How do I calculate the odds of winning preflop in texas holdem?
Say I have Ace of spades and Ace of diamonds while my opponent(2 players including me) has King of hearts and King of clubs. How do I calculate the chance of winning if I go all in preflop, before any of the cards show on the board?
I know I can find an odds calculator online, but I want to know how(writing a paper on probability).
Thanks 
How to calculate Texas Holdem odds
As mentioned above, all gambling is based on odds. If the odds of a horse winning a race are 10-to-1 against, you win ten times your bet if the horse you’re betting on wins the race. If the horse wins just once for every ten times it loses, you break even. If it wins more often you should win and if it wins less often you come out behind. In most bets, like a horse race, you do not get the opportunity for repeated trials, so you either have to be lucky enough to have placed your bet the one time out of eleven that the horse wins, or you need to continually make bets where the odds of hitting are shorter than the odds you are getting paid off at.
Pot Odds in Texas Hold’em
Pot odds in Texas Hold’em work exactly the same way. If the bet is $1 to you and there is $5 in the pot, you are getting 5-to-1 pot odds. Just as in the horse race, you need to win that pot once for every five times you lose it to break even. If you’ll win the pot more often, you have positive expected value or +EV. If you’ll win it less often, you have a negative expected value play (-EV).
Calculating Pot Odds in Poker
Usually, the bet will be more than $1 to you. Simply reduce the ratio by dividing the size of the pot by the size of the bet to you. For example if there is a $10 bet to you and you have a chance to win a $50 pot, divide 50 by 10 to reach 5-to-1 pot odds. If the pot is $97 and the bet is $25 to you, you are getting about 4-to-1; these calculations do not need to be exact (it’s 3.88-to-1 exactly, but this precision is not worth the distraction during an in-game situation).
Using Pot Odds in Poker Games
Once you know how to calculate pot odds, you’ll know whether you should call a bet by knowing your odds of winning the hand, also known as poker odds. This can be established by calculating the ratio of cards remaining to cards that will give you the win.
February 1st, 2010 at 1:58 pm
How to calculate Texas Holdem odds
As mentioned above, all gambling is based on odds. If the odds of a horse winning a race are 10-to-1 against, you win ten times your bet if the horse you’re betting on wins the race. If the horse wins just once for every ten times it loses, you break even. If it wins more often you should win and if it wins less often you come out behind. In most bets, like a horse race, you do not get the opportunity for repeated trials, so you either have to be lucky enough to have placed your bet the one time out of eleven that the horse wins, or you need to continually make bets where the odds of hitting are shorter than the odds you are getting paid off at.
Pot Odds in Texas Hold’em
Pot odds in Texas Hold’em work exactly the same way. If the bet is $1 to you and there is $5 in the pot, you are getting 5-to-1 pot odds. Just as in the horse race, you need to win that pot once for every five times you lose it to break even. If you’ll win the pot more often, you have positive expected value or +EV. If you’ll win it less often, you have a negative expected value play (-EV).
Calculating Pot Odds in Poker
Usually, the bet will be more than $1 to you. Simply reduce the ratio by dividing the size of the pot by the size of the bet to you. For example if there is a $10 bet to you and you have a chance to win a $50 pot, divide 50 by 10 to reach 5-to-1 pot odds. If the pot is $97 and the bet is $25 to you, you are getting about 4-to-1; these calculations do not need to be exact (it’s 3.88-to-1 exactly, but this precision is not worth the distraction during an in-game situation).
Using Pot Odds in Poker Games
Once you know how to calculate pot odds, you’ll know whether you should call a bet by knowing your odds of winning the hand, also known as poker odds. This can be established by calculating the ratio of cards remaining to cards that will give you the win.
References :
http://www.learn-texas-holdem.com/texas-holdem-odds-probabilities.htm