Interesting MultiStrike Statistics

[AJ1]

Steve Jacobs said :

<snip>

Please think about that for a moment. If your specific objective
is to reach some target bankroll or go bust trying, then the
min-risk approach not only maximizes your probability of
success, but also maximizes the average value of your outcome
based on the specified constraint of "hit the goal or go bust".
When situations call for a min-risk strategy, that strategy
maximizes the expected value of the _permitted_ outcomes.
In effect, minimizing risk maximize _constrained_ ER.

<snip>

I completely agree. I probably should have preceded my previous post
with the statement that I agree with virtually all you have been
saying about alternative strategies. As a matter of fact, I have
often played a reduced variance strategy in progressive chases.
However, I can never remember being in a situation that would call
for playing a higher variance strategy than the max ER strategy. For
most serious players, I think that variance increasing strategies are
mostly just of academic interest. I do believe that there is real
value in exploring and understanding alternative strategies in some
reasonably common situations - way more than the pennies to be gained
by playing penalty card situations correctly. Keep up the good
work!

AJ

[Steve_Jacobs]

Steve Jacobs said :

<snip>

> Please think about that for a moment. If your specific objective
> is to reach some target bankroll or go bust trying, then the
> min-risk approach not only maximizes your probability of
> success, but also maximizes the average value of your outcome
> based on the specified constraint of "hit the goal or go bust".
> When situations call for a min-risk strategy, that strategy
> maximizes the expected value of the _permitted_ outcomes.
> In effect, minimizing risk maximize _constrained_ ER.

<snip>

I completely agree. I probably should have preceded my previous post
with the statement that I agree with virtually all you have been
saying about alternative strategies. As a matter of fact, I have
often played a reduced variance strategy in progressive chases.
However, I can never remember being in a situation that would call
for playing a higher variance strategy than the max ER strategy. For
most serious players, I think that variance increasing strategies are
mostly just of academic interest.

I believe there are probably real applications for this stuff in tournament
situations and special promotions. If the underlying game is inherently
negative but matchplay or a prize or some other "outside help" turns the
game into a positive opportunity, then the optimal strategy could be
the maximum boldness plays which lead to higher variance.

I do believe that there is real
value in exploring and understanding alternative strategies in some
reasonably common situations - way more than the pennies to be gained
by playing penalty card situations correctly. Keep up the good
work!

Thanks for the feedback and encouragement.

···

On Monday 26 January 2004 10:28 pm, AJ wrote:

[brucem]

I found your discussion of variance in relation to risk very
interesting.

I know why I tend to equate risk with variance. If two games have an
EV of 101%, but much different variances, and I play 5000 games of
them both, my chance of ending up a net loser are greater for the
high variance game. To me that means the high variance game has a
greater "risk" (in terms of my bankroll) than the low variance game.

But, in a game like Roulette, where all the plays have the same

EV ...<<

Actually, that's not entirely correct. All bets favor the house by
5.26% except for one ... the 5-number bet (0,00,1,2,3) which favors
the house by 7.29%.

Seems that way, but one can actually ignore EV and variance

completely when studying risk.>>

I think I partly understand what you are saying (or maybe I
don't) ... if I play enough games (very accurately) then the game
variance is irrelevant because my return will ultimately be the EV
(the % above 100 anyway). But I don't understand how you can
evaluate the risk of a game without considering the EV. I'm
using "risk" in the sense of the impact on my bankroll. Is there a
simple way to explain, or define, what you mean by risk?

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:

[claysonwood]

Harry Porter:

First, thanks for one of the most fascinating articles I've ever seen
posted here. Very interesting reading.

As I understand your comments, a player could choose to get much (not
all) of the increased return of MultiStrike, but at a lower variance,
by playing just two lines instead of four, and making the appropriate
strategy modifications.

Playing only two lines (10 coins risked per game), a person would
have just two strategies:
  
  1. The basic single line game strategy for line 2.
  2. The Dancer "+2" strategy for the first line.

I'm assuming that, since the extra bonus of advancing (potentially)
three additional lines for the +6 strategy and two additional lines
for the +4 strategy are gone, you would no longer need those
strategies.

Is that understanding correct?

Clayson Wood

--- In vpFREE@yahoogroups.com, "Harry D. Porter" <harry.porter@v...>
wrote:

There's another outcome of this analysis that I find even more
fascinating.
When only 2 or 3 Levels are played, the variance is actually smaller
than a single line game played at the identical total wager (e.g.
comparing 2 Level $.25 play with single line $.50 play).

When the variance associated with a total wager in one game is lower
than another game, in this case say 2-Level $.25 play vs. $.50

single

line play, and yet the ER of both games is largely identical, the
2-Level game becomes advantageous in presenting smaller risk. (And
2-Level play ER is actually slightly higher than single line JB,

99.60 -

mind you, this assumes an optimized strategy for 2-Level play is

used

that's different from 4-Level. The 2-Level strategy can be

determined

···

by adjusting the "2-4-6" strategy, using the method discussed in the
Dancer article))

[Harry_Porter]

Clayson Wood wrote:

Harry Porter:

As I understand your comments, a player could choose to get much
(not all) of the increased return of MultiStrike, but at a lower
variance, by playing just two lines instead of four, and making
the appropriate strategy modifications.

Playing only two lines (10 coins risked per game), a person would
have just two strategies:
  
  1. The basic single line game strategy for line 2.
  2. The Dancer "+2" strategy for the first line.

Is that understanding correct?

You're on target, Clayson.

It's the case though that you do lose a moderate portion of the
boost in ER of Multistrike vs, the base game when you play "short-
level". In the case of 9/6 JB, where 4-Level "6/4/2" optimized play
has a ER of 99.77%, playing just 3 Levels offers 99.66% and 2 Levels
99.60%. (I hadn't intended to omit these numbers from my post.)

I'm not touting "short level" play as advantageous over 4-Level
play, despite the decrease in variance ... but it's the case that
when you compare 2-Level $.25 play with single-line $.50 play the MS
game has both higher ER and lower variance.

As you note, the adjusted strategy merely consists of sliding each 4-
Level game strategy "down" appropriately. E.g. in the 3-Level game,
you apply Lev 4 (standard) strategy for the 4-Level game to Lev 3 of
the 3-Level game, Lev 3 to Lev 2, and Lev 2 to Lev 1.

- Harry