This post is kinda general in nature...

As many of you probably know, propokertools has created hand rankings that differ from each other depending on the number of hands being dealt.

10-handed
6-handed
3-handed

I have studied the 10-handed ordering fairly extensively but have not looked in detail at the 6 and 3-handed versions. I do notice that when I rank a particular hand, the value (between 1 and 100) will vary quite a bit depending on which version of the hand ordering is used.

Is it worth looking in detail at the 6 and 3-handed versions? Should there be major adjustments in the valuation of hands based on the number of opponents? If so, what aspects of a hand become more valuable as the number of players decrease?

you'll mostly see "kicker problems" in shorthanded pots. A432 is much closer to AK32 10-handed than 6-handed or 3-handed, IMO.

likewise: any extra flush draw (ds>ss>ns) is a big boost to one's hand shorthanded. 10-handed, the baby flush draw isn't much... however, the nut flush draw (with a suited A) is big 10-handed, but not much better than the K, Q or even J-high flush draw 3-handed.

I'll add if I think of more (there's obviously more...)

Very good thread, BTW!

Excellent thread. This also seems to imply that promoting your draws can be huge, in a 10-handed game. I.e., if you have several things working for you, but each of them is quite weak, if you can promote your non-nut flush draws over larger (but also non-nut draws), this can be pretty powerful.

I.e., like this hand:
http://forumserver.twoplustwo.com/44...g-gro-1226768/

Just did some plugging away on propokertools and came up with these charts to compare hand attributes in the different ranking orders (3, 6, and 10-handed).

These charts should be read carefully... a lower ranking = higher value hand. 1 = best hand, 100 = worst hand.







At first glance at this last chart, it looks like in general it is much less important in shorthanded games to have nutty low draws. This seems to match my intuition.

In the 2nd chart, we can see that hands containing medium pairs (66-88) go up in value in the 3-handed ordering, presumably because those pairs will win for high much more often than in 6 or 10 handed. Or perhaps because when those hands are coupled with another low card(s) it will more often win for low... not sure.

Very interesting. I like that you made graphs. Nice.

It makes a difference for the best if you exclude A for *. Otherwise your best hand in each grouping is A2(the card you're comparing)A. I think all AA2* hands are in the top percentile ranking.

For example,
Rankings for A28*

Hand	Average	Best	Worst
10H	11.73	1.0	34.0
3H	15.82	1.0	47.0
6H	12.73	1.0	38.0
VR	18.6	1.0	60.0

Rankings for A28*!A28A

Hand	Average	Best	Worst
10H	12.1	4.0	34.0
3H	16.34	4.0	47.0
6H	13.13	4.0	38.0
VR	19.2	4.0	60.0

Doesn't matter for the worst hand in each grouping (the rainbow hand), but it does matter for the best (double suited) and the average.

Interesting work. Good work. Thanks.

Buzz

WORST

Hand	10H	6H	3H	VR
A23*	22.0	26.0	34.0	43.0
A24*	23.0	26.0	31.0	42.0
A25*	23.0	26.0	31.0	43.0
A34*	36.0	35.0	34.0	39.0
A35*	39.0	34.0	33.0	34.0
A45*	43.0	37.0	31.0	32.0
234*	76.0	79.0	89.0	93.0
235*	71.0	75.0	86.0	91.0
245*	71.0	74.0	82.0	90.0
345*	72.0	78.0	86.0	91.0

If we look at the worst (the rainbows) hand of each three wheel card grouping, it looks like the worst of every three card grouping without an ace is poor, regardless of the number of players.

Of the hands with an ace, looks like those with an ace plus a deuce do better, on average, against more opponents, the hand without either a deuce or trey (A45*r) is higher rated against fewer players, and the farther we get away from the ideal A23*, the more we like fewer opponents.

I think a lot depends on suitedness. It's nice to get paid off by non-nut flushes when you have the nut flush.

In any event, it's difficult to compare a single variable when many variables need to be included in prediction of the overall results. For example, that fourth card matters. For short handed play, in general, depending on the board, you really like sufficient high card strength. Any suitedness adds to pre-flop high card strength, but then after the flop, you want to be in synch with the flop while still having high card strength.

And what your opponents think and how they play matters.

Some food for thought:

Hand	10H	6H	3H	VR
2345r	38.0	48.0	69.0	90.0
2346r	48.0	56.0	75.0	90.0
2347r	64.0	72.0	84.0	92.0
2348r	76.0	79.0	89.0	93.0
2349r	69.0	67.0	79.0	89.0
234Tr	67.0	67.0	76.0	86.0
234Jr	58.0	59.0	68.0	82.0
234Qr	52.0	52.0	57.0	72.0
234Kr	45.0	43.0	44.0	54.0

A few comparisons:

Hand	10H	6H	3H	VR
234Kr	45.0	43.0	44.0	54.0
2s3h4dKs	23.0	23.0	27.0	32.0

Hand	10H	6H	3H	VR
2345r	38.0	48.0	69.0	90.0
2s3h4d5s	23.0	28.0	40.0	71.0

Hand	10H	6H	3H	VR
2s3h4d4c	20.0	24.0	32.0	45.0
2s3h4d4s	34.0	39.0	53.0	76.0

All of these primarily low card hands seem to be rated better against more opponents. I'd call them all pulling hands.

Enough! (maybe too much!)

Buzz

Thanks for putting those graphs together!

- Dan @ ProPokerTools

+1. Thanks efficacy

Buzz, I am not sure how to make sense of those numbers (maybe format is messed up on my phone app?). Can you please explain how one should read the data, thanks.

I remember making some graphs over ten years ago, but I don't remember, off hand, how I did it.

For the following set of data, maybe someone who knows how to make graphs could plot the hand along the X-axis and the rank along the Y-axis.

There would be four different colored plots, red for ten handed, yellow for six handed, blue for three handed, and green for heads-up (VR).

Hand	10H	6H	3H	VR
A23*	22.0	26.0	34.0	43.0
A24*	23.0	26.0	31.0	42.0
A25*	23.0	26.0	31.0	43.0
A34*	36.0	35.0	34.0	39.0
A35*	39.0	34.0	33.0	34.0
A45*	43.0	37.0	31.0	32.0
234*	76.0	79.0	89.0	93.0
235*	71.0	75.0	86.0	91.0
245*	71.0	74.0	82.0	90.0
345*	72.0	78.0	86.0	91.0

Maybe just use the first six lines of data to see the trends.

That is, just plot the following to see the trends:

Hand	10H	6H	3H	VR
A23*	22.0	26.0	34.0	43.0
A24*	23.0	26.0	31.0	42.0
A25*	23.0	26.0	31.0	43.0
A34*	36.0	35.0	34.0	39.0
A35*	39.0	34.0	33.0	34.0
A45*	43.0	37.0	31.0	32.0

Buzz