Discussion:
The best hand...on average and the phenomenon of clustering
(too old to reply)
Edward Bird
2004-04-04 14:42:52 UTC
Permalink
This post is in further response to the 'Stealing the blinds question'. My
initial response was to steal, especially with a low stack. However I've
given it some more thought and have one or two questions that have been
troubling me for some time on this particular problem.

1. This scenario is designed in order to replicate a ten handed NL
tournament table, where players are raising all in before the flop.

Deal ten holdem hands.
Out of those ten hands find which one is the best 'heads-up'
Repeat and infinite number of times, creating a set of 'best hands for a
given deal'
List those hands in order of best to worst heads-up
Find the median hand (i.e. the hand in the middle of the list)
This is the 'best hand on average'

Does anyone have an idea as to what this hand might be? i.e. the best hand
for an average deal to ten players.

2. The phenoma of clustering.

By clustering I mean, that if the first 7 players in a hand fold, the last 3
players will have the best hands out of all the cards that were originally
dealt, or at least one of them does? Is this a reasonable idea, assuming all
the players are typical?

Now consider the original problem of stealing blinds on the button, when
everyone has folded in front of you. Is it sensible to raise with crap, when
the players on the blinds are likely to have better hands than average? In
this case would you always need the 'best hand on average' or better to
raise in any position?

Discuss...
Iceman
2004-04-04 15:11:04 UTC
Permalink
Post by Edward Bird
2. The phenoma of clustering.
By clustering I mean, that if the first 7 players in a hand fold, the last 3
players will have the best hands out of all the cards that were originally
dealt, or at least one of them does? Is this a reasonable idea, assuming all
the players are typical?
Short answer: No. Holdem being very positional, players will often fold
hands in early position that they would call or raise with in late
position. Also, there's not necessarily a "best hand" unless someone has
a premium hand - which is best out of A7s, KJo, and 88 depends entirely on
the situation.

People have studied whether the factor that "folded hands tend to contain
low cards and vice versa" is significant or not, and have found that it is
extremely small in holdem and should not affect your play. Lots of aces
and kings and queens are folded preflop, while many hands containing one
or two lower cards are played (so if there are four limpers to you on the
button in a normally tight game you can't automatically conclude that high
cards are out).

It is an important consideration in some forms of poker. In lowball, for
example, each player has five cards and high cards never have positive
value, so if the first five players all pass, it's significantly more
likely that the last three players have strong hands (i.e. low cards). Or
if lots of players are in, chances are that many low cards are out.
Post by Edward Bird
Now consider the original problem of stealing blinds on the button, when
everyone has folded in front of you. Is it sensible to raise with crap, when
the players on the blinds are likely to have better hands than average?
It depends entirely on the players in the blinds. I would play almost
anything against a SB who almost always folds preflop and a BB that won't
bluff and won't call on the flop without at least a pair. Against a SB
that's a calling station and a BB that's an intelligent bluffer and
tenacious heads-up player, I'd be much tighter.
Post by Edward Bird
In this case would you always need the 'best hand on average' or better
to raise in any position?
Absolutely not. There are many reasons to raise. Playing only premium
hands would make you too predictable, and in most limit games you'd lose
too much to the ante or blinds to make up for when you do get a hand.
Against idiots you'd still make money, but you'd make far more if you
adjusted to take advantage of their play by playing drawing hands in the
right spots.

_________________________________________________________________
Posted using RecPoker.com - http://www.recpoker.com
Edward Bird
2004-04-04 17:16:43 UTC
Permalink
Also, there's not necessarily a "best hand" unless someone has
Post by Iceman
a premium hand - which is best out of A7s, KJo, and 88 depends entirely on
the situation.
The situation is heads-up all-in before the flop - i.e. 'Our Hero' is on the
button, short stacked and wants to steal the blinds. So ...

