Characteristics of Optimalf 181
Now we will see the same thing, only this time we will operate from
a combined bank starting at 100 units. Rather than betting $1 for every $4
in the combined stake for each system, we will bet $1 for every $8 in the
combined bank. Each trade for either system affects the combined bank, and
it is the combined bank that is used to determine bet size on the subsequent
play:
System A System BTrade P&L Trade P&L Combined Bank
100.00
2 25.00 2 25.00 150.00
− 1 −18.75 − 1 −18.75 112.50
2 28.13 2 28.13 168.75
− 1 −21.09 − 1 −21.09 126.56
2 31.64 2 31.64 189.84
− 1 −23.73 − 1 −23.73 142.38
−100.00
Total net profit of the combined bank= $42.38
Notice that using either a combined bank or a separate bank in the
preceding example shows a profit on the $100 of $42.38. Yet what was
shown is the case where there is positive correlation between the two
systems. Now we will look at negative correlation between the same
two systems, first with both systems operating from their own separate
bankrolls:
System A System BTrade P&L Cumulative Trade P&L Cumulative
50.00 50.00
2 25.00 75.00 − 1 −12.50 37.50
− 1 −18.75 56.25 2 18.75 56.25
2 28.13 84.38 − 1 −14.06 42.19
− 1 −21.09 63.28 2 21.09 63.28
2 31.64 94.92 − 1 −15.82 47.46
− 1 −23.73 71.19 2 23.73 71.19
−50.00 −50.00
Net Profit 21.19140 21.19140
Total net profit of the two banks= $42.38