Introduction: Why Gambling Sucks
Casinos are businesses, not charities. Every game is carefully designed with a mathematical edge that ensures the house will profit over time. This website demonstrates how even seemingly fair games are actually rigged against players in the long run.
What is "House Edge"?
The house edge is the mathematical advantage the casino has over players. It's expressed as a percentage of each bet that the casino expects to keep over the long run. A house edge of 5.26% (like in American Roulette) means that for every $100 wagered, the casino expects to keep $5.26 as profit.
Try our simulations below to see how these mathematical principles work in practice. You'll notice that while you might win in the short term, the longer you play, the more likely it is that you'll lose money overall.
Coin Flip
Not As Fair As You Think
A coin flip seems perfectly fair - 50% chance of heads, 50% chance of tails. But what if the casino pays out less than 1:1 on a win?
Starting Balance
$1000
Current Balance
$1000
Flips
0
Wins
0
How It Works:
In this simulation, you bet $10 on heads each time. If you win, you get back $19 (your $10 bet plus $9 winnings). If you lose, you lose your $10 bet.
This creates a 10% house edge, because even though the odds of winning are 50%, the payout doesn't match the true odds. A fair payout would be $20 (your $10 bet plus $10 winnings).
The formula for house edge is: 100% - (true odds * payout percentage). In this case: 100% - (50% * 90%) = 100% - 45% = 55%.
Slot Machine
The Ultimate House Advantage
Slot machines have some of the highest house edges in the casino, often ranging from 5% to 15%. Let's see how they work.
Starting Balance
$1000
Current Balance
$1000
Spins
0
Win Rate
0%
How It Works:
Each reel has 6 different symbols. You need all three slots to match to win. The probability of getting any specific symbol is 1/6 for each reel.
The probability of getting a match on all three reels is (1/6) × (1/6) × (1/6) = 1/216 or about 0.46%.
Payouts work like this:
- Three 7s: 100x your bet ($500)
- Three BAR symbols: 20x your bet ($100)
- Three cherries: 10x your bet ($50)
- Three lemons: 5x your bet ($25)
- Three oranges: 3x your bet ($15)
- Three bells: 2x your bet ($10)
The house edge in this game is around 12%, meaning that for every $100 you bet, you'll lose about $12 on average in the long run.
Roulette
The Wheel of Misfortune
Roulette is a classic casino game with a clear mathematical disadvantage for players. The American roulette wheel has 38 slots (0, 00, and 1-36), but only pays out at 35:1 for a single number bet.
How It Works:
In American roulette, you can bet on specific numbers (which pays 35:1), colors (red/black pays 1:1), or green (0/00) which pays 17:1.
The true odds would pay $37 for a $1 bet on a specific number, but the casino pays only $35, creating a house edge of 5.26%.
The formula for the house edge is: (true probability - payout probability) / true probability.
In American roulette: (1/38 - 1/36) / (1/38) = 5.26%
Blackjack
The Deceptive Card Game
Blackjack offers some of the best odds in the casino, but the house still maintains an edge through rules like the dealer hitting on soft 17 and paying only 3:2 on blackjack.
Dealer
Player
How It Works:
In our blackjack game, the house edge comes from several rules:
- Dealer hits on soft 17 (when the dealer has an Ace counted as 11 and a total of 17)
- Blackjack pays 3:2 instead of the true odds value
- Player loses 100% of their bet on a bust, even if the dealer later busts too
These seemingly small rules create a house edge of about 0.5% to 2% depending on the specific rules and your strategy. This means that for every $100 bet, you can expect to lose $0.50 to $2 in the long run.
Plinko
The Illusion of Control
Plinko is a popular gambling game where you drop a disc from the top of a pegged board and it bounces randomly until it lands in one of the multiplier slots at the bottom. Despite its apparent simplicity, it's carefully designed to favor the house.
Starting Balance
$1000
Current Balance
$1000
Drop Count
0
Average Win
$0.00
How It Works:
Plinko is a perfect example of the binomial distribution in action. Each time the disc hits a peg, it has a roughly 50% chance of going left or right.
The payouts are not symmetrically distributed to match the probability. The highest payouts are at the edges where it's least likely for the disc to land, but the expected value of each drop is always less than your bet amount.
Our payouts from left to right are: $25, $3, $1.5, $0, $1.5, $3, $25
If the probabilities were perfectly symmetrical and the payouts matched the true odds, the average return would equal your bet. Instead, the house edge in our Plinko game is about 10-15%, meaning you'll lose about $1-$1.50 for every $10 bet in the long run. The rare 25x wins create excitement, but aren't enough to overcome the mathematical disadvantage.
Craps
The Deceptive Dice Game
Craps is a dice game where players bet on the outcome of the roll, or a series of rolls, of a pair of dice. While some bets have a low house edge, many of the flashy proposition bets have poor odds for players.
How It Works:
In our simplified craps game, we focus on the Pass Line bet, which is the most basic and popular bet in craps:
- On the "come out" roll (first roll), you win if you roll 7 or 11, and lose if you roll 2, 3, or 12 (called "craps").
- If you roll any other number (4, 5, 6, 8, 9, 10), that number becomes the "point."
- After establishing a point, you continue rolling until you either roll the point again (win) or roll a 7 (lose).
The house edge for the Pass Line bet is approximately 1.41%. This means that for every $100 bet, you can expect to lose $1.41 over time. The house edge comes from the uneven distribution of winning and losing outcomes in both phases of the game.
Conclusion: Why You Can't Beat the House
All casino games are designed with a mathematical edge that ensures the house will profit over time. While individual players might win in the short term due to variance (luck), the law of large numbers guarantees that the longer you play, the closer your results will get to the expected mathematical outcome.
Key Takeaways:
- The house always has a mathematical edge in every game
- Short-term wins are possible due to variance (luck)
- Long-term losses are inevitable due to the law of large numbers
- The only winning strategy is to play for entertainment only, with money you can afford to lose
- Set limits on time and money, and stick to them
If you do choose to gamble, remember that it should be viewed as paid entertainment, not as a way to make money. The cost of this entertainment is the mathematical house edge, which is the price you pay for the experience.