Question about SK hand rankings

[GrekeHaus]

Most of you are familiar with these, you can see them at:

http://www.decf.berkeley.edu/~chubukov/rankings.html

My understanding was that these rankings assume that you're only going to get called when you're behind, and your opponent will fold every other time.

However, when I ran the numbers, I got different answers. I set up the equation like so:

SP=stealing percentage
WP=win percentage when called
X=size of your stack

Then we get

EV(push) = 1.5SP + (1-SP)*[(X+1.5)*WP + (1-WP)(-X)]

To figure out what X needs to be to break even, set the EV=0 and solve for X giving:

X = [1.5SP/(SP-1) - 1.5WP]/(2WP-1)

For KK then, we get SP=1218/1225 and WP=0.2262. Plugging these numbers in gave me a value of around 477, which differs significantly from the ones posted at the web site.

What's up with this?

[karlson]

It sure looks like you have it exactly right, except I set up the problem with blinds of 1 and 2 instead of 1/2 and 1. Multiplying 477 by 2 gives 954, which is basically the value listed.
I think there's an extra .5 in your second term though. (It was set up so that X is your stack after posting the blind (the first term is consistent with this), so the second one should have an X+1, not an X+1.5 (or X+2 instead of X+3 when you mutliply everything by 2)). Doesn't affect the answer much for KK /images/graemlins/smile.gif

[GrekeHaus]

Thanks for the response. That explains a lot if you multiplied everything by 2.

The purpose of my exeriment is to try and extend this idea to other positions to find out when it's ok to push with other hands from the button and so forth. So the steal percentage reduces and the 1.5 can become something else entirely depending on the position.

[The Yugoslavian]

[ QUOTE ]
Thanks for the response. That explains a lot if you multiplied everything by 2.

The purpose of my exeriment is to try and extend this idea to other positions to find out when it's ok to push with other hands from the button and so forth. So the steal percentage reduces and the 1.5 can become something else entirely depending on the position.

[/ QUOTE ]

Is there any way to build in ICM evaluations into this? For instance, the way you're currently thinking about doing it is just CEV.....is there a way to make it icmEV?

Maybe Eastbay would know? Or Karlson himself!

I'm too stupid to figure these things out... /images/graemlins/frown.gif.

Yugoslav

[karlson]

Sure. You could use some kind of ICM evaluation instead. It wouldn't be even be that hard.

But I'm kind of skeptical of the value. Chances are that your opponent's estimates of your hand range are going to make your decision right/wrong much more than any difference between CEV and $EV.

The original exercise was meant mostly as a demonstration that moving all-in is certainly right in a lot more situations than people admit. The fact that you would move in even if you flipped your cards face up is likely to more than counterbalance any extra considerations from non-chip-count tournament equity, unless the stacks are absolutely extreme.

[karlson]

I remember there was a guy who tried to do this about a year ago. It was on the poker theory forums, but I can't seem to find it right now. As far as I remember, he didn't even finish it for the case when opponents's cards are also universally known and they are sequentially allowed to call or fold. Anything else makes it a good deal harder.

It could be a useful exercise. My suspicion is that results will actually be on the other side, that is, they will suggest more conservative play than what most people would do in a real game. I think that most people tend to underestimate the chances of winning HU, but tend to overestimate the chances of winning in a multi-way pot.

[eastbay]

[ QUOTE ]
Thanks for the response. That explains a lot if you multiplied everything by 2.

The purpose of my exeriment is to try and extend this idea to other positions to find out when it's ok to push with other hands from the button and so forth. So the steal percentage reduces and the 1.5 can become something else entirely depending on the position.

[/ QUOTE ]

I wouldn't bother. The calling assumption in this exercise in this problem is pretty silly.

Generalize it to chosen sets of calling hands, add ICM valuation, and you're well on your way to what SGA does.

eastbay

[citanul]

[ QUOTE ]
Or Karlson himself!

[/ QUOTE ]

Well, hey, at least one good thing may come out of this, karlson might start posting more if you guys keep asking about the K/S hand rankings. And who knows, maybe he'll get interested in poker again.

citanul

[the shadow]

karlson, welcome back to the board! It'd be great to hear from you more often.

BTW, I think you might be referring to NLHE Tournament Hand Ranking for All-In (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Number=727277&page=&view=&sb=5&o =&fpart=1&vc=1) by Aisthesis.

The Shadow

[SuitedSixes]

[ QUOTE ]
karlson, welcome back to the board! It'd be great to hear from you more often.

BTW, I think you might be referring to NLHE Tournament Hand Ranking for All-In (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Number=727277&page=&view=&sb=5&o =&fpart=1&vc=1) by Aisthesis.

The Shadow

[/ QUOTE ]

I think that you should make a search function tutorial because you are better at it than anyone I have ever seen.

*Yes, you can print this post out and put it on your refrigerator.

[The Yugoslavian]

[ QUOTE ]
[ QUOTE ]
karlson, welcome back to the board! It'd be great to hear from you more often.

BTW, I think you might be referring to NLHE Tournament Hand Ranking for All-In (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Number=727277&page=&view=&sb=5&o =&fpart=1&vc=1) by Aisthesis.

The Shadow

[/ QUOTE ]

I think that you should make a search function tutorial because you are better at it than anyone I have ever seen.

*Yes, you can print this post out and put it on your refrigerator.

[/ QUOTE ]

The Shadow is good....

He's no me though, /images/graemlins/tongue.gif.

He just has a way cooler and more mysterious name /images/graemlins/frown.gif /images/graemlins/frown.gif.

Yugoslav