 Odds of flopping a flush
The odds of flopping a flush assuming you hold two suited cards can be calculated as follows. Since there are 52 cards in a deck 13 of each suite--------- the following remain somewhere other than in your hand 11 suited cards out of a remaining 50 cards. so we are trying to first hit one of those 11 out of 50 cards. If we hit one of the cards ,, then their will remain 10 of that suite out there somewhere out of a remaining 49 cards in the deck. (focus here is only on the cards that you know about which is the two in your hand and each street put on the felt) . This does properley account for cards in other players hands as they are part of the unknown deck that we use to calculate. So now the odds of hitting the first flopped card will be 11 out of 50 (11/50). Given this happens there will only be 10 suited cards left out there and now there are 49 unknown cards. The odds of hitting the second card of your suit will therefore be 10 out o 49 (10/49) . Same logic for third flopped card. So we have
11/50 of hitting the first flopped card x 10/49 of hitting the second flopped card , and 9/48 of hitting the third flopped card. so we have 11/50 x10/49 x9x48 . this is 11x10x9 / 50x49x48 which is a very small decical number .008418 which when divided into 1 equals 118.78. (the 1/x) button on the calculator will convert the decimal to the number.
118.78 or about 1/119.
THis can be more ruoughly calculated as follows: aprox 1/5 x 1/5 x1/5 or about 1 in 125 times.
the 1/5 corresponds to the 11/50 or 10/49 and 9/48 which are almost all close to 1 in 5  |