The long run can be easily defined in mathematical terms as long as
you set the tolerance paramater. Rather than guaranteeing a profit,
you simple set the paramater to say 999/1000 chance of winning, or
9999/10000 etc. (personally, I probably subconsciously require a risk
of ruin bankroll of 1 in 10,000 just to be safe) To abandon perfect
play just because a long run win cannot be guaranteed by the math is
not the way to go. Just as there is no guarantee the next plane
flight I take will not crash (I think 1 in 40,000 flights crash), it
does not stop me from flying and opting to drive instead... which is
even worse yet! Just as playing a hand badly is worse than the
perfect choice. So best to play the right play and not worry about
what coulda or shoulda been. Good luck. TomSki
The long run
<<<
The long run can be easily defined in mathematical terms as long as
you set the tolerance paramater. Rather than guaranteeing a profit,
you simple set the paramater to say 999/1000 chance of winning, or
9999/10000 etc.
Right.
I don't have the data or even a link to it, but I have
seen some graphs that precisely define this. If anyone
out there has them, pleas post a link. These graphs
cover all aspects of what it means when we speak about
the long term and the level of certainty that we will
be ahead as well as how likely it is that we will be
above any specific win or loss.
These curves show how it is possible to be 'certain' of
being ahead after playing for a long time.
Let's look at a simpler example. Suppose you gamble on
tossing a fair coin.
Now let's add a 0.5% 'slot club' to the game.
This scenario is actually pretty similar to DB, but with
far less variance
If you play 10$ a game and play 10 games, you will have
a very strong chance of losing (a little under 50%). You
will win 50 cents cashback, but that won't be enough to
change things.
Now suppose you play this game 1,000,000 times. Now you
will receive $50,000 cashback. You will break even, or
better, if you manage to win at least 475,000 of the
games you play. It can be proved that winning fewer games
than this is HIGHLY unlikely.
If we now play 10,000,000 times, we only need to win
4,750,000 hands to break even. That kind of result is
virtually impossible.
Variance is a factor.
Inceasing the variance makes the probability of very extreme
results more likely. The impact on this situation is simply
to increase the number of hands one must play to be very sure of
being ahead. As an extreme case, a game like a lottery with a
high jackpot might take trillions of games to become 'certain'
of showing a profit.
QZ