http://wizardofodds.com/games/video-poker/strategy/a-1-b-44-c-1-d-0-d-1-d-2-d-3-d-4-d-4-d-10-d-12-d-20-d-200-d-800/

Why hold 4 to a straight (0 gaps) but not 4 to a flush when you have 1 wild?

Quote:malgoriumI would imagine it's because with 4 to a flush with 1 wild, you only have 13 outs (10 more suits + 3 wilds), whereas if you have a 3-card straight with a wild (from 567-TJQ), you have 19 outs (16 possible straight cards + 3 wilds).

thought an open ended straight draw was 8 outs and a flush draw was 9 outs?

Quote:100xOddsthought an open ended straight draw was 8 outs and a flush draw was 9 outs?

Malgorium got it in one, except he was incorrect about the number of flush outs, though the correct number makes his point even better.

Here is the reason why:

Flush

Think of every deck as having twelve Flush cards rather than the usual thirteen, in terms of natural Flushes. If you have the deuce and three Natural Flush Cards, then that leaves nine Natural Flush Cards and Three Deuces for 12 possible Flush outs out of 47 cards:

(12/47) * 3 = 0.7659574468

In the meantime, there are also nine other cards that can potentially result in 3OaK:

(9/47) * 1 = 0.1914893617

The result is 0.7659574468 + 0.1914893617 = 0.9574468085

Straight

Now, let's look at a hand such as 5-6-7-2-x:

In this case, you have to consider all of the Straights Possible. First of all, any of the other three deuces gives you a straight, so that's three. If you get a three, the Deuce acts as a four, so there are four more. If you get a four, the deuce acts as a three, so there are four. If you get an eight, the deuce acts as a nine, so there are four. If you get a nine, the deuce acts as an eight, so there are four.

Thus, you have nineteen straight outs.

(19/47) * 2 = 0.80851063829

You still have nine 3OaK cards:

(9/47) * 1 = 0.1914893617

0.1914893617 + 0.80851063829 = 1.00 (Rounded)

wow 19 outs for a wild straight draw. :o

hm.. going from 12 outs (flush draw) to 19 outs (straight draw) only gives me +0.04 EV?

How often does it come up is the important part.Quote:100xOddsThx for the explanation!

wow 19 outs for a wild straight draw. :o

hm.. going from 12 outs (flush draw) to 19 outs (straight draw) only gives me +0.04 EV?

Quote:100xOddsStrategy for 97.6% DW:

My question is why do you want to play such a horrible game?

It's probably the best game near him.Quote:pokerfaceMy question is why do you want to play such a horrible game?

Quote:pokerfaceMy question is why do you want to play such a horrible game?

I explained here:

http://wizardofvegas.com/forum/gambling/video-poker/20818-3k-hands-to-have-roughly-50-chance-of-getting-4-deuces-or-natural-royal/#post429464

Quote:100xOddsThx for the explanation!

wow 19 outs for a wild straight draw. :o

hm.. going from 12 outs (flush draw) to 19 outs (straight draw) only gives me +0.04 EV?

Yeah, a Straight pays less than a Flush.

If you're playing for $$$ at $5 total per hand, though, that's a $0.20 difference every time.