Game Theory Quiz

[jogsxyz]

Your answers are total nonsense.
Look a question 1. Why would you ever call with the duece? The duece loses every showdown.

Never call with the duece.
Always bet the ace.
Never bet the trey. Opponent can only have the ace which he knows is the winner or and duece which he knows is the loser.

I will read your link and repost afterwards.

[jason1990]

Maybe you misread the problem. Ace is low.

[jogsxyz]

It's normal to give cards in order. Ace is the low card? When this problem is presented in a game theory class the three cards given as high, mid(dle), and low. No chance for misunderstanding.

This is the key paragraph.

[ QUOTE ]

You cannot win with the optimal strategy.


So the object of the game is not to play optimally. It is to spot the times when your
opponent is not playing optimally, or even to induce him not to play optimally, to recognize
the way in which he is deviating from optimality, and then to choose a non-optimal strategy
for yourself which capitalizes on his mistakes. You must play non-optimally in order to
win. To capitalize on your opponent's mistakes, you must play in a way that leaves you
vulnerable.

[/ QUOTE ]

[jason1990]

[ QUOTE ]
6. You have the trey. Opponents bets. What percentage of the time should you call?

[/ QUOTE ]
I'm going to assume you misread the problem and thought the ace was high. So in the setting of the original problem, you are simply asking how often you should call with the deuce. This is covered by my questions 1 and 5.

[ QUOTE ]
7. You have the deuce. What percentage of the time should you bet?

Please show the work for optimization. This is a question from STAT 168(game theory).

[/ QUOTE ]
Again, in the setting of the original problem, you're simply asking how often you should bluff with the ace. If you're the dealer, this is covered by my questions 2-4. If you're the opener, then the answer is: anything between 0 and 1/3. (Compare this with the answer to #5.)

You can see the article I posted for a derivation.

[jogsxyz]

I first saw this execise in 1970. The purpose was to demonstrate that it was right to occasionally bluff in poker. The results of bluffing 1/3 of the time is misleading. This is a special case. Both the high and low cards are equally likely. When you apply this execise to a real hold'em situation, the high card(nuts) is much less likely than the low card(missing).
x was used for bluffing frequency. y was used for calling frequency. p was reserved for the probability of having the high card. It's 1/2 in this special case.

Apply the three card deck to a hold'em
situation. You hold 9s9h. The board
is AdQh9c 7c 2c. Your opponent is a
strong solid player. The betting thru
the turn makes it obvious to you that
opp started with AQ. Your opp knows
you have 99. Your hand is now like the
middle card of the three card deck. The
2c has made your opp's hand the high
card if he holds AcQc, else his hand is
like the low card. Now the probability
of opp holding the high and low cards are
not equal like in the three card deck
execise. There are nine possible ways
to hold the remaining AceQueens. He only
has one chance in nine of holding AcQc or
the high hand.
Construct the 2X2 matrix to solve the value
of the game. To simplify the execise you
will check and only call or fold to a bet.
Also opp will only bet the size of the pot
or check.

Now answer similiar questions.

1. You have the set of nines. The opp bets.
In order to play optimally according to game
theory, you should call with probability y.
What is y?

2. Opp does not have the AcQc. He only has
Aces and queens. In order to play optimally
according to game theory, he should bet with
probability x. What is x?

3. What is the value of the game? Use the size
of the pot as one unit.

Note again. The probability of opp holding the
flush and two pair are not equal.
You will find that under these conditions opp's
best bluffing frequency is much lower than 1/3.

[lamer]

dude, your essay rocks.
i was looking for sth like this recently, where a newbie like me can understand this bluffing-concept without reading whole books of A. Rapoport ;> [i know books are to be read but i have enough without Ol'Rapoport already :]

Thanx.

[ffredd]

I think that this is too good a post to be buried deep down in another thread. I find this problem very interesting. Unfortunately I'm a bit to lazy to work out all the details. I'm getting the impression that you already have. Would you mind sharing the correct answers with us?