suited connector odds

[rybones]

In sng play the starting stacks are so small and the blinds rise so quickly that it is rarely wise to play drawing hands. The common advice is to avoid connectors, But then it is also said playing small and medium pairs is great as long you you fold when you don't hit your set. I happen to think the same type of logic should be applied to connectors. Just like a set, they are great for getting paid off when you really hit a flop. That said I do not have the math to prove this to myself. Alas, my question: what are the odds of suited connectors hitting two pair, or a full house, or a straight, or a flush. Note, I am looking for the combinded odds of hitting anyone of these hands. As a side question, am I right that a pair improving to a set on the flop is 8:1?

Thanks in advance to anyone who has the answer.

Ryan

[LetYouDown]

This is like the new 3 doors problem. Search function is your friend. Check out this (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=3489828&page=2&view=colla psed&sb=5&o=14&fpart=1) post, which links to another post about the exact same topic.

[rybones]

Thank you for the link. However, the problem with that link and the other information I have found is that is always includes hitting 4 to a flush or a str8. In an sng, it is rarely wise to chase a draw. Someone may argue that you should then push your draw; however, in low limit you will get called too often to make this profitable. What I need is either the odds or someone to tell me how to do the calculation.

Anyone?

Ryan

[ QUOTE ]
What I need is either the odds or someone to tell me how to do the calculation.

[/ QUOTE ]

Sounds like: "Please someone, teach me how to use my brain."

You can't do any math or are you just lazy?

[rybones]

[ QUOTE ]
You can't do any math or are you just lazy?

[/ QUOTE ]

Actually no I really can't "do" math. I read the post the other guy linked to and the math made sense -- kind of -- but not to a point where I could figure out the equations to calculate the made str8 and flush hands and then combine those with the 2 pair, 3 of a kind, and full house odds.

Plus, I thought the forum was exactly for "teaching people how to use their brains." A person canot do what they do not know until they are taught.

Thanks for the kindness

Ryan

[BruceZ]

[ QUOTE ]
[ QUOTE ]
You can't do any math or are you just lazy?

[/ QUOTE ]

Actually no I really can't "do" math. I read the post the other guy linked to and the math made sense -- kind of -- but not to a point where I could figure out the equations to calculate the made str8 and flush hands and then combine those with the 2 pair, 3 of a kind, and full house odds.

Plus, I thought the forum was exactly for "teaching people how to use their brains." A person canot do what they do not know until they are taught.

Thanks for the kindness

Ryan

[/ QUOTE ]

You can't make a straight or a flush and at the same time make 2-pair, trips, or a full house, so you can just add the corresponding probabilities from this post (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=2948434&page=&view=&s b=5&o=&vc=1). The 3.47% for 2-pair or trips includes full houses and quads.

about 24.7%

[BruceZ]

[ QUOTE ]
about 24.7%

[/ QUOTE ]

No, 5.6% if you add the numbers for 2-pair, trips, full house, straight, and flush. You added the 8-out straight draws and flush draws.

[rybones]

Thanks a ton!!!

[ QUOTE ]
[ QUOTE ]
about 24.7%

[/ QUOTE ]

No, 5.6% if you add the numbers for 2-pair, trips, full house, straight, and flush. You added the 8-out straight draws and flush draws.

[/ QUOTE ]

right, I thought he wanted draws too, my bad

/images/graemlins/diamond.gifDave

[subzero]

suited connector (like 6/images/graemlins/heart.gif5/images/graemlins/heart.gif) will flop...

straight-flush: 4/19600
quads: 2/19600
full house: 18/19600
flush (without straight-flush): 161/19600
straight (without straight-flush): 252/19600
trips (without full house): 264/19600

Add all the probabilities: (4 + 2 + 18 + 161 + 252 + 264) / 19600 = 701/19600 = .035765 or 3.5765% or about 27:1 against.

