Optimalf 145
thef. There is a paradox involved here, in that if a system is good enough
to generate an optimalfthat is a high percentage, then the drawdown for
such a good system will also be quite high. While optimal fallows you to
experience the greatest geometric growth, it also gives you enough rope to
hang yourself.
CONSEQUENCES OF STRAYING TOO FAR
FROM THE OPTIMALf
The fact that the difference between being at the optimal value forfand
being at any other value increases geometrically over time is particularly
important to gamblers. Time in this sense is synonymous with action. For
years, a simple system for blackjack has been to simply keep track of how
many fives have fallen from the deck. The fewer the fives contained in
the remaining deck, the greater is the player’s advantage over the casino.
Depending on the rules of the casino, this advantage could range to almost
as high as 3.6% for a deck with no remaining fives. Roughly, then, the optimal
ffor this strategy would range from 0 to about .075 to .08 for each hand,
depending on how many fives had fallen (i.e., you would use a different
fvalue for each different number of remaining fives in a deck. This is a
dependent trials process, and therefore your optimal betting strategy would
be to trade variable fraction based on the optimalffor each scenario of
the ratio of fives left in the deck). If you go into the casino and play through
only one deck, you will not be penalized for deviating from the optimalf
(as you would if you were to play 1,000 hands). It is incorrect to think that if
you have an edge on a particular hand, you should simply increase the size
of your wager. How much you increase it by is paramount.
To illustrate, if you have a stake of $500 and start playing at a table
where $5 is the minimum bet, your minimum bet is therefore 1% of your
stake. If you encounter, during the course of the deck, a situation where all
fives are depleted from the deck, you then have an edge of anywhere from
3 to 3.6%, depending on the house rules. Say your optimalfnow is .08, or
one bet per every $62.50 in your stake ($5, the maximum possible loss on
the next hand, divided by .08).
Suppose you had been breaking even to this point in the game and
still had $500 in your stake. You would then bet $40 on the next hand
($500/$62. (^50) *$5). If you were to bet $45, you could expect a decrease
in performance. There is no benefit to betting the extra $5 unit. This de-
crease in performance grows geometrically over time. If you calculate your
optimal fon each hand, and slightly over- or underbet, you can expect a
decrease in performance geometrically proportional to the length of the