How To Calculate Odds 11 Steps With Pictures

Let’s say we bet that we’ll roll either a one or a two. In this case, there’s two possibilities where we win - if the dice shows a two, we win, and if the dice shows a one, we also win. Thus, there are two favorable outcomes.

In the example with the die, if we bet that we’ll roll either a one or a two, that means we’ll lose if we roll a three, four, five, or six. Since there are four ways that we can lose, that means that there are four unfavorable outcomes. Another way to think of this is as the Number of total outcomes minus the number of favorable outcomes. When rolling a die, there are a total of six possible outcomes - one for each number on the die. In our example, then, we would subtract two (the number of desired outcomes) from six. 6 - 2 = 4 unfavorable outcomes. Similarly, you may subtract the number of unfavorable outcomes from the total number of outcomes to find the number of favorable outcomes.

You may choose to represent this ratio as a fraction. In this case, our odds are 2/4, simplified as 1/2. Note - 1/2 odds don’t mean we have a one-half (50%) chance of winning. In fact, we have a one-third chance of winning. Remember when expressing odds that odds are a ratio of favorable outcomes to unfavorable outcomes - not a numerical measurement of how likely we are to win.

If you express the odds against winning as a fraction, you get 2/1. Remember, as above, that this isn’t an expression of how likely you are to lose, but rather the ratio of unfavorable outcomes to favorable outcomes. If it were an expression of how likely you were to lose, you’d have a 200% chance of losing, which is obviously impossible. How do you like those odds? In reality, you have a 66% chance of losing - 2 chances to lose and 1 chance to win means 2 losses / 3 total outcomes = . 66 = 66%

It’s easy to convert between probability and odds. To find an odds ratio from a given probability, first express the probability as a fraction (we’ll use 5/13). Subtract the numerator (5) from the denominator (13) : 13 - 5 = 8 . The answer is the number of unfavorable outcomes. Odds can then be expressed as 5 : 8 - the ratio of favorable to unfavorable outcomes. To find probability from a given odds ratio, first express your odds as a fraction (we’ll use 9 / 21 ). Add the numerator (9) and denominator (21) : 9 + 21 = 30. The answer is the total number of outcomes. Probability can be expressed as 9/30 = 3/10 = 30% - the number of favorable outcomes over the number of total possible outcomes. A simple formula for calculating odds from probability is O = P / (1 - P). A formula for calculating probability from odds is P = O / (O + 1).

Independent events are events whose odds aren’t effected by previous events. Flipping a coin and getting a heads is an independent event - you’re not more likely to get a heads based on whether you got a heads or a tails last time.

Let’s do an example problem. To calculate the odds of rolling two dice with a sum of four (for instance, a 1 and a 3), begin by calculating the total number of outcomes. Each individual dice has six outcomes. Take the number of outcomes for each die to the power of the number of dice: 6(number of sides on each die)2(number of dice) = 36 possible outcomes. Next, find the number of ways you can make four with two dice: you can roll a 1 and a 3, a 2 and a 2, or a 3 and a 1 - three ways. So the odds of rolling a combined “four” with two dice are 3 : (36-3) = 3 : 33 = 1 : 11 Odds change exponentially based on the number of events occurring simultaneously. Your odds of rolling a “yahtzee” (five dice that are all the same number) in one roll are very slim - 6 : 65 - 6 = 6 : 7770 = 1 : 1295!

In real life, of course, if you already have cards in your hand, you’re rarely being dealt cards from a complete fifty-two card deck. Keep in mind that the number of cards in the deck decreases as cards are dealt. Also, if you’re playing with other people, you’ll have to guess what cards they have when you’re estimating your odds. This is part of the fun of poker.

Decimal (or “European format”) odds. These are fairly easy to understand. Decimal odds are simply expressed as a decimal number, like 2. 50. This number is the ratio of the payout to the original stake. For instance, with odds of 2. 50, if you bet $100 and win, you’ll receive $250 dollars - 2. 5 times your original stake. In this case, you’ll make a tidy profit of $150. Fractional (or “UK format”) odds. These are expressed as a fraction, like 1/4. This represents the ratio of the profit (not total payout) from a successful bet to the stake. For instance, if you bet $100 on something with 1/4 fractional odds and win, you’ll profit by 1/4 of your original stake - in this case, your payout will be $125 for a profit of $25. Moneyline (or “US format”) odds. These can be difficult to understand. Moneyline odds are expressed as a number preceded by a minus sign or a plus sign, like -200 or +50. A minus sign means the number represents how much you need to wager to make $100. A positive sign means the number represents how much you’ll win if you bet $100. Remember this subtle distinction! For example, if we wager $50 with moneyline odds of -200, when we win, we’ll get a payout of $75 for a total profit of $25. If we wager $50 with moneyline odds of +200, we’ll get a payout of $150 for a total profit of $100. In moneyline odds, a simple “100” (no plus or minus) represents an even bet - whatever money you stake, you’ll earn as profit if you win.

In moneyline odds, a simple “100” (no plus or minus) represents an even bet - whatever money you stake, you’ll earn as profit if you win.

Let’s look at an example. A standard roulette wheel has 38 numbers - 1 through 36, plus 0 and 00. [14] X Research source . If you bet on one space (let’s say 11 ), you have 1 : 37 odds of winning. However, the casino sets the payout odds at 35 : 1 - if the ball lands on 11, you’ll win 35 times your original stake. Notice that the payout odds are slightly lower than the odds against you winning. If casinos weren’t interested in making money, you would be paid out at 37 : 1 odds. However, by setting the payout odds slightly below the actual odds of you winning, the casino will gradually make money over time, even if it has to make the occasional large payout when the ball lands on 11.

You’re never “due” to win. If you’ve been at the Texas Hold ‘Em table for an hour and you haven’t been dealt a single good hand, you may want to stay in the game in the hopes that a winning straight or flush is “right around the corner. " Unfortunately, your odds don’t change with the amount of time you’ve been gambling. The cards are randomly shuffled before every deal, so if you’ve had ten bad hands in a row, you’re just as likely to get another bad hand as you are if you’ve had a hundred bad hands in a row. This extends to most other games of chance - roulette, slots, etc. Sticking with one specific bet won’t increase your odds. You may know someone who has “lucky” lotto numbers - though it can be fun to bet money on numbers that have special personal meaning, in random games of chance, you’re never more likely to win by betting on the same thing every time than you are by betting on a different thing every time. Lottery numbers, slots, and roulette wheels are completely random. In roulette, for example, it’s just as likely that you’ll roll “9” three times in a row as it is that you’ll roll any specific three numbers in order. If you’re one away from the winning number, you weren’t “close. " If you pick the number 41 for the lottery and the winning number is revealed as 42, you may feel absolutely crushed, but cheer up! You weren’t even close. Two numbers that are close together, like 41 and 42, aren’t mathematically connected in any way in random games of chance.