IMO you would go with the whole sample, $9,300 million
of coin-in and your EV is $93 million for the entire universe.
So. If $10 million was lost to ROR casualties, then the rest
of the universe would be expected to make up the difference
and their $9,000 million of coin-in would have accounted
for $93 million of EV.
However, I think you've done something like dividing by
zero in setting up your problem. The risk of ruin for a $10,000
bankroll playing quarter 101% Jokers which have a variance
of 33.6 is 0.0%. The machine in your example would have
a much lower variance and is only $1 per pull, so it's unlikely
that many (any?) of the rocket scientists would have gone broke.
ยทยทยท
"blaw57" <blaw57@yahoo.com> wrote:
Suppose you have a new single coin $1 VP game that eliminates the
Royal and makes other changes, such that 3 Std Devs (99%+) of players
achieve long term results after about 1 million hands. It is a
positive game returning 101%, and a group of 10,000 rocket scientists
who always play perfect set about playing it with $10,000 bankrolls,
which are deemed adequate for this game using a 10% ROR assumption.
Well, in the course of play 1000 players will go bust and 9000 will
make 1% of $1 million or $10,000. So at the end we have:
9000 players x $10,000 profit = $90,000,000
1000 players x $10,000 loss = -$10,000,000
Net for group = $80,000,000
Total hands played were 9,000,000,000 for the successful players
We don't know exactly for the ruined players, but we know it was less
than 1,000,000,000 and probably was front-weighted, so lets call it
300,000,000.
Thus the group had $80 million gain on 9300 million hands/dollars of
coin in, or 0.86%.
Yet the 101% machines had to have paid out $93 million more than they
took in – after 9.3 billion hands they had to have normalized.
So where did the other $13 million go?