Probability Explanation and Conversions

There are a few ways that we can describe the chance of something happening. Here's a quick rundown of the four possible ways that probabilities and thus, poker odds could be described.

"1 in X" - This is the most practical application while sitting at a table. If you have 1 card in the deck that'll save you, and 46 cards are remaining in the deck, it'd be a "1 in 46" chance. Meaning you have one out from X number of chances. It's really a fraction sideways: 7/8ths is the same as "7 in 8". So "1 in 2" would be a 50% chance or a "1 to 1" chance.

"X to 1" - This is very commonly used in holdem books. If you are in a situation where you'll win 1/3rd of the time, and the other 2/3rds you lose, you have a "2 to 1" chance of winning. So "4 to 1" would be the same as a 20% chance or a "1 in 5" chance". "2 to 1" can also be worded as "2 to 1 against", which means your chances are 2 to 1 against winning.

"Percentage" - This is a widely accepted form that is difficult to calculate at the table in most cases. A 4% chance of winning is the same as a "1 in 25" chance or "24 to 1".

"Probability" - To do basic math with probabilities it needs to be in this form. Also, if you calculate the chance of an event occurring using algebra, it will come out in this form. It is simply the percentage chance divided by 100 with no % sign. So a 25% chance is the same as a probability of .25, and 100% is a probability of 1.0 .

Conversion

To convert between these odds, use the following equations (if you can call them that)...

Conversion	Equation
"1 in X" and "X to 1"	Subtract or add one ("1 in 3" = "2 to 1")
Prob and %	Probability times 100 = % -OR- % divided by 100 = Probability
"1 in X" to %	One-hundred divided by X = Percentage
"1 in X" to Prob	One divided by X = the Probability
% to "1 in X"	One-hundred divided by the % will give you the X in "1 in X"
Prob to "1 in X"	One divided by the probabilty will give you the X in "1 in X"
"X to 1" to %	Add one to X, then one-hundred divided by that number = Percentage
"X to 1" to Prob	Add one to X, then one divided by that number = Probability
% to "X to 1"	One-hundred divided by the %, then subtract 1, will give you the X in "X to 1"
Prob to "X to 1"	One divided by the probability, then subtract 1, will give you the X in "X to 1"

Here's an Odds Converter page for easy conversion.

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