or 11: 22.22% (win)
- Come-out 2, 3, or 12: 11.11% (lose)
- Point established: 66.67%
- 7-out before point: 16.67% average
The house edge is small but consistent - over thousands of rolls, the casino will always come out ahead.
Slot Machine Mathematics
Slot machines have the highest house edge of any casino game, typically ranging from 5% to 15% depending on the machine and jurisdiction.
| Machine Type | Cost per Spin | House Edge | Return to Player |
|---|---|---|---|
| Mario Slots | 5 coins | ~8% | 92% |
| Classic Slots | 10 coins | ~10% | 90% |
| Bonus Slots | 25 coins | ~12% | 88% |
Understanding Slot Odds
- Three of a kind: ~0.46% chance (1 in 216)
- Two of a kind: ~7.6% chance (1 in 13.1)
- No matches: ~91.9% chance
- Expected loss per spin: Varies by machine cost
Slot machines are designed for entertainment, not profit. The bright lights and sounds mask the mathematical reality that you're likely to lose money over time.
Roulette Mathematics
Roulette has a house edge of 2.7% on even-money bets (European) or 5.26% (American with double zero). This wheel uses European rules.
| Bet Type | True Odds | House Odds | House Edge |
|---|---|---|---|
| Red/Black | 48.65% | 47.37% | 2.70% |
| Even/Odd | 48.65% | 47.37% | 2.70% |
| 1-18/19-36 | 48.65% | 47.37% | 2.70% |
Wheel Probabilities
- Single number: 2.70% chance (1 in 37)
- Red or Black: 48.65% chance (18 in 37)
- Even or Odd: 48.65% chance (18 in 37)
- Zero: 2.70% chance (house advantage)
The house edge is small but guaranteed. Over time, the casino will always profit from roulette due to the zero pocket(s).
Blackjack Mathematics
Blackjack has the lowest house edge of any casino game when played with perfect basic strategy (about 0.5%). However, most players play poorly, increasing the edge to 2-5%.
| Strategy | House Edge | Notes |
|---|---|---|
| Perfect Basic Strategy | 0.5% | Optimal play decisions |
| Average Player | 2-5% | Common mistakes |
| Card Counting | -1% to -2% | Advanced technique |
Key Probabilities
- Dealer bust rate: ~28% (dealer hits soft 17)
- Player blackjack: 4.83% (2.5% after dealer peeks)
- Push (tie): ~8.5% of hands
- Double down advantage: Increases edge by ~0.2%
Blackjack is the only casino game where skilled players can reduce the house edge to near zero. However, most players increase the house advantage through poor decisions.
Video Poker Mathematics
Video Poker combines the best elements of poker and slot machines. Jacks or Better has a house edge of about 0.46% when played with perfect strategy, making it one of the better casino games.
| Hand | Payout (5 coin bet) | Probability |
|---|---|---|
| Royal Flush | 250 coins | 0.000025% |
| Straight Flush | 50 coins | 0.0014% |
| Four of a Kind | 25 coins | 0.024% |
| Full House | 9 coins | 0.14% |
| Flush | 6 coins | 0.20% |
| Straight | 4 coins | 0.39% |
| Three of a Kind | 3 coins | 2.11% |
| Two Pair | 2 coins | 4.75% |
| Jacks or Better | 1 coin | 21.44% |
Key Probabilities
- Winning hand: ~21.7% (any paying combination)
- Loss rate: ~78.3% (no winning hand)
- Expected return: ~97.3% (with perfect play)
- House edge: ~2.7% (with poor play)
Video poker is a game of skill as well as luck. Learning optimal strategy can significantly improve your chances of winning.
Texas Hold'em Mathematics
Texas Hold'em is the most popular poker variant worldwide. The house edge comes from the rake (commission) taken from each pot, typically 5-10%.
| Starting Hand | Win Probability | Notes |
|---|---|---|
| AA | 31.2% | Best starting hand |
| KK | 26.3% | Strong premium hand |
| AKs | 20.4% | Strong suited connector |
| 21.8% | Good pocket pair | |
| AKo | 16.7% | Strong offsuit |
Key Probabilities
- Pre-flop fold rate: ~70-80% (depending on position)
- Showdown rate: ~15-25% of hands
- Expected value: Depends on skill level
- House edge: 5-10% (from rake)
Texas Hold'em is a game of incomplete information where skill can overcome luck over time. Position and aggression are key factors.
Omaha Poker Mathematics
Omaha is similar to Texas Hold'em but each player receives 4 hole cards and must use exactly 2 of them with 3 from the community cards. This creates more action and higher variance.
| Starting Hand Type | Win Probability | Notes |
|---|---|---|
| Double Suited Aces | 25-30% | Premium starting hand |
| AAKK Double Suited | 35%+ | Monster hand |
| Connected Wrap | 15-20% | Strong drawing hand |
| Suited Aces | 12-15% | Good but vulnerable |
| Random 4 Cards | 8-10% | Speculative hand |
Key Probabilities
- Pre-flop fold rate: ~60-70% (more action than Hold'em)
- Showdown rate: ~20-30% of hands
- Expected value: Highly variable
- House edge: 5-10% (from rake)
Omaha rewards players who can calculate complex odds and understand multi-way pot dynamics. The game has higher variance than Texas Hold'em.