"Small logical errors" in Sklansky hand rankings?

[WRX]

In his thesis, available here, p. 42, Darse Billings states, "There are also a few instances of small logical errors in Sklansky's rankings. For example, 43s is ranked in Group 7, ahead of 53s in Group 8, but it can be shown that 53s logically dominates 43s, because it has the same straight and flush potential, with better high-card strength. Similarly, 52s dominates 42s and 32s, but 52s is not ranked in any of the eight groups, whereas the latter are members of Group 8."

The Sklansky rankings he is using are from Hold'em Poker for Advanced Players.

Comments?

[mwette]

Well, I don't have an answer for you, but thanks for
the reference to Billings' thesis. Over the last few
days I have started to put together a poker simulator
for the fun of it. This thesis should be an interesting
read ...

[SplawnDarts]

Post deleted by SplawnDarts

[SplawnDarts]

I'd say there are some not-so-small errors in the table too. Simple put, the hands in various groups do NOT play mostly alike as Slansky suggests at the top of page14 in HEP:FAP. The idea that a ATo and a 54s play mostly alike in ANY scenario is pretty much ludicrous. The former needs weak opponents and a heads up pot. The later needs a volume pot.

DS's table simply mis-explains the point by classifying those two hands as in any way similar. There are analogous errors throughout the table.

[El_Hombre_Grande]

You are missing the point. While 53s most certainly does dominate 43s, the hand ranking ARE NOT heads up hand rankings, they reflect playability in a full ring 10-20 LHE game. Thus neither hand has any highcard showdown value (the only reason domination matters), and 43 more often leads to straights or open ended draws that can be semi-bluffed.

If there is a weakness to the hand rankings, I think that it is that they assume more multiway action than is currently prevalent in common online games, where VPIPs are quite low compared to their live counterparts. In any event, the author points out how to adjust the tables for tighter and more aggressive games, namely by dropping hands that need many opponents and cheap flops. Thus to call it a weakness is a stretch.

[plexiq]

[ QUOTE ]
You are missing the point. While 53s most certainly does dominate 43s, the hand ranking ARE NOT heads up hand rankings, they reflect playability in a full ring 10-20 LHE game. Thus neither hand has any highcard showdown value (the only reason domination matters), and 43 more often leads to straights or open ended draws that can be semi-bluffed.

[/ QUOTE ]

53 has the same straight potential as 43, and the same chance to flop an OESD.

Straights, using both hole cards:
53: 467,462,42A
43: A25,256,567

Straights, using one hole card:
53: 6789
43: 5678

OESD's:
53: 42,46
43: 25,56

If anything, i think 43 is slightly worse considering straights.

With 5/3, when getting a straight (w/ both hole cards) on an otherwise uncoordinated board, you usually have the nuts. Only exception is the 467-straight. But here, opponent would have to play 5/8 - which is rarely played, and less likely because we are holding one 5.

With 4/3, the 567-straight is likely to run into 89 from time to time.

[El_Hombre_Grande]

Good post. i've always taken it as gospel that the no gapped connectors led to more straights without examining it.

Its close, but i think you MAY have made a mistake. If you look at your comparison of "straights using one card" you've "required" A six card straight for 43; the 8 is unnecessary, whereas the nine was necessary for the 53 to hit. So i think the difference is that on one you have only three necessary occurences and the other is 4. Conceptually, I'm not sure how this works with the fact that that we've already counted 567.

The point about 5/8 and 8/9 is well taken, and over infinity would make a substantial difference.

It also appears they both use an Ace an equal amount of time-- and the Ace likely makes a second best hand to pay you off.

[DrVanNostrin]

[ QUOTE ]
Good post. i've always taken it as gospel that the no gapped connectors led to more straights without examining it.

If you look at your comparison of "straights using one card" you've "required" A six card straight for 43; the 8 is unnecessary, whereas the nine was necessary for the 53 to hit...

[/ QUOTE ]
This just makes a stronger case for 53s, because now there's one fewer straight 43s can make.

[plexiq]

Yup, i think you guys are right.

There is no "1-hole-card-straight" for 43s which is not covered by the 2-card straights already. So, 43s should in fact have a lower straight probability than 53s.