88>A7s>KJo

I'm interested in the distribution of cards between ten players on average,
so that he can make an estimate of how good his hand is.
John Forsberg
2004-04-04 21:34:10 UTC
Permalink
Post by Iceman
Also, there's not necessarily a "best hand" unless someone has
Post by Iceman
a premium hand - which is best out of A7s, KJo, and 88 depends entirely on
the situation.
The situation is heads-up all-in before the flop - i.e. 'Our Hero' is on the
button, short stacked and wants to steal the blinds. So ...
88>A7s>KJo
That's true when against a random hand distribution, but is not
necesseraly true when up against other distributions. Don't know if that
makes any difference for your purposes though...
Post by Iceman
I'm interested in the distribution of cards between ten players on average,
so that he can make an estimate of how good his hand is.
Gaash
2004-04-04 21:54:03 UTC
Permalink
I once had a table (can't find it though) which showed every possible hand
combination type (i.e 93o, AKs) and the % chance it has of ending up the
best with 2,3,4,5...10 players in the pot. This table has all the answers
you are asking, try searching for starting hands and texas hold 'em AI, or
bot or something with demon or daemon, as was the name of the research bot
whose paper had this thing;

***however, in tournament play, a lot of it depends on what kind of an
edge you would like. since EV is not the only consideration (one could
even argue, Risk premium is an even more important consideration, i.e. the
chance you will not lose the hand, regardless of how much you will win)

Here's an example of what I mean:

Let's say you are getting called.

If you went in with KQ, you are a 40%-50 dog (40% chance to win) against a
large number of hands (all pairs, all Ax) that would call you; however,
you are only a BIG underdog to very few hands (QQ, KK, AQ, AK, AA), on the
other hand the biggest favorite you can really hope to be is about 70%
against something like Q10

On the other hand, if you are playing 88. You are a small favorite (55 or
so % ) over many hands, but a big favorite over very few (probably no hand
that he would call with, except maybe an A7, 77 or something) and a big
dog against all higher pairs, which is not a lot of hands, but of the set
of hands that will call you, not such a small number.

So which hand is "better on average"? It's hard to say, because in
tournaments EV is not all that matters, as risk/reward plays a HUGE role.
It all depends on what type of risk you are willing to take.

If you are willing to take a 50% gamble with a slight edge and a risk of
being totally out of it, I would say 8s are better. If you don't want to
risk being dominated if he calls, the KQ looks more appealing.
Edward Bird
2004-04-04 22:16:44 UTC
Permalink
Thanks for the reply Gaash, does this mean you don't hate my guts any more
[ref: whinge about limit poker]?

You've given me some excellent ideas there on domination factor. I suppose
the general scenarios are:

1 overcard,
ie. AT vs KQ, AT vs KT, AT vs QQ
2 overcards,
ie. AK vs QJ, AK vs 99
overpair,
ie. KK vs QJ, KK vs 99

Theres the suited factor and straight interference factors that also
complicate matters.

This game is like a pandoras box!

As for the risk / reward thing...I totally agree. If you've got a small
stack and you think you're opponet may fold if you raise...you have to
raise. I tried the Sklansky approach of raising all in for intimidation
purposes (being a little more discriminating with starting hands than he
suggests due to the looseness of players in the small stakes tournaments)
and it works a treat. There are times when you run into AA, but that's going
to happen from time to time. It's better to play to win in these tournaments
than play to survive though I think.
Post by Gaash
I once had a table (can't find it though) which showed every possible hand
combination type (i.e 93o, AKs) and the % chance it has of ending up the
best with 2,3,4,5...10 players in the pot. This table has all the answers
you are asking, try searching for starting hands and texas hold 'em AI, or
bot or something with demon or daemon, as was the name of the research bot
whose paper had this thing;
***however, in tournament play, a lot of it depends on what kind of an
edge you would like. since EV is not the only consideration (one could
even argue, Risk premium is an even more important consideration, i.e. the
chance you will not lose the hand, regardless of how much you will win)
Let's say you are getting called.
If you went in with KQ, you are a 40%-50 dog (40% chance to win) against a
large number of hands (all pairs, all Ax) that would call you; however,
you are only a BIG underdog to very few hands (QQ, KK, AQ, AK, AA), on the
other hand the biggest favorite you can really hope to be is about 70%
against something like Q10
On the other hand, if you are playing 88. You are a small favorite (55 or
so % ) over many hands, but a big favorite over very few (probably no hand
that he would call with, except maybe an A7, 77 or something) and a big
dog against all higher pairs, which is not a lot of hands, but of the set
of hands that will call you, not such a small number.
So which hand is "better on average"? It's hard to say, because in
tournaments EV is not all that matters, as risk/reward plays a HUGE role.
It all depends on what type of risk you are willing to take.
If you are willing to take a 50% gamble with a slight edge and a risk of
being totally out of it, I would say 8s are better. If you don't want to
risk being dominated if he calls, the KQ looks more appealing.
EZBux
2004-04-05 05:10:47 UTC
Permalink
This is a link to Steve Brecher's (yet another Steve) Hand Rank/Odds
table. I believe this is the chart that 'Gaash' was talking about.
It gives showdown odds for every hand combination when played vs 1 to
9 opponents.

