Starting Hand Odds for a Poker Novice

TangledUpinBlue

Have been suffering some peculiar bad beats lately on PPP. However what goes around comes around and I know I'll get the benefit some day.

In suffering the bad beats on 2 occasions, I pushed with KK and AKo to be met by lower suited connectors which in turn hit the flush and two pair. Now I have a relatively primitive approach to calculating the odds in any specific situation but I'm f***ed if it becomes in any way complicated. Suited connectors are a hand that I rarely play except with a good position but the bad beats got me thinking that at least I should understand the probabilities attached to such a starting hand. So the questions are

What are the odds of getting 2/3 cards of the same suit on the flop to get the flush draw/flush if holding suited connectors
Same question for the straight draw/straight and do those probabilities diminish by much if there is a one card gap

No problem post flop on the turn and on the river, the odds I can work out

Thanks in advance to those of you who are mathematically inclined

ArmaniJeanss

I often get these combos/permos totally wrong but here goes.
*****
To flop the flush its 50/11 * 49/10 * 48/9 = 118/1.

To flop the flush draw its 50/11 * 49/10 * 48/39 = 26/1.

50 and 49 etc are the cards left in the deck as the flop is dealt. 11 and 10 are the cards left which must be hit to get the flush or flushdraw.

I've only a diploma, I'll leave the straights and 1gapper straights for the degree people to explain.

dvdfan

Heres a detailed and boring explanation but theres plenty of other sites aswell:

http://www.tightpoker.com/poker_odds.html

or you can add this background to your desktop and/or print it off to help you remember:

http://www.tightpoker.com/software/

Look for the desktop backgorunds near the bottom

Hitman Actual

ArmaniJeanss wrote:

I often get these combos/permos totally wrong but here goes.
*****
To flop the flush its 50/11 * 49/10 * 48/9 = 118/1.

To flop the flush draw its 50/11 * 49/10 * 48/39 = 26/1.

Flopping the flush looks right, AJ, but I think your figures are wrong for the flush draw. Here's my take (working in combs):

There are 50 cards left after your two whole cards, giving 50C3 flop combs = 19600 (50*49*48/3*2*1). There are 11 flush cards left to hit, giving 11C3 possible combs = 165. So the odds for flopping the flush are 165/19600 = ~118/1.

For the draw, you're looking for a XYz flop, where XY is your flush draw, and z is one of the other 39 cards left. XY can be arranged in 11C2 ways, = 55 combs. 'z' is 39, as stated. So there are 55*39 = 2145 combs of flush draw flops, giving the odds of a draw = 2145/19600 = ~8/1.

So to flop either the flush or the flush draw, there are 2145 + 165 combs = 2310/19600 = ~7.5/1.

For the straight, the amount of ways you can hit your straight makes a big difference i.e. 67 has more straight possibilities than, say, A2. For 67, you hit a straight with 345, 458, 589, 89T. Also, the odds of flopping any exact three cards in their various suits can be worked out as 4*4*4 = 64 (i.e. there are 64 ways of arranging 345, given all the possible suits). So this gives 4 * 64 ways of flopping a straight for 67, giving the odds as 256/19600 = ~75/1.

For A2, there is only one possible straight: 345. Again this can be arranged in 64 ways, giving the odds of 64/19600 = ~305/1.

Working out the odds for flopping the straight draw is trickier than just the flush draw, and it's ages since I did it, but I might have a look at it later.

In any case, I think the best case odds (i.e. hands like 67 which have a maximum stretch) of flopping either a flush, straight, or draw with suited connectors comes in around 2/1, iirc. Perhaps even better than that.

The best book out there for this sort of stuff is Mike Petrivs "Holdem Odd(s) Book". All these calcs are done there for you, and it's easy to follow.

TangledUpinBlue

Thanks for the Web link. Looks like v useful reading for somebody who left school many moons ago

Mellor

TangledUpinBlue wrote:

Same question for the straight draw/straight and do those probabilities diminish by much if there is a one card gap

To answer this question, the odds change alot. Well take a number of hands drawing to straights. 5 6, 5 7, 5 8, 5 & 9

For 5 9, your chances of flopping the straight are 19600/64 = ~300/1
For 5 8, you are twice as likely(as you have two possible straights, ~ 150/1
For 5 7, its 3x as likely as 5 9, so ~ 100/1
And for 5 6, the best chance of flopping the straight , is as previously said ~ 75/1

You are ten times more likely to git any hand by the river than the flop.
So the above hands have 30/1, 15/1, 10/1 and 7.5/1 respectivly.

So with one gap your chance of hitting the straight, (by the river), is 75% the chance of connectors. Two gap is 50%, and three gap is 25%.

ArmaniJeanss

lenny_leonard wrote:

Flopping the flush looks right, AJ, but I think your figures are wrong for the flush draw. Here's my take (working in combs):

LL's maths is correct, I was way off with the flush draw odds.