enlighten me please (on the trivial)

[pheasant tail (no 18)]

On 2 dimes I put in the following two hands (AsKs vs. 6c6d) and (AsKs vs 8c8d). They were played HU. The results were as follows:

AsKs vs. 6c6d--AKs won 47.7, 66 won 51.93
AsKs vs. 8c8d--AKs won 47.54, 88 won 52.11

Why the difference? If anything, I'd expect that 88 would be less since there is one less straight that it can win (9TJQ) since AK would be on the high end. It seems that such an advantage would more than offset for the times that the board contains a 7 high flush in clubs or diamonds?

Trivial, I know, but you were warned in the subject line.

PT

[PairTheBoard]

Also notice the 88's tie .35% while the 66's tie .37%. I'd have to guess the increase in ties is due to the 7 LOW Flushes on board in clubs or diamonds. So the advantage the 88's get from that case doesn't even account for the overall .18% difference - ignoring the straight case you mention. Must be something else going on we aren't thinking of.

PairTheBoard

[jdl22]

This sort of thing has come up before. It basically boils down to more combinations of cards that cancel the pair. For example if the board is 99772 then the eights would win versus the AK but the sixes would lose because they would playing the two pair on board and the six would be outkicked by the ace. It's similar for boards like 7777xy. The higher the pp the fewer possible boards like this that wash out the pair. You see this in actual play when you have a small pocket pair and you get that bad feeling in your gut when the river makes two higher pair and you know that your hand was good but certainly isn't any more.

[PairTheBoard]

yep.

[pheasant tail (no 18)]

Of course. My neurosis can now focus on something else.

[pzhon]

[ QUOTE ]
On 2 dimes I put in the following two hands (AsKs vs. 6c6d) and (AsKs vs 8c8d). They were played HU. The results were as follows:

AsKs vs. 6c6d--AKs won 47.7, 66 won 51.93
AsKs vs. 8c8d--AKs won 47.54, 88 won 52.11

Why the difference? If anything, I'd expect that 88 would be less since there is one less straight that it can win (9TJQ) since AK would be on the high end.

[/ QUOTE ]

This is not trivial. The calculator (http://www.twodimes.net/poker/) at Twodimes.net allows you to remove cards from the deck, eliminating some of the possible ways to win. Every straight contains a 5 or a 10, so removing these eliminates the effect of straights, with only slight distortions on the other ways to win.

pokenum -h as ks - 6c 6d / 5c 5d 5h 5s ts th td tc
cards %win %tie EV
A/images/graemlins/spade.gifK/images/graemlins/spade.gif 49.92 0.21 0.500
6/images/graemlins/club.gif6/images/graemlins/diamond.gif 49.87 0.21 0.500

pokenum -h as ks - 8c 8d / 5c 5d 5h 5s ts th td tc
cards %win %tie EV
A/images/graemlins/spade.gifK/images/graemlins/spade.gif 49.04 0.15 0.491
8/images/graemlins/club.gif8/images/graemlins/diamond.gif 50.80 0.15 0.509

If you remove the additional straights that 66 wins, the advantage of 88 increases from 0.18% to 0.93%. So, straights are an important factor. Counterfeited flushes make up about 0.006% of the hands (you need to consider not just the 7-low, but also the 6-low flushes on the board), so this is not an important factor. Overbalancing the additional straights 66 wins are the times that 88 produces a greater 2-pair (e.g., TT773) and much less common times 88 produces an overboat rather than an underboat (e.g, 7778K gives 88 a win over AK but 7776K gives AK a win over 66). To see that these are important, note that QQ does even better against AKs (EV .538) even though QQ does not make as many straights.