http://gocee.com/poker/HE_Value.htm

---
Que le vaya bien...Steve
antman
2004-04-04 23:05:31 UTC
Permalink
From Mike Caro and CardPlayer odds calculator:

(http://www.cardplayer.com/?sec=poker_odds_calculator&source=WPTbanners#)

Heads up:

4s 4d > Ah Kc (54.4%)
Ah Kc > Js Ts (58.7%)

but... Js Ts > 4s 4d (52.8%)

So, there is not necessarily a "best hand."
Post by Iceman
Also, there's not necessarily a "best hand" unless someone has
Post by Iceman
a premium hand - which is best out of A7s, KJo, and 88 depends entirely on
the situation.
The situation is heads-up all-in before the flop - i.e. 'Our Hero' is on the
button, short stacked and wants to steal the blinds. So ...
88>A7s>KJo
I'm interested in the distribution of cards between ten players on average,
so that he can make an estimate of how good his hand is.
_________________________________________________________________
Posted using RecPoker.com - http://www.recpoker.com
Iceman
2004-04-05 01:04:08 UTC
Permalink
Post by Iceman
Also, there's not necessarily a "best hand" unless someone has
Post by Iceman
a premium hand - which is best out of A7s, KJo, and 88 depends entirely on
the situation.
The situation is heads-up all-in before the flop - i.e. 'Our Hero' is on the
button, short stacked and wants to steal the blinds. So ...
I'm interested in the distribution of cards between ten players on average,
so that he can make an estimate of how good his hand is.
In that case, you can disregard the first seven players, and focus on the
distribution of cards between the three players (you included) that are
left to act. But it's also important to consider factors including the SB
and BB stacks, how they tend to play, whether their current status in the
tournament would make them more or less likely to call, and what would
happen if both of them call and how likely is that? In general, hands
matter much less in this situation than opponents and situations.

