On 21 Jun 2008 17:29:29 GMT, cowboy blue <null@[EMAIL PROTECTED]
> wrote:
>I've started a NEW ( for me)betting strategy. The amount I bet depends
upon
>the previous roll. If I made money the previous roll, I increase my
bet(s),
>If I lost money on the previous roll, I decrease my bets.
>default: pass line, double odds, place 6,8 for $12.
What is the pass line bet?
>If I lose money, cut
>the 6.8 to $6. If I loose again, nothing on 6,8,If I loose money third
>time,I remove my odds, only pass line bet at risk.
>Conversely, If I make money on a roll, I up my Odds ( if permitted), or
>increase the place 6,8 to $18 , or $24, etc.
Not enough specific info to really test this.
>
> The premise is that while the dice are random, it is NOT a uniform
>distibution. We all know there are "hot' and "cold" spells. Thus this
>stategy (should) yeild smaller loses during cold spells, and more winning
>during the "hot" streaks.
This kind of strategy gets hammered by WLWL-type distributions. When
you win and raise your bet, you lose your winning plus the additional.
When you lose and cut back, then win, you don't make up for the loss.
I promise you that, if you squeeze the balloon on one side, it will
puff out somewhere else. There is no way around this.
>I've tried it 3 times, profit each time..... but 3 is insufficient to
>be statisticly meaningfull.
To be sure.
>
>The problem is defining a measure, a quantifiable number, for the "
>hot/cold" streaks. and calculating wether this strategy has any advantage
>over "flat amount" betting.
It has no advantage; it is only different. You are chasing different
distributions, that's all. Sometimes it will work well, others it
won't. The more you vary your bets, the wider the swings between your
good and bad sessions, i.e. you will have more volatility.
I agree with RRT that the odds bet should stay up longer than the
place bets.
In order to illustrate how pressing/regressing affects your outcome,
let's just look at a sequence of 4 place-6 bets. Here are the possible
outcome distributions:
WWWW
WWWL
WWLW
WLWW
LWWW
WWLL
WLWL
LWWL
WLLW
WLWL
LLWW
WLLL
LWLL
LLWL
LLLW
LLLL
We can assign a probability to each one of these outcomes, using
..454545 as p(W) and .545454 as p(L):
WWWW .042688341
WWWL .051226009
WWLW
WLWW
LWWW
WWLL .061471211
WLWL
LWWL
WLLW
WLWL
LLWW
WLLL .073765453
LWLL
LLWL
LLLW
LLLL .088518544
So, we have one, then four, then six, then four, then one, and if we
multiply each probability by its number of occurrences, we get
..99999999999, or, not to put too find a point on it, 1.
So, let's compare flat $24 betting against this scheme
24
if win, add six
if lose, reduce by six
flat scheme
WWWW +112 28 + 35 + 42 + 49 = 154
WWWL + 60 28 + 35 + 42 - 42 = 63
WWLW + 60 28 + 35 - 36 + 35 = 62
WLWW + 60 28 - 30 + 28 + 35 = 61
LWWW + 60 -24 + 21 + 28 + 35 = 60
WWLL + 8 28 + 35 - 36 - 30 = - 3
WLWL + 8 28 - 30 + 28 - 30 = - 4
LWWL + 8 -24 + 21 + 28 - 30 = - 5
WLLW + 8 28 - 30 - 24 + 21 = - 5
LLWW + 8 -24 - 18 + 14 + 21 = - 7
LWLW + 8 -24 + 21 - 24 + 21 = - 6
WLLL - 44 28 - 30 - 24 - 18 = -44
LWLL - 44 -24 + 21 - 24 - 18 = -45
LLWL - 44 -24 - 18 + 14 - 18 = -46
LLLW - 44 -24 - 18 - 12 + 7 = -47
LLLL -96 -24 - 18 - 12 - 6 = -60
So, as you can see, at top and bottom, the scheme works much better,
and a 3-1 and 1-3 they're close to equal, but when breaking even, 2-2,
the flat bettor has a small win instead of a small loss.
If you add up all the weighted numbers, for each 4 bets, here are the
results:
flat scheme
net $-1.4545 $-1.4048
Why does the "schemer" lose less? Because he/she bets less, of course!
In both cases, the result is exactly -.01515 of the average amount bet
for the four bets, $96 for the flat bettor, $92.72 for the
progressive/regressive bettor. Does that surprise anyone? I hope not.
If we did a progressive scheme without the regression, then that
scheme would expect to lose more due to betting more, with somewhat
larger wins in the 3-1 series, somewhat larger losses in the 1-3
series, etc.
In theory, simulation and in the real world counting everybody's play,
it "all comes out in the wash", but in one individual's play it is not
expected to.
As Van posted, it is a matter of utility, or: what are you trying to
achieve and how much are you willing to risk to achieve it?
Cheers,
Alan Shank
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