Probability

[RolandaM]

A player decides to play a maximum of 4 times, betting on red each time. The player will quit after losing twice. In the tree, any possible last plays will be an ending point of the tree. Branches of the tree should indicate the winning or losing, and how that affects whether a new play is made. I know the possible ways to win and lose: I just can't picture the tree. I need some help with the structure and how to read it.

winning combinations:
w,w,w,w
w,w,w,l
w,w,l,w
w,l,w,w
l,w,w,w

losing combinations
w,l,l,w
w,w,l,l
w,l,w,l
l,w,l,w
l,w,w,l

 

[soroban]

Hello, RolandaM!

A player decides to play a maximum of 4 times, betting on red each time.
The player will quit after losing twice.
In the tree, any possible last plays will be an ending point of the tree.
Branches of the tree should indicate the winning or losing,
. . and how that affects whether a new play is made.

I know the possible ways to win and lose: I just can't picture the tree.
I need some help with the structure and how to read it.

Winning combinations: WWWW, WWWL, WWLW,WLWW, LWWW

Losing combinations: WLLW, WWLL, WLWL, LWLW, LWWL

I tried to type a tree diagram, but failed abysmally.
So I will try to describe it.

Reading from the leftmost branch of the tree diagram:

. . \(\displaystyle \begin{array}{ccc}\text{1st branch:} & WWWW \\ \text{2nd branch:} & WWWL \\ \text{3rd branch:} & WWL\,W \\ \text{4th branch:} & WW\,L\,L \\ \text{5th branch:} & WL\,WW \\ \text{6th branch:} & WL\,WL \\ \text{7th branch:} & WL\,L\quad\; & * \\ \text{8th branch:} & LWWW \\ \text{9th branch:} & L\,WWL \\ \text{10th branch:} & L\,W\,L\quad & * \\ \text{11th branch:} & L\,L\qquad & *\end{array}\)


* Recall that he quits at the second loss.