Second Challenge to Jason "The Mathematician" Palowski

[ramashiva]

Based on my second challenge to Abdul Cameljockey --

https://groups.google.com/group/rec.gambling.poker/msg/9118e3e468827f96

OK, Jason. Assuming that you answer the three questions in my first
challenge with ease, and I am assuming you can, since you have these
great conceits about being a brilliant mathematician -- here is a
somewhat more challenging question for you --

Please make an exhaustive enumeration of all strategic options
available to both players in headsup action in limit holdem after the
river card has been dealt. Please summarize these strategic options
as an NxN game payoff matrix.

What is the value of N?

What is the correct labelling for the rows and columns of this NxN
payoff matrix?

Please give the mathematical value of each of the elements, or cells,
of the payoff matrix.

Those of you who know the answer to this elementary problem in
applying mathematical game theory to holdem strategy, please remain
silent and let's see if Jason even understands the question, let alone
is able to provide the correct answer.


William "The Life" Coleman (ramashiva)

[Jason Pawloski]

So this is what happens when an unintelligent, mathematical failure, who
couldn't get tenure at one of the shittiest schools in Arizona, goes nuts.

William, you are right, you probably know a lot more about game theory
than me. I also know a lot more about measure theory and group algebra
than you. I also know how to take averages and interpret them in
meaningful ways. The fact you think that this knowledge of one small
section of math proves you are a better mathematician than me really shows
how badly I've tilted you.

Question: are you going to continue this anklebiting and thread stalking?

--
RGP's Stupidest Poster by popular vote - 3/22/09 to 6/13/10

Jerry "The Savant" Sturdivant - making up a position for reality since
1926.

[ramashiva]

On Jun 3, 10:39 am, "Jason Pawloski" <a679...@webnntp.invalid> wrote:

> So this is what happens when an unintelligent, mathematical failure, who
> couldn't get tenure at one of the shittiest schools in Arizona, goes nuts.

LOL. I have explained why I didn't get tenure at Arizona Western
College. It had nothing to do with my ability as a mathematician or
as a professor. I got the highest ratings in those categories. I was
denied tenure because I got into a big conflict with the College
President about the acquisition of a new computer system.

> William, you are right, you probably know a lot more about game theory
> than me. I also know a lot more about measure theory and group algebra
> than you. I also know how to take averages and interpret them in
> meaningful ways. The fact you think that this knowledge of one small
> section of math proves you are a better mathematician than me really shows
> how badly I've tilted you.

Jason, seriously. Probability, Statistics, Game Theory, and
Mathematical Optimization Techniques are NOT one small section of
mathematics. In fact, they are the only mathematics which interest
me, because that is the mathematics which is applicable to the
analysis of poker strategy.

> Question: are you going to continue this anklebiting and thread stalking?

Jason, this all came about because you simply couldn't admit that you
didn't know that the mean of a set of data points on an ordinal scale
is undefined.

I will address your challenges after you answer mine to my
satisfaction, or admit you don't know the answers.

But since I am unfamiliar with most of the technical mathematical
terminology in your questions, and since I haven't taken a course in
group theory or even thought about group theory for 45 years, I would
prefer questions like mine.

My questions require no knowledge of mathematics beyond that taught in
undergraduate courses in finite mathematics. My questions do not
require knowledge of any technical terminology, but they do require
the ability to solve problems which don't have a predefined solution
algorithm.

I suspect you are not smart enough to have this ability. I have
always thought you were stupid, and you have yet to give me any reason
to think otherwise.

[Tim Norfolk]

In theory, depending on the number of raises allowed, N could be very
large, couldn't it?

[phlash74]

Theoretically, it could be infinite - it's limited only by the amount of bets in the shorter stack. Most LHE games have no cap on raises when a betting round starts with only two active players in the hand. So my guess is the value of N is (shorter stack/big bet). Maybe you have to add one to account for both players checking.

Full disclosure - I absolutely suck at math. My wife is the one who earned a master's in mathematics.

Michael

[ramashiva]

See my reply to Professor Norfolk.

[phlash74]

I don't see a reply from you to his post on either Google Groups or
recgroups. Can you please repost it? I'm sure my answer is wrong - like I
said, I suck at math. But it is an interesting question.

