What are the odds?

Being a successful gambler, be it for a weekend or as a career, requires a strong knowledge of a game’s odds and edges. Every game is unique in this regard, and it’s important you figure out how to minimize the house’s edge and give yourself the greatest advantage possible.Most gambling best practices revolve around having a basic understanding of probability and making wagers appropriate for the game situation. If it seems like a lot to learn, we assure you that you don’t need to be a mathematician to gain a level of understanding for casino game odds that will work in your favor.

Our guide on the odds of various casino games will help you reach that level of proficiency quickly.

How casino game odds work

Betting odds tell you how likely a specific event is to happen within a game, and how much you will win if that event occurs. This likelihood (aka probability) is usually written one of two ways:

Fractional Odds

These types of odds are written as 10/1, 5/2, etc. and with them you can easily calculate how much you stand to win: if you bet the second number, you win the first number. So, in the first example, if you bet $1 you would win $10.

Odds Fractional Table

If at 5/2 odds you bet $4, you would also win $10 (for every value of the second number you bet, you win the first number plus the return of your stake).

Percentages

Those same fractional odds can be converted to a percentage with a simple formula: Probability (%) = B / (A+B), where A and B are the first and second numbers in the fractional odds, respectively.

Odds Percentages Table

So plugging in the 9/1 example, the completed formula would then look like 1 / (10 + 1) = 0.09, meaning there is a 9% chance that the event will happen.

It’s more common in sportsbooks/betting odds than on casino games, but occasionally you will see odds written as decimals, too (as in 9.0).

Beyond that, every casino game’s odds are a little different.

Texas Hold ‘Em

If you’ve ever watched poker on TV, then you’ve seen graphics that display a player's’ chance of winning a hand based on what they are holding and what is out on the table. This percentage is based off the number of cards remaining in the deck that will help you improve your hand (also called “outs”).

Odds Poker Table

If, say, you are holding Q♠ and 9♠ and on the board is J♠ 2♠ 7♦ A♦, you would calculate your chance of winning the hand by:

Taking the number of cards in any suit (13), then subtracting the number of spades on the table and in your hand (4):

13
4
=
9

This means you have nine outs. To then calculate your approximate odds of completing your flush from this, you would do:

52
Cards in a deck
2
Cards in your hand
4
Community cards dealt thus far
=
46
46
9
=
37
=
ODDS:
4/1
FRACTIONAL
ODDS:
20%
PERCENTAGE

Of that 46, there are 9 cards remaining that could complete your flush and give you a win. Thirty-seven cards remain that will cause you to lose if any of them are the last card to come out. This makes your odds of getting the win 37:9, which simplified down is around 4:1 (or 20%).

A quicker way to do all this is:

Calculate the number of outs left in the deck after the flop

Multiply the number of outs by 4 for the chance getting a winning card on the turn or river

Multiply the number of outs by 2 after the turn for chance of winning on the river

Roulette

There are two main versions of roulette, American and European, and both have their own particular set of odds. The house edge (the edge that a casino has over a player) on almost all bets is 5.26% (2/38) in American roulette and 2.70% (1/37) in European roulette. This percentage is calculated by dividing the amount of zeroes on the wheel by the total number of slots.

House
Edge
5.26%
(2/38)
House
Edge
2.70%
(1/37)

From here, we know that the odds on an even money bet (such as red/black, odd/even) are 47.37% (18/38) on an American wheel and 48.6% on a European wheel.

Bets on an individual number give you much lower odds of winning, as does betting on anything else besides red, black, odd, even, 1-18, and 19-36:

Roulette Table
BETS
PAYOUT (AMER.)
PROBABILITY (AMER.)
PAYOUT (EURO)
PROBABILITY (EURO)
1:12
2:1
31.58%
2:1
32.4%
13-24
2:1
31.58%
2:1
32.4%
25-36
2:1
31.58%
2:1
32.4%
Single number
35:1
2.63%
35:1
2.7%
2 number combo
17:1
5.26%
17:1
5.4%
3 number combo
11:1
7.89%
11:1
8.1%
4 number combo
8:1
10.53%
8:1
10.8%
6 number combo
5:1
15.79%
5:1
16.2%
Combo of 1-2-3-0-00
6:1
13.16%
n/a
n/a

Blackjack

Blackjack is commonly regarded as the casino game with the best odds for you to win. However, this claim assumes you know blackjack basic strategy and don’t deviate from it. When you do that on a multi-horse shoe, your odds look like:

Odds you’ll bust
31%
38%
46%
54%
62%

As you’d imagine, your odds obviously continue to decrease as your hand increases in value. Know that there are countless varieties and rule sets for blackjack, for which the odds and your strategy will all vary slightly.

