Quote:
Originally Posted by fogodchao
Awesome, thank you. Definitely taking advantage of this
Odds of flopping an oesd with a one gapper?
This one is more difficult to be exact on, but I will give it a go...
A3 and AQ can flop open ended on very specific boards:
456 (A3) and 9TJ (AQ). Of course, we should be wary of the fool's side of the draw (A3), but the AQ on a JT9 flop is a great draw because you get the nuts with a K while others get fooled.
The odds:
Unique Flops = 50*49*48 cards / 3*2*1 orders = 19,600
Flops that fit the bill = 4*4*4 (i.e. 4 (J) * 4 (T) * 4 (9)) = 64
64 / 19,600 = 1 / 306.25 (~0.33%)
right flop for 1-gappers 42 and KJ:
More likely to flop open ended here as it only takes two specifc cards on the flop, but these are still limited on one end...
We still have the 3 board from before (i.e. 89T for KJ)..
but we also have QTx and 53x for each respective hand, so we add more combos into our total flops that qualify as open ended:
4 * 4 * 40 (40 others that do not make A FLOPPED STRAIGHT) = 640 additional ways
flopped straights:
4*4*8 = 128 (i.e. QT9 and AQT)
So bringing our open ended tally to 64 (three cards) + 640 (two cards) = 704
704 / 19,600 = 1 in 27.8 (~3.6%)
(note odds of flopping straight are 1 / ~153)
right flop for 1 gappers 53,64 and QT,J9:
Now we have two different ways to flop 2 cards to make open ended (i.e. J9x and KJx for QT). All the previous mentioned ways still exist too (including 987 run, etc) - let's just add the new way (like KJ for QT hole cards):
4*4*40 = 640
So 704 (from before) + 640 new ways =
1344 / 19,600 = 1 in 14.6 (~6.9%)
(note 64 more combos of flopped straights too, up to 192 / 19600 flopped straight, ~1%)
right flop for 1 gappers 75 through T8:
..still going.. these can get 3 run boards on both sides (T8 could get 567 or JQK)... not that you really want one end of this for combos < Tx:
but it is still 4*4*4 = 64 more flops to make an open ender by definition:
1408 / 19,600 = 1 / 13.9 (~7.2%)
Note, some of these include paired boards, monotone flops.. and a lot of 2 to a flush, so results not guaranteed even if OESD comes in!
Last edited by bip!; 03-22-2013 at 11:12 PM.