Michael

-----------------
"> phlash
On your circle jerk k00l kidz email list. Should be disqualified for
that, but I'll give him a pass because he is smart." - ramashiva,
8/22/2010

"Hitler has already been forgiven, but you have not." - Reptillian AKA
Igotskillz, 4/6/2011

[ramashiva]

On Jun 13, 9:51 am, "phlash74" <a102...@webnntp.invalid> wrote:

> On Jun 13 2012 9:08 AM, ramashiva wrote:

> > See my reply to Professor Norfolk.

> I don't see a reply from you to his post on either Google Groups or
> recgroups. Can you please repost it? I'm sure my answer is wrong - like I
> said, I suck at math. But it is an interesting question.

No, I can't repost it, because Google Groups doesn't have a sent
messages folder. It's lost in the innertubes. It will show up
eventually.

Google Groups does have an option to send an email of every post
made. I could use that, but I have never had a post just disappear,
although posts can get lost for awhile.

[ramashiva]

On Jun 13, 8:37 am, Tim Norfolk <timsn...@aol.com> wrote:

> On Jun 3, 1:17 pm, ramashiva <ramashiv...@gmail.com> wrote:

> > Based on my second challenge to Abdul Cameljockey --

> >https://groups.google.com/group/rec.gambling.poker/msg/9118e3e468827f96

> > OK, Jason.  Assuming that you answer the three questions in my first
> > challenge with ease, and I am assuming you can, since you have these
> > great conceits about being a brilliant mathematician -- here is a
> > somewhat more challenging question for you --

> > Please make an exhaustive enumeration of all strategic options
> > available to both players in headsup action in limit holdem after the
> > river card has been dealt.  Please summarize these strategic options
> > as an NxN game payoff matrix.

> > What is the value of N?

> > What is the correct labelling for the rows and columns of this NxN
> > payoff matrix?

> > Please give the mathematical value of each of the elements, or cells,
> > of the payoff matrix.

> > Those of you who know the answer to this elementary problem in
> > applying mathematical game theory to holdem strategy, please remain
> > silent and let's see if Jason even understands the question, let alone
> > is able to provide the correct answer.

> In theory, depending on the number of raises allowed, N could be very
> large, couldn't it?

Nope. One of the strategic options is how you respond to a raise.

One strategic option is to always respond to a raise with a reraise.

If both players employ that strategic option, then the result (payoff)
is just the matrix cell at the intersection of the row and column of
that strategic option for player A and player B.

The actual value of that cell will depend on whether there is a cap on
the number of raises headsup.

[phlash74]

So would the rows and columns be listed by a player's response to no
bet/player's response to a bet or raise? Something like check/fold,
check/call, check/raise, bet/fold, bet/call, bet/raise? That would make N
6, and seem to cover most of the strategic options.

I guess my confusion is how do you account for number of bets a player is
willing to go? A player could easily be willing to bet and go a few
raises, but not the maximum number of raises (if such a restriction is
imposed headsup) if they hold a strong non-nut hand. Does that make N
larger?

[phlash74]

On Jun 13 2012 9:04 AM, ramashiva wrote:

OK, I took a stab at it. Apologies if the formatting gets all fucked up:

PLAYER A (first to act on river)
C/F C/C C/R B/F B/C B/R
P C/F 0 0 0 1 1 1
L C/C 0 0 0 2 2 2
A C/R 0 0 0 3 4 max
Y B/F 1 2 3 1 1 1
E B/C 1 2 4 2 2 2
R B/R 1 2 max 3 4 max

B

*******
C/F - check/fold to a bet
C/C - check/call a bet
C/R - check/raise a bet or raise
B/F - bet/fold to a bet or raise
B/C - bet/call a bet or raise
B/R - bet/raise a bet or raise

The numbers in the cells represent the amount of big bets the winner of
the hand will receive above and beyond the amount in the pot prior to the
river, whether there is a showdown or not. 1 obviously means the player's
bet is returned to him due to the opponent folding. The cells with max
assume that both players will continue to raise until the cap (if it
exists) is reached or one of the players runs out of money and is all-in.

How far off am I?

[phlash74]

On Jun 13 2012 3:01 PM, phlash74 wrote:

> The numbers in the cells represent the amount of big bets the winner of
> the hand will receive above and beyond the amount in the pot prior to the
> river, whether there is a showdown or not. 1 obviously means the player's
> bet is returned to him due to the opponent folding. The cells with max
> assume that both players will continue to raise until the cap (if it
> exists) is reached or one of the players runs out of money and is all-in.
>

That first sentence should probably say "correspond to the number of big
bets" rather than "represent the amount of big bets". Grammar FAIL.

