double down/bad math

[Dan2]

It doesn't matter whether you double up or not. It's still a negative expectation game, so the RoR is 100% either way. But doubling up is likely to result in losing it all faster.

The only way to reduce the RoR on a negative expectation game is to play only during a promotion that turns it into a positive situation.

Dan

···

Steve Jacobs <jacobs@xmission.com> wrote:

On Sunday 29 February 2004 10:09 am, Dan Paymar wrote:

The double up has two bad effects:
1. It slows your play. Fewer hands per hour means a lower expected
win rate. (Of course slower play is good in a sub-100% situation.)
2. By increasing the variance, it increases your risk of ruin. The
more you double up, the greater your risk.

Here we go again. A comment similar to this is what launched the
"other strategies" thread.

In positive games, double up increases risk.

In negative games, double up reduces risk. Risk and variance
are _not_ equivalent concepts.

--
Dan Paymar, author of "Video Poker - Optimum Play"
Editor and publisher of "Video Poker Times" newsletter
Visit my web site at www.OptimumPlay.com

"Chance favors the prepared mind"
- Louis Pasteur

[Steve_Jacobs]

>> The double up has two bad effects:
>> 1. It slows your play. Fewer hands per hour means a lower expected
>> win rate. (Of course slower play is good in a sub-100% situation.)
>> 2. By increasing the variance, it increases your risk of ruin. The
>> more you double up, the greater your risk.
>
>Here we go again. A comment similar to this is what launched the
>"other strategies" thread.
>
>In positive games, double up increases risk.
>
>In negative games, double up reduces risk. Risk and variance
>are _not_ equivalent concepts.

It doesn't matter whether you double up or not. It's still a negative
expectation game, so the RoR is 100% either way. But doubling up is
likely to result in losing it all faster.

I didn't say RoR, I said "risk". One can frame risk in terms of the
probability of failing to reach a finite goal. For example, if the goal is
to turn an $100 bankroll into a $150 or go bust trying, then the risk
is the probability that the player will fail to reach the goal. Unless
the game makes it completely impossible to ever win, the probability
of success for such a finite goal will always be greater than zero,
and the risk will always be less than 100%, whether the game is
positive or negative.

In the context of negative games and such finite goals as described
above, using double up reduces risk.

The only way to reduce the RoR on a negative expectation game is to
play only during a promotion that turns it into a positive situation.

Risk of _ruin_ isn't the only way to define risk. However, the same
math that is used for RoR can be applied to finite risk scenarios for
either positive or negative games. The value of the risk parameter
R is less than one for positive games, and greater than one for
negative games. In either case, the probability of turning a B unit
bankroll into a G unit bankroll is given by:

p(win) = (1 - R^B) / (1 - R^G)

and the probability of failure (risk) is given by:

p(fail) = 1 - p(win) = (R^B - R^G) / (1 - R^G)

···

On Sunday 29 February 2004 09:18 pm, Dan Paymar wrote:

Steve Jacobs <jacobs@xmission.com> wrote:
>On Sunday 29 February 2004 10:09 am, Dan Paymar wrote: