Question

[Cyrus]

I apologize. The correct average winning percentage of my QQ vs AKs is of course approximately 54% (and not 65%).

The rest of the argument remains valid, IMO, calling for TT as the most preferred hand when the opponent holds either AKs or AA. It's slightly ahead of QQ and JJ.

--Cyrus

[Nottom]

[ QUOTE ]
I apologize. The correct average winning percentage of my QQ vs AKs is of course approximately 54% (and not 65%).


[/ QUOTE ]

No need for apologies, I think most of us knew the true odds and it didn't really matter anyway as the rest of you post still follows.

[Ryan_21]

"77 with a board of 89TJQ will beat AA"

Im half in the bag right now, but even I can realize that 77 vs. AA w/ a board of 89TJQ is a split!

Ryan_21

[pankwindu]

[ QUOTE ]
The crucial factor must be that it also reduces the ways in which AA and AKs can win be eliminating boards resulting in the low end A-5 straight. 76s also does this to an extent but not in as many ways as 65s.

[/ QUOTE ]

Can someone explain why 65s is better than 76s? My understanding from the above and other comments was that the main benefit of 65s was to give you the winning straight on a 2-3-4-5 board. But, 76s does this also, with slightly higher card values and still low enough to catch a winning straight on the high side...? So, what am I missing that makes 65s better than 76s?

[M.B.E.]

[ QUOTE ]
Can someone explain why 65s is better than 76s? My understanding from the above and other comments was that the main benefit of 65s was to give you the winning straight on a 2-3-4-5 board. But, 76s does this also, with slightly higher card values and still low enough to catch a winning straight on the high side...? So, what am I missing that makes 65s better than 76s?

[/ QUOTE ]
In this post, Bozeman points out that 76s wins more pots outright, but 65s has more ties which puts it over the top.

In particular, if I have 65 the tie board JT987 can come up 4^5 ways, but if I have 76 it can come up only 4^4*3 ways (i.e. 75% as much). Similarly if I have 65 the tie board T9876 can come up 4^4*3 ways, but if I have 76 it can come up only 4^3*3^2 ways (again 75% as much).

The extra ties that 65 gets more than makes up for the few extra wins 76 has (e.g. 76 will win against AA on the four boards J7655, J7644, J7633, and J7622, but 65 has only three corresponding boards: T6544, T6533, and T6522).

[Nottom]

[ QUOTE ]
The extra ties that 65 gets more than makes up for the few extra wins 76 has (e.g. 76 will win against AA on the four boards J7655, J7644, J7633, and J7622, but 65 has only three corresponding boards: T6544, T6533, and T6522).

[/ QUOTE ]

AA wins in all these cases, unless I am missing something obvious.

[M.B.E.]

[ QUOTE ]
[ QUOTE ]
The extra ties that 65 gets more than makes up for the few extra wins 76 has (e.g. 76 will win against AA on the four boards J7655, J7644, J7633, and J7622, but 65 has only three corresponding boards: T6544, T6533, and T6522).

[/ QUOTE ]

AA wins in all these cases, unless I am missing something obvious.

[/ QUOTE ]
Oh yeah, you're right. My examples were wrong.

[Morbo]

Uhm, wouldn't the correct answer simply be AA? [img]/images/graemlins/grin.gif[/img]

EDIT: Ok, I figured it would be too easy so I read the original post again... [img]/images/graemlins/blush.gif[/img]

[BobK]

This is perfect data for TT which appears to me to be the best.
Hope my math is the same.

Unpaired suited hands do much worse.

1712304 total possible boards per matchup type
One unit bet per board

_________Wins________Ties
AsKs____786350_______6244
TdTc____919710_______6244
P/L_____133360___________3 of 6 no common suit

AsKs____779838_______7703
TsTh____924763_______7703
P/L_____144925___________3 of 6 one common suit
Avg. P/L when AKs vs TT (133360 + 144925) / 2 = 139142.5 units avg. win


AsAh____1368728______5092
TdTc_____338484______5092
P/L____-1030244__________1 of 6 no common suit

AsAh____1379434______6471
TsTc_____326399______6471
P/L____-1053035__________4 of 6 one common suit

AsAh____1390140______7850
TsTh_____314314______7850
P/L____-1075826__________1 of 6 two common suit
Avg. P/L when AA vs TT (-1030244/6) + ((-1053035/6)* 4) + (-1075826/6) = -1053035 units avg. loss

Total possible boards 1712304 * 5 = 8561520

Overall P/L for TT vs. (AA or AKs)
(-1053035 * 6) + (139142.5 * 4) =-5761640 loss on 8561520 boards

Per board loss 5761640/8561520 = 0.6729692 units

So you're about a 2 to 1 dog if you don't know which hand they hold.

Bob

P.S.
Maybe someone can tell me how to columnize items without using the underscore?

[Cyrus]

Try the "Code" button from the "Instant UBB code" table. It respects the spacebar, see:

<font class="small">Code:</font><hr /><pre>

Table Important Finding Less Important

1 0.568% 75k </pre><hr />