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#Post#: 16--------------------------------------------------
Chapter One: Homework Problems
DIR By: A
Date: May 28, 2014, 9:03 am
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See how many of these you can do. They're just a small sample
of questions and should be about a 1 out of 10 on the difficulty
level for what we'll probably be doing. If you find yourself
struggling, just let me know, and we'll figureout another way to
go about things.
1) Calculate the number of possible starting hands in Hold 'Em.
Detail your calculation (either describe how you went about it,
show all the work, or just scan the way you wrote it and send it
to me).
1a) How would this number change if the order of your cards
actually mattered? In other words, would the number be
different if AcKd was a different hand than AdKc?
2) Give a verbal interpretation of Equation 1.4 (Page 16). Why
do we subtract P(A ^ B)?
3) Give an example of a wager which has positive expected
value, but which you would not take.
4) Derive a formula that expresses the expected value of
calling a river bet in terms of the following three variables:
The Size of the Bet
The Size of the Final Pot
The Equity of Your Hand Against The Opponent's Betting
Range
#Post#: 19--------------------------------------------------
Re: Chapter One: Homework Problems
DIR By: xxHaZ
Date: May 28, 2014, 1:19 pm
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1) There are 52 ways to choose a first card, and 51 ways to
choose a second card. There are two ways to order this
combination.
(52 x 51) / 2 = 1326
1a) AcKd is a different hand than AdKc (I think you meant AcKd /
KdAc). 52 x 51 = 2652 if you care about order.
2) Written explanation: We subtract P(A ^ B) in equation 1.4 to
account for "double counts" from non-mutually exclusive events A
and B in P(A) + P(B). Example: The chance of pulling a heart or
King out of a standard deck of 52 cards is: 13/52 + 4/52 - 1/52
= 16/52
Example for equation 1.2: flipping a coin, it cannot be both
Heads and Tails. P(A ^ B) treats these outcomes as independent
events. P(A ^ B) = p(A)p(B) = 0.
3) One which requires an infinite bankroll to net a
substantially small yield. In theory you take it if it's your
best option, IRL I choose not to.
4) x = equity
y = bet/call
EV = (x)(pot + y) + (1-x)(-y)
#Post#: 21--------------------------------------------------
Re: Chapter One: Homework Problems
DIR By: A
Date: May 28, 2014, 1:34 pm
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3) Give an example which requires a very small bankroll to net
a potentially infinite yield, which you still would not take.
4) There is a much cleaner formula. Try again. Express the
equation using only the variables in the question.
#Post#: 22--------------------------------------------------
Re: Chapter One: Homework Problems
DIR By: A
Date: May 28, 2014, 1:41 pm
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2) The last line of what you wrote isn't quite true. (It is
true, though, that the coin will not be both heads and tails)
#Post#: 23--------------------------------------------------
Re: Chapter One: Homework Problems
DIR By: xxHaZ
Date: May 28, 2014, 5:15 pm
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--- Quote from: A link ---
>
> 3) Give an example which requires a very small bankroll to
net a potentially infinite yield, which you still would not
take.
>
> 4) There is a much cleaner formula. Try again. Express the
equation using only the variables in the question.
>
--- End Quote ---
3) If I lose money after the wager. Example in poker: if have a
marginally profitable flop call, but expect to lose money
against my opponent's range on the next street.
4) Where X = Equity
EV = (X)(Final Pot - Bet Size) - (1 - X)(Bet Size)
I used a "+" before because the book says EV is always additive.
#Post#: 24--------------------------------------------------
Re: Chapter One: Homework Problems
DIR By: xxHaZ
Date: May 28, 2014, 5:20 pm
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--- Quote from: A link ---
>
> 2) The last line of what you wrote isn't quite true. (It is
true, though, that the coin will not be both heads and tails)
>
--- End Quote ---
Because Event B is impossible after Event A, P(A ^ B) = p(A)p(B)
= 0.
Only zero is satisfied for B.
A and B
T T = 1
T F = 0
F T = 0
F F = 0
#Post#: 27--------------------------------------------------
Re: Chapter One: Homework Problems
DIR By: A
Date: May 28, 2014, 6:07 pm
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2) The description was good but your equation is not right.
You're looking for something different. This is the equation
you gave for the fair coin:
P(A ^ B) = p(A)p(B) = 0
One of the terms is off, right?
#Post#: 28--------------------------------------------------
Re: Chapter One: Homework Problems
DIR By: A
Date: May 28, 2014, 6:10 pm
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4) Keep going and you'll have it....
#Post#: 30--------------------------------------------------
Re: Chapter One: Homework Problems
DIR By: xxHaZ
Date: May 28, 2014, 8:05 pm
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--- Quote from: A link ---
>
> 2) The description was good but your equation is not right.
You're looking for something different. This is the equation
you gave for the fair coin:
>
>
> P(A ^ B) = p(A)p(B) = 0
>
>
>
> One of the terms is off, right?
>
--- End Quote ---
For a coin flip it's a mutually exclusive event so I was trying
to explain P(A U B) = p(A) + p(B) - p(A ^ B) becomes P(A U B) =
p(A) + p(B) because P(A ^ B) = p(A)p(B) = 0. Unless I'm missing
something?
P(A U B) = p(A) + p(B) - p(A ^ B)
P(A U B) = 0.5 + 0.5
Probability of flipping flipping Heads (Event A) or Tails (Event
B) = 100%
#Post#: 31--------------------------------------------------
Re: Chapter One: Homework Problems
DIR By: xxHaZ
Date: May 28, 2014, 8:12 pm
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--- Quote from: A link ---
>
> 4) Keep going and you'll have it....
>
--- End Quote ---
4) Where X = Hand Equity, and Y = Bet Size Relative to Pot
EV = (X)(1 + Y) - (1 - X)(Y)
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