Jean Jacques Robert: Optimal betting romp

[Jean Jacques Robert]

Can someone explain why the increase in units in an optimal betting romp (at least with shoe games) is exponential rather than linear, (ex: 1,1,1, 2,2, 3,4 , 6,8,10) particularly when the increase in advantage is of the said magnitude for each true count (ex: 0.5% per increase in unit of true count). strict Kelly betting would result in a linear increase in the optimal betting romp. Has Standard deviation something to do with it?

Thanks in advance for your replies.

[Francis Salmon]

The optimal betting ramp is proportional to your advantage which is not the same as your count because we have a disadvantage at count 0, but it's still a linear function with the formula
B = (TC-1)*f this applies only to TC>=1
So if we bet 2 units for TC+2, the formula tells us to bet 4 units at TC+3 and 8 units at TC+5.
Nothing to do with standard deviation because this is also proportional to your bet size.

Francis Salmon

> Can someone explain why the increase in
> units in an optimal betting romp (at least
> with shoe games) is exponential rather than
> linear, (ex: 1,1,1, 2,2, 3,4 , 6,8,10)
> particularly when the increase in advantage
> is of the said magnitude for each true count
> (ex: 0.5% per increase in unit of true
> count). strict Kelly betting would result in
> a linear increase in the optimal betting
> romp. Has Standard deviation something to do
> with it?

> Thanks in advance for your replies.

[Don Schlesinger]

> Can someone explain why the increase in
> units in an optimal betting romp (at least
> with shoe games) is exponential rather than
> linear, (ex: 1,1,1, 2,2, 3,4 , 6,8,10)
> particularly when the increase in advantage
> is of the said magnitude for each true count
> (ex: 0.5% per increase in unit of true
> count). strict Kelly betting would result in
> a linear increase in the optimal betting
> romp. Has Standard deviation something to do
> with it?

The optimal ramp is neither perfectly linear nor is it exponential. Especially when we use index numbers, certain of those values "kick in" at different true counts, adding extra advantage at those levels. Just look at the Chapter 10 chart edges to see this.

Standard deviation varies only in the second place, as the count changes, so that has virtually no effect on what you're discussing.

Don

[Don Schlesinger]

One other thing: We constrain our bets, conforming to the table min and max, or to a certain spread that we wish to adhere to. This puts an artificial condition on the way the bets are configured, which wouldn't be there if the betting were unconstrained, so the ramp may look a bit peculiar in certain spots just before the max bet.

Don