AA vs suited connector in Holdem.

[thylacine]

Ignoring betting, and just considering chance of winning showdown with 5 boardcards:

Consider A/images/graemlins/spade.gif A/images/graemlins/club.gif vs suited connectors of your choice.

Obviously AA is a big favorite.

1a. But amongst suited connectors, which has the best chance?

1b. Why?

2a. Amongst suited connectors, which has the worst chance?

2b. Why?

[Eric P]

78 suited (red ones) has the best chance against aces obviuosly cause the straights don't connect, and the pairs are all the same since you need to hit two. AK has the worst chance (unless you count A2?)

[Bozeman]

Actually 76 does better


AsAc 7h6h
% chance of outright win 76.806922 22.871932
% chance of win or split 77.128068 23.193078
expected return, % of pot 76.967495 23.032505
fair pot odds:1 0.299250 3.341690
pots won: 1317917.50 394386.50

AsAc 7h8h
% chance of outright win 76.832268 22.873976
% chance of win or split 77.126024 23.167732
expected return, % of pot 76.979146 23.020854
fair pot odds:1 0.299053 3.343888
pots won: 1318117.00 394187.00

[FastCards]

Versus black Aces, red suited connectors perform as follows:

KhQh is 17.68%
QhJh is 19.70%
JhTh is 21.72%
Th9h is 22.77%
9h8h is 22.62%
8h7h is 23.02%
7h6h is 23.03%
6h5h is 23.06%
5h4h is 21.65%
4h3h is 19.63%
3h2h is 17.60%

In all cases, the flush accounts for 7.10% on the wins.

So, best is 6h5h, worst is 3h2h.

Why? It is to do with the way that the suited connectors can make straights.

[FastCards]

Sorry, missed out A2 and AK:

AhKh is 12.14%
KhQh is 17.68%
QhJh is 19.70%
JhTh is 21.72%
Th9h is 22.77%
9h8h is 22.62%
8h7h is 23.02%
7h6h is 23.03%
6h5h is 23.06%
5h4h is 21.65%
4h3h is 19.63%
3h2h is 17.60%
Ah2h is 12.11%

So A2 is the worst.

Worst hand of any type against black Aces? Ah9s. (wins 5.92%)

[Bozeman]

Though my post was technically correct, (I knew that a lower one did better than 78s) I missed the best hand like the original response did: 56s.

Though these tiny difference are unimportant for non-academic interest,
Craig

[Copernicus]

The confusion comes from not splitting out ties from outright wins. 76s and 65s have the exact same percentage of outright wins, 22.87%. However, 65s has slightly more ties because there are more over straights, overflushes and overstraight flushes that can hit the board and be played by AA and the suited connectors.

[thylacine]

There are some good explanations in this thread. Thanks. Now in the numbers below the percentages increase then decrease, except 9h8h is an abberation to this pattern. Why?

Is there a list that separates wins from ties? Thanks.

[ QUOTE ]

AhKh is 12.14%
KhQh is 17.68%
QhJh is 19.70%
JhTh is 21.72%
Th9h is 22.77%
9h8h is 22.62%
8h7h is 23.02%
7h6h is 23.03%
6h5h is 23.06%
5h4h is 21.65%
4h3h is 19.63%
3h2h is 17.60%
Ah2h is 12.11%


[/ QUOTE ]

[the mayor]

[ QUOTE ]
There are some good explanations in this thread. Thanks. Now in the numbers below the percentages increase then decrease, except 9h8h is an abberation to this pattern. Why?

[/ QUOTE ]

i would believe that its because if the board comes up K,Q,J,10,x aces make the bigger straight.

[thylacine]

[Deadbuddha]

im definitely in love with either 78 or 89 suited, i have found that i tend to disrupt high pairs well with these hands.