What is the probability that Fra wins? Fra and Sam want to play a game. They have two classic coins Head-Tail.
They flip the coins at the same time. 
If the result is $HH$, Fra wins. If the result is $HT$ (or $TH$), they flip again and result is again $HT$( or $TH$) Sam wins. In the other cases they continue.
So for example if happens $HT$ and after $HH$, Fra wins. The important for Fra is that $HH$ is an outcome.
The question is: what is the probability that Fra wins?
My work:
There is the outcome $TT$ that is the canceler of the game in the sense that is like they start again from the beginning. So for finishing the game the possible outcomes are:
$HHXX,HTHH,HTHT,HTTH,THHH,THHT,THTH$ where $XX \in \{HH, HT, TH, TT\}$ so Fra wins in $6$ cases on $10$. So the probability is $\frac{3}{5}.$
What do you think about it? Thanks and sorry for my bad English.

ns=10000
For t=1 to ns
[alfa]
x=rnd(1)
if x<0.25 then f=f+1:goto[beta]
if x>0.75 then goto[alfa]
y=rnd(1)
if y<0.25 then f=f+1:goto[beta]
if y>0.75 then goto[alfa]
[beta]
next t
print f/ns
Simulation with Just Basic; ns is number of simulations, try other values. 
