- The probability of being dealt an ace is 452 . The probability of being dealt an ace again from the remaining pack of 51 cards is 351. Therefore, the probability of a pocket ace hand will be given byP Pocket Aces= 452×351=122652≡1221
- There are an equivalent number of kings as there are aces. It, therefore, implies that the odds of being dealt pocket kings are the same as that of being dealt pocket aces. The probability of a pocket kings hand is therefore
- There are 13 sets of cards with the same denomination in a set of playing cards. Therefore, from b., there are 13 possible pocket pairs. Therefore, the probability of having any pocket pair is the probability of a particular pocket pair times the number of possible pairs.
PAny pocket pair=Ppocket pair×13=1221×13=13221≡117
- The probability of a flop containing 1 card of the denomination of a pocket pair can be given by
Pflop with at least same denominator=1-Pflop without similar denominator
the probability of picking the first flop card that is not similar to the pocket pair is 4850. On the second pick, the probability is 4749 and on the third pick it is 4648.
Therefore,
Pflop without similar denominator=4850×4749×4648=10811225
Pflop with at least same denominator=1-10811225=1441225
- The probability of a flop that gives you "trips" can be calculated bearing in mind that the chances of picking a card similar to the one in hand is250, picking a second card different from this one, after making this pick, has a probability of 4849 . The last pick will have a probability of 4448 .Because, there are three cards that would form a pair with the one picked (with a probability of 250) and the remaining card from your pocket pair denomination that has a 148 chance of being included in the flop. The resulting probability is multiplied by 3; since the order the cards appear in the flop is not important.
Ptrips=3×250 ×4849×4448=1321225
- The find the probability of a flop being "quads" we observe that the probability of picking the first card similar to the pocket pair is 250 and that of the consecutive card is 149 in the event that the first card picked was of the same denomination. This, therefore, implies that the last card picked will be from another denomination implying a probability of one or 4848. there are three possible arrangements for this flop set.
Therefore
PQuads=(250×149×1)×3=62450≡31225
- The probability of picking a card similar to your hand is 250. The probability of picking another card from the remaining set of 49 cards that is different from your hand is 4849. Picking a card similar to this one has a probability of 348. Bearing in mind that the three cards are drawn together and therefore can be arranged in three different ways, we calculate the probability of a boat
Pboat=(250×4849×348)×3=91225
