math Problem in Tournament poker for advanced Players ( Sklansky)

[folding_the_nuts]

Hi!! Can anybody help me?
Referring to DAVID SKLANSKY - TOURNAMENT POKER For Advanced Players


I've got some problems with one of David's calculations!
I don't know if I and my folks are just too stupid for this one or i miss something in the context because English isn't my native tongue.

My problem:

Chapter You're broke You're done:

two bets:
$200 to $100 on a coinflip
$120 to $100 on a coinflip

first bet is described in the book:
Expected value: 0,5 * (-100 $) + 0,5 * (200$) = 50

sounds pretty simple
According to this I apply this formula on the second bet:

Expected value : 0,5* (-100$) + 0,5* (-120$) = 10

he now claims that if he had the money and would make both bets he would have an EV of 35

That's my problem. At first glance I see that the average of my bets should be 30

Using the old formula:
I would win one time bet 1
I would win one time bet 2
I would lose 2 times ( 1+2)

0,5* (-100$) + (0,25 * 120$) + ( 0,25* 200$) = 30

that's my reasoning

David makes it so without detailed explanations:

0,5* (-100$) + 0,25*( 20$) +0,25 * (320$) which gives us an EV of 35

Can someone help me with this one. I'm pretty pissed off that I don't get this calculation

Formal and informative replies are appreciated

Folding_the _nuts

[plexiq]

Hm, the actual setup is:

You are offered a 120$:100$ coin-flip today.
You are offered a 200$:100$ coin-flip tomorrow.
But you only own 100$.

So, the thing you are missing here is that, if we loose the first coin-flip, we will pass out on the second one.

So, 50% of the time we will end up with nothing (-100$), because we loose our first bet. 25% of the time we win both coin-flips for winnings of +320$, and 25$ of the time we win the first, but not the second flip, resulting in +20$.

So, taking the first bet, we have an expectation:
0.5*(-100$)+0.25*320$+0.25*20$ = +35$

If we skip the first bet, and only take the second one, we have an expectation of +50$.

[folding_the_nuts]

Hi plexig!!
Now I get the context right, thanks a lot.

Ftn