The probability by changing cards

Not everybody realizes how important maths can be in poker, especially in 5cd poker. Meanwhile statistics and probability calculus. This time the importance of probability calculus will be demonstrated on the example of the all cards, not only a single card. In the Freeroll poker, it is sufficient to base on the mathematical calculations, every time you have to make some decision. This property is called PotOdds. This topic will be discribed later. However now we will show the probability of getting some cards at the beginning and the probability of matching some combinations. A probability table for getting different cards’ combinations by a deal. Combination  The number of possible combinations Probability Poker   40  about 0,0000154 Four of kind 624  about 0,00024 Full  3744  about 0,00144 Colour   5108  about 0,00197 Strit  10200  about 0,00392 Three  54912   about 0,0211 Two pairs  123552  about 0,0475 A pair  1098240  about 0,423 A high card  1302540  about 0,501 The probability of getting the combination by changing some cards: You have a pair – You want to change three cards. Two pairs - 18,6% Three - 12,2% You have two pairs – you want to change a card. Full - 8,3% You have four cards in the same colour- You change a card Colour - 18,75% You have four cards, each following the previous one (for example: 9, T, J, Q) – You want to change a card. Strit - 16,6% (you will get a Strit by every eight and every King) You have cards like above but there is one card between missing (for example: 9, T, Q, K) – You want o change a card. Strit - 8,3%