[ramashiva]

> OK, I took a stab at it. Apologies if the formatting gets all fucked up:

>         PLAYER A (first to act on river)
>         C/F     C/C     C/R     B/F     B/C     B/R
> P C/F     0       0       0       1       1       1
> L C/C     0       0       0       2       2       2
> A C/R     0       0       0       3       4     max
> Y B/F     1       2       3       1       1       1
> E B/C     1       2       4       2       2       2
> R B/R     1       2     max       3       4     max
>
> B
>
> *******
> C/F - check/fold to a bet
> C/C - check/call a bet
> C/R - check/raise a bet or raise
> B/F - bet/fold to a bet or raise
> B/C - bet/call a bet or raise
> B/R - bet/raise a bet or raise
>
> The numbers in the cells represent the amount of big bets the winner of
> the hand will receive above and beyond the amount in the pot prior to the
> river, whether there is a showdown or not. 1 obviously means the player's
> bet is returned to him due to the opponent folding. The cells with max
> assume that both players will continue to raise until the cap (if it
> exists) is reached or one of the players runs out of money and is all-in.
>
> How far off am I?

You are getting very warm. The correct answer is a 6X6 payoff matrix,
so you got that right. But you need to account for the amount in the
pot that is won by the winner. In general, the cells in the payoff
matrix should be algebraic expressions, not numbers. In general, the
payoff for the winner of a pot which goes to showdown is pot + action,
while the payoff for the loser of the pot is - action.

Thanks for confirming my opinion that you are very smart. This
problem was far beyond Jason's capabilities to answer. It was far
beyond the capability of Abdul Cameljockey to answer. I am certain
that there are only a few people on RGP or the BARGE list who could
figure this out, no matter how much time they had.

To put this all together, you need a variable which shows who will win
the pot if the hand goes to a showdown. This could be a variable
whose value is 0 is the two players have the same hand, 1 if player A
has the best hand, and 2 if player B has the best hand.

That variable is then incorporated into the algebraic formula in all
cells where the winner of the pot is determined by a showdown.

If one player folds at some point, then the winner of the pot wins the
pot plus action of player who folds, while the folding player loses
his river action.

There are still some problems here, and it's been a long time since I
even thought about the problem. In a traditional payoff matrix, it is
assumed that player A's loss is player B's gain, and vice versa.

In this situation there is an asymmetry between how much the winner of
the pot wins and the loser of the pot loses.

[Tim Norfolk]

> William "The Life" Coleman  (ramashiva)- Hide quoted text -
>
> - Show quoted text -

But that wouldn't necessarily be the case, would it? Each additional
raise gives more information (unless one knows that one has the
absolute nuts), like the old 'red hat' puzzle.

[Tim Norfolk]

> William "The Life" Coleman  (ramashiva)- Hide quoted text -
>
> - Show quoted text -

If it's not zero-sum, then there is an additional strategy for
agreement between the parties, or collusion.

[ramashiva]

On Jun 13, 8:46 pm, Tim Norfolk <timsn...@aol.com> wrote:

> If it's not zero-sum, then there is an additional strategy for
> agreement between the parties, or collusion.

If you look at the headsup situation on the river, then of course it's
not a zero-sum game, because someone is going to win the pot.

To get a classic zero sum game, you would have to set pot size to 0,
so the players only win what their opponent puts in the pot on the
river, or lose what they put in the river.

In a classic two-player zero sum game, result of player A + result of
player B = 0.

[ramashiva]

On Jun 13, 8:44 pm, Tim Norfolk <timsn...@aol.com> wrote:

> But that wouldn't necessarily be the case, would it? Each additional
> raise gives more information (unless one knows that one has the
> absolute nuts), like the old 'red hat' puzzle.

Yes, technically you are correct, but that results in an arbitrarily
large payoff matrix not amenable to analysis. It's much simpler if
you just confine raising options to

raise, fold to reraise

raise, call reraise

raise, raise reraise

That covers virtually all situations that actually come up in limit
holdem games, since few players are going to raise a reraise without
the nuts, in which case they are going to reraise forever.

It also gets you to the nice 6X6 payoff matrix described by phlash.