_________________________________________________________________
Posted using RecPoker.com - http://www.recpoker.com
Barbara Yoon
2004-04-05 05:03:35 UTC
Permalink
Post by Edward Bird
This post is in further response to the 'Stealing the blinds question'.
My initial response was to steal, especially with a low stack. However
I've given it some more thought and have one or two questions that
have been troubling me for some time on this particular problem.
1. This scenario is designed in order to replicate a ten handed NL
tournament table, where players are raising all in before the flop.
Deal ten holdem hands.
Out of those ten hands find which one is the best 'heads-up'
Repeat and infinite number of times, creating a set of 'best hands
for a given deal'
List those hands in order of best to worst heads-up
Find the median hand (i.e. the hand in the middle of the list)
This is the 'best hand on average'
Does anyone have an idea as to what this hand might be? i.e. the
best hand for an average deal to ten players.
Edward.....if I am understanding you correctly, a good estimate for that
here might be the top (1 - (1/2)^(1/10)) of all 1,326 possible different
starting hands -- that is, something like around A-Q, or better.....OK?!
Post by Edward Bird
2. The phenoma of clustering.
By clustering I mean, that if the first 7 players in a hand fold, the last 3
players will have the best hands out of all the cards that were originally
dealt, or at least one of them does? Is this a reasonable idea, assuming
all the players are typical? Now consider the original problem of stealing
blinds on the button, when everyone has folded in front of you. Is it
sensible to raise with crap, when the players on the blinds are likely to
have better hands than average? In this case would you always need the
'best hand on average' or better to raise in any position? Discuss...
This further part of your question is way too complicated for any exact
answer (at least by ME, anywise)...but I do hope that my "A-Q" answer
to your first part is helpful to you somehow anyway.....OK?!
Barbara Yoon
2004-04-05 19:01:13 UTC
Permalink
Post by Barbara Yoon
Post by Edward Bird
Deal ten holdem hands.
Out of those ten hands find which one is the best 'heads-up'
Repeat and infinite number of times, creating a set of 'best hands
for a given deal'
List those hands in order of best to worst heads-up
Find the median hand (i.e. the hand in the middle of the list)
This is the 'best hand on average'
Does anyone have an idea as to what this hand might be? i.e. the
best hand for an average deal to ten players.
Edward.....if I am understanding you correctly, a good estimate for that
here might be the top (1 - (1/2)^(1/10)) of all 1,326 possible different
starting hands -- that is, something like around A-Q, or better.....OK?!
Edward (or any other volunteers).....interesting question.....perhaps you
would take the time to deal out your scenario here a hundred or so times,
and keep a record of the 'best hand' each time (which is not necessarily
the ultimate 'WINNING' hand).....and report back to us here.....OK?!
Edward Bird
2004-04-05 21:06:21 UTC
Permalink
I'm working on a computer program to figure it out. I'm not sure if the
results will have any meaning, but I'll certainly report them back to the
group when I get them, and may be some of you can put the correct
interpretation on them?
Post by Barbara Yoon
Post by Barbara Yoon
Post by Edward Bird
Deal ten holdem hands.
Out of those ten hands find which one is the best 'heads-up'
Repeat and infinite number of times, creating a set of 'best hands
for a given deal'
List those hands in order of best to worst heads-up
Find the median hand (i.e. the hand in the middle of the list)
This is the 'best hand on average'
Does anyone have an idea as to what this hand might be? i.e. the
best hand for an average deal to ten players.
Edward.....if I am understanding you correctly, a good estimate for that
here might be the top (1 - (1/2)^(1/10)) of all 1,326 possible different
starting hands -- that is, something like around A-Q, or
better.....OK?!
Post by Barbara Yoon
Edward (or any other volunteers).....interesting question.....perhaps you
would take the time to deal out your scenario here a hundred or so times,
and keep a record of the 'best hand' each time (which is not necessarily
the ultimate 'WINNING' hand).....and report back to us here.....OK?!
Bill Reich
2004-04-05 11:52:33 UTC
Permalink
Post by Edward Bird
This post is in further response to the 'Stealing the blinds question'. My
initial response was to steal, especially with a low stack. However I've
given it some more thought and have one or two questions that have been
troubling me for some time on this particular problem.
1. This scenario is designed in order to replicate a ten handed NL
tournament table, where players are raising all in before the flop.
Deal ten holdem hands.
Out of those ten hands find which one is the best 'heads-up'
Repeat and infinite number of times, creating a set of 'best hands for a
given deal'
List those hands in order of best to worst heads-up
Find the median hand (i.e. the hand in the middle of the list)
This is the 'best hand on average'
Does anyone have an idea as to what this hand might be? i.e. the best hand
for an average deal to ten players.
2. The phenoma of clustering.
By clustering I mean, that if the first 7 players in a hand fold, the last 3
players will have the best hands out of all the cards that were originally
dealt, or at least one of them does? Is this a reasonable idea, assuming all
the players are typical?
Now consider the original problem of stealing blinds on the button, when
everyone has folded in front of you. Is it sensible to raise with crap, when
the players on the blinds are likely to have better hands than average? In
this case would you always need the 'best hand on average' or better to
raise in any position?
Discuss...
I think your premise, that they will have better hands than average,
is wrong. Hands that aware early-position NLHE players will fold can
often have a great many attractive cards, just not in good
combinations. With only fourteen or sixteen cards gone from the deck,
there isn't enough change in the deck to say that the blinds have
above-average hands.

In any case, a "better than average" hand is probably J8o or 87s or
somewhere in that vicinity. How many players, except those who know me
very well, are likely to call with a hand like that? If you don't
steal, you will need to show down winning hands. That can be
impossible if you aren't DEALT any. Remember, you can't lose more than
your buy-in. Strategies that lead to losing less lead to slowly
bleeding ones way into short-land, last stop before the rail.

--
Will in New Haven

Farmers have chips so that bandits can steal them
Continue reading on narkive:
Loading...