Got a PH.D. in Mathematics? No. Who Cares, You Can Still Work the Maths for No-Limit Texas Hold’EM.

For the game No-Limit Texas Hold'EM you merely have to learn the formula for establishing the pot odds. Pot odds just means the probability of winning the bet based on card play. So, if the pot contains $200 and your competition bets $50, your pot odds are 5-1, this is because it will cost you $50 to win $250, this is the pot plus the bet made by your opponent.

Next you have to establish the probability that you will manage to acquire a card that can allow you to win the pot. To do this, you have to count the number of out, which are the cards that will improve your hand.

So; if there are nine outs at the flop, you'll have a 2:1 chance of losing the pot. At times when you flop a flush draw, this is a useful rule. If you played, for example, the 6 of hearts and the 7 of hearts and the flop comes as the king of hearts, jack of hearts and three of diamonds, and then your competitor decides to bet, your competitor will have a better chance of getting the flush. Therefore, in this situation you should be very careful about how and if you play.

However, with thirteen outs at the flop, the probability will still be in favour of your competitor, but the gap between you will be closer, you have more chance in this scenario than in the nine card scenario, you will be a powerful hand against any potential hand of the competition. If you, for example have a pair and a straight draw, holding the eight of diamonds and the seven of spades with a flop at five of clubs six of diamonds and seven of hearts. For a straight, you would need either a seven or a nine, to get three of a kind you will need a seven and an eight to make a pair.

With fourteen out for the flop, you'll have a 1:2 chance of winning the pot. With a hand of 14 outs your position could look something like this; you have a four of hearts and a five of hearts and the flop is five of diamonds, seven of hearts and the queen of hearts. To hold a strong hand you either need a heart (at nine outs) a four (at three outs) and a five (at two outs).

At 15 outs on the flop you will have a slightly higher probability of winning the pot, than your opponent. For example, if you have the six of clubs and the eight of clubs and the flop is seven of diamonds nine of clubs and the ace of clubs. You will need any one of nine clubs, to make a flush or one of six cards to make a straight. Remember not to count the five and ten of clubs twice.

At the turn the mathematics gets even easier, start by counting the outs, then you this rule at the turn:
Count as a 7% chance that you will win the pot for every three outs you have at the turn. For example, if you have a flush draw, you would have nine outs, which means you have to times 7% by three, so your odds of a win are only 21%. Or another example would be; if you are all in with an ace and a queen and your competitor has an ace and a king, with only three cards left to you need to obtain one of only three remaining queens, with only three outs this is just a 7% of winning, and the odds mean that, obviously, it is not worth it.

Some other maths that you can use to establish your chance of winning is as follows, if you have an odd number of outs, add two percent for each out additionally to the original 7% for three outs, so for five outs you will have a probability of acquiring the card you need 11% of the time.

So you see, you really don't need a PH.D. in mathematics, or even a GCSE, to employ maths to improve your chances of winning the pot in No-Limit Texas Hold'EM.