midconnectors prob of hitting a straight (challenging)

[richroehl]

I have been wondering about these 'Straight / Flush Probability' questions for a while; especially why is a Straight ranked below a Flush when the odds of making a Flush are better? (see below). I know the following isn't perfect... i only take into account the cases of:
- starting with connectors (54 - JT); 2 Suited cards
- flopping an OESD / flopping a Flush draw
- and then making the Straight / Flush by the River.


Straight study
probability of 'good connectors' i.e. 54 - JT => about 1/10 = 28/52 x 8/51; these 'good connectors' each give you 4 sets of 3 cards which make a Straight. For ex. w/JT (AKQ, KQ9, Q98 or 987 make Straight).

I calculated the probability of having a Straight-Draw on the Flop: (about 1/10)

Probability of hitting Straight on Turn or River with an Open-ended draw is 16/46.5 (rounded off to 3/10 or .33)

so .1 x .33 = 1/30 to flop a Straight-draw and then make Straight by the River (when starting with connectors 54 - JT).

1/300 = (.1 x .1 x .33) to be dealt connectors 54 thru JT, Flop a OESD, and make straight by river.


Flush Study
Probability of being dealt suited cards (about 1/4)

Probability to Flop a Flush-draw when dealt suited cards: 1/7 (.143)

Probability to make Flush on Turn or River: about 4/10 (.39)

so .143 x .39 = .056 or about 1/18 to Flop a Flush-draw and then make a Flush by the River (when starting with suited cards).

1/72 = (.25 x .143 x .39) to be dealt suited cards, Flop a Flush-draw, and make Flush by river.


voila voila, sorry if this is completely messed up, but... from this, a Flush (1/72) is about 4 times more likely than a Straight (1/300)????!!!!!!

When I'm playing, I 'round' all of this off to:
1/30 chance of a Straight when dealt Connectors;
+ 1/15 chance of a Flush when dealt 2 suited-cards;
= 1/10 to make a Straight or Flush when starting with 54s thru JTs.

see you,
rich

[Jernej Zorec]

your numbers are wrong
flush is less likely to occour than a straight

u only have 13 hands for a flush u can make
for a straight there is 20 cards that make a single straight alone, and when u hold connecting cards it can go both ways unless u hold A2 so that only adds more chances to it

[Kemics]

why is A2 more unlikely than AK?

[Jernej Zorec]

its not , i just used it as example