Craps

With so many different bets that can be made, craps is perhaps the hardest game to understand your odds with. Before tackling all the different bet possibilities, you should first understand your odds simply of rolling different numbered combinations:

Dice Total
Possible Combinations
Odds
Odds %
2
1-1
35:1
2.78%
3
1-2   2-1
17:1
5.56%
4
1-3   3-1   2-2
11:1
8.83%
5
1-4   4-1   3-2   2-3
8:1
11.11%
6
1-5   5-1   4-2   2-4   3-3
31:5
13.89%
7
1-6   6-1   2-5   5-2   3-4   4-3
5:1
16.67%
8
2-6   6-2   3-5   5-3   4-4
31:5
13.89%
9
3-6   6-3   4-5   5-4
8:1
11.11%
10
4-6   6-4   5-5
11:1
8.83%
11
5-6   6-5
17:1
5.56%
12
6-6
35:1
2.78%

As you play more and more craps, you (or someone at your table) will occasionally go on a seemingly unbeatable streak. However you’ve probably never seen a streak as hot as the at the Las Vegas Desert Inn in 1950. Reports say an anonymous gambler made 27 straight passes (wins), a feat that has odds against of 12,467,890 to 1. Although his bets were more modest in size, had he bet the house limit on each roll he would have racked up $268 million.

Once you have a feel for the game and its language, reference this chart of the five best and five worst craps bets you can make:

Bet
True Odds
Odds Paid
House Edge
Pass Odds / Come Odds
Same as paid
2:1 on 4,10;
3:2 on 5,9;
6:5 on 6,8
0%
Don’t Pass Odds / Don’t Come Odds
Same as paid
1:2 against 4,10;
2:3 against 5,9;
5:6 against 6,8
0%
Don’t Pass / Don’t Come (Bar-12 or Bar-2)
976:949
1:1
1.36%
Pass / Come
251:244
1:1
1.41%
Place 6 / Place 8
6:5
7:6
1.52%
Horn (the combined bet)
5:1
27:4 on 2,12;
3:1 on 3,11
12.5%
Whirl/World (the combined bet)
2:1
26:5 on 2,12;
11:5 on 3,11;
0:1 (push) on 7
13.33%
2
35:1
30:1
13.89%
12
35:1
30:1
13.89%
Any 7
5:1
4:1
16.67%

Slots

The result of a slot spin is determined by a random number generator (RNG) the moment you press ‘spin’. Contrary to popular belief, there is no set order of “payoff cycles” that a machine rotates through: every spin is independent from the last. Slots have one of the highest house edges to be found in the casino (typically over 7%) and because you can play a large number of turns very quickly makes slots nearly impossible to win money on over the long-term.

On online slots, you can typically find out a game’s theoretical return to player (RTP) on either the paytable menu or the rules screen. This will typically be written as a percentage such as 93.00%. Subtracting that number from 100 will give you the house edge, or 7% in this case (100-93). What this means is that if you spun the machine 1000 times, you could theoretically expect a return of $93 if you staked $100.

Know that this would be a pretty good edge to get on a machine--the laws are different everywhere but in Vegas, for instance, the RTP can legally be as low as 73% (a house advantage of 27%). Even though it seems like you always hear about someone who knows someone that hit a big a Vegas jackpot, don’t let yourself think that it’s a common occurrence: The winner of the largest slot prize ever ($39,710,826.36) had to beat odds of 16 million to one.

Using the Odds To Your Advantage

Only when you gain an understanding of how the odds work in different casino games can you truly hope to make money playing long-term. Sometimes the most important part of understanding the odds is simply learning when to walk away, especially if you happen to get up big quickly.

Remember, the casino always holds the edge, and they wouldn’t stay in business if the odds weren’t in their favor.

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