question about thee of a suit in the starting hand

[flexus]

How much does a hand decrease in value by having three of a suit instead of two, for example:
A [img]/images/graemlins/heart.gif[/img] 4 [img]/images/graemlins/heart.gif[/img] J [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/club.gif[/img] would perhaps be playable in some situations.

compared to

A[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/heart.gif[/img] J[img]/images/graemlins/heart.gif[/img] J[img]/images/graemlins/spade.gif[/img]

My qestion is if the difference needs to be considered when deciding when to play or not?

[Wintermute]

Personally I don't give it a second thought. It'll reduce your chances of making the flush from 5% to 4.5% or something like that... not a huge effect. BTW, I basically made those numbers up, I think they're about right but don't hold me to it.

[LetYouDown]

If you have only two hearts, the odds of making a heart flush:

[C(11,3) * C(45,2)]/C(48,5) = ~9.539778%

If you have three hearts:

[C(10,3) * C(45,2)]/C(48,5) = ~6.9380204%

If you have four hearts:

[C(9,3) * C(45,2)]/C(48,5) = ~4.8566142%

[Buzz]

[ QUOTE ]
How much does a hand decrease in value by having three of a suit instead of two

[/ QUOTE ]

Flexus - Depends. Pretty hard to figure before the flop, because you have various ways to find a fit with the flop and various ways to win with the hand.

The air humper has given you a good answer here.

I wouldn't play much differently before the flop with one hand as compared to the other.

Even after a flop of K[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/club.gif[/img], 6[img]/images/graemlins/heart.gif[/img], having three cards in the suit as compared to just two cards in the suit would not make much of a difference in the way I'd play.

With two cards in the suit (nine out draw), you have 360/990 ways to make the flush. (630 to 360 or 1.75 to one against).

With three cards in the suit (eight out draw), you have 324/990 ways to make the flush. (666 to 324 or 2.06 to one against).

If you figure to go all-in for $100 on the second betting round, and if you figure to win $200 if you make the flush but you'll lose the $100 second betting round investment if you miss, then you have favorable odds to play the nine out draw, but unfavorable odds to play the eight out draw. But it's not a big difference one way or the other.

If you have enough to bet on both the second, third, and fourth betting rounds, and if it costs you $10 on the second round and you plan to re-evaluate after the second betting round, the odds against making your hand on the turn are 36 to 9 (4 to 1 against) with the nine out hand and 37 to 8 (4.625 to 1 against) with the eight out hand.

If you figure to gain $42 if you make your flush on the turn, then you have slightly favorable odds to continue with the nine out hand but slightly unfavorable odds to continue with the eight our hand.

If you figure to only gain $30 if you make your flush on the turn, then you don't have favorable odds to play either hand.
If you figure to gain $50 if you make your flush on the turn, then you do have favorable odds to play either hand.

Again it's not a big difference one way or the other.

Never a guarantee about my math.

Buzz