It really seems like you ought to include some of the stronger draws such as:
Flush Draw + OESD + Pair
Flush Draw + OESD/Double Gutshot
Flush Draw + ISD + Pair
Flush Draw + 3Straight + Pair
OESD+Pair+BD Flush Draw

[rybones]

[ QUOTE ]
It really seems like you ought to include some of the stronger draws such as:
Flush Draw + OESD + Pair
Flush Draw + OESD/Double Gutshot
Flush Draw + ISD + Pair
Flush Draw + 3Straight + Pair
OESD+Pair+BD Flush Draw

[/ QUOTE ]

I quite agree, but how the hell to I figure those odds out and then how do I add them to the other odds? See, if I were a math person this would be no problem. If there is anyone who can add these hand odds to the ones others have given I would really appreciated it. That said when figuring these odds out, how do you account for hand possibilites that meet these criteria, but were already figured in as part of the made hand odds? does that make sense?

Ryan

[Innocentius]

I think that the fundamental difference between a pocket pair and suited connectors is that with the pair, you are much more likely to have a strong made hand on the flop (that is, a set). The normal way of winning with connectors is getting a strong draw on the flop, which hopefully comes in on the turn or river. Problem is, in SnGs you often cannot afford to draw on the flop, or will simply face bets that are too large to call.

[ QUOTE ]
I think that the fundamental difference between a pocket pair and suited connectors is that with the pair, you are much more likely to have a strong made hand on the flop (that is, a set). The normal way of winning with connectors is getting a strong draw on the flop, which hopefully comes in on the turn or river. Problem is, in SnGs you often cannot afford to draw on the flop, or will simply face bets that are too large to call.

[/ QUOTE ]

Naturally, poket pairs are very strong, but , with:
Pair + Flush Draw + OESD

You're looking at 2 Straight Flush, 7 Flush, 6 Straight, 3 two pair, and 2 set outs. That means if you go all-in on the flop, you'll hit two pair or better something like 80% of the time. Whether you're willing to accept the risk in tournament play obviously depends on the situation, but your odds are better with a draw like this than with a made hand, say pocket aces, against open ended straight or flush draws.

[ QUOTE ]
[ QUOTE ]
It really seems like you ought to include some of the stronger draws such as:
Flush Draw + OESD + Pair
Flush Draw + OESD/Double Gutshot
Flush Draw + ISD + Pair
Flush Draw + 3Straight + Pair
OESD+Pair+BD Flush Draw

[/ QUOTE ]

[ QUOTE ]
I quite agree, but how the hell to I figure those odds out and then how do I add them to the other odds?

[/ QUOTE ].

Let's start with flush+OESD+Pair:
Clearly we want to have a pair with one of the hole cards. So the flop must contain: 1 of the 6 cards that pair with the hole cards.
In addition, there are three possible combinations of cards that make the OESD/Flush draw. That's a total of 18 possible flops that make that draw for you.

For the double-gutshot+flush draw, you need one of two combinations of values:
(For example, for 65 - you need 973 or 842) and you need exactly two of those three cards to be of the same suit as your hole. That makes for 2*3*3=18 possible flops that make gutshot+flush draws. Clearly none of these are OESD situations, so they're seperate from the ones above.

For an OESD+Flush draw, you need to get one of the three possible combinations of extra values, and an additional card chosen from the 8 unused values(we don't want the boar to pair) Exactly two of the three are suited, so we're looking at 3*3*3*8=72 possibilities.
Now, there are four pairs of values that give inside straight draws. (For 56 they are 23, 89, 37 and 48.) Now, for each of the values, there are 6 possible cards that make the pair with your hole (since this is Flush+IESD+Pair the two must both be suited) for a total of 24 possibilities.

We're really only interested in 3 straight draws that involve the cards in the hand, so there are two possible values (for 65, 7 and 4). For each of the two, you need to see one of 6 pairing cards, and one of the remaining 8 flush cards. (There are 10 cards that form a 4-flush, but 2 of them make for better straight draws.) That's a total of 96 possible hands.

Now, the OESD+Pair+BD Flush:
There are 3 possible pairs of values that make the OESD, and the remaining card must be chosen from 6 in the deck. In addition, since we're looking for exactly 3 suited cards, there are 6 suit combinations for each of the pairs. That makes for a total of 3*3*6=54 possibilities.
[ QUOTE ]
That said when figuring these odds out, how do you account for hand possibilites that meet these criteria, but were already figured in as part of the made hand odds? does that make sense?

[/ QUOTE ]

You have to make sure you don't count the same hand twice.

The draws above total to 282 possibilities.

With the 701 other possibilities, that makes for a total of 983 viable card combinations of 19600 which is close to 1 in 20.