Wins of 2 standard deviations over time
December 28th, 2013 at 3:47:16 AM
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I know that when I stand at the craps table I am basically paying rent on my spot and I am happy with this. However I would like some guidance on when to walk away ahead.
Working on the assumption that I bet one unit on the line each role and take full odds if I wanted to walk away whenever my winnings were two standard deviations from the middle of the probability distribution when should I conclude I am 2 standard deviations up. i.e how many units after would I need to be up to achieve a 2SD outcome after say 30, 60, 90, 120, etc rolls?
Regards,
Pete
Working on the assumption that I bet one unit on the line each role and take full odds if I wanted to walk away whenever my winnings were two standard deviations from the middle of the probability distribution when should I conclude I am 2 standard deviations up. i.e how many units after would I need to be up to achieve a 2SD outcome after say 30, 60, 90, 120, etc rolls?
Regards,
Pete
December 28th, 2013 at 10:31:58 AM
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To figure this out:
Calculate (or look up) the house edge of a single bet. Call this EDGE
Calculate (or look up) the variance of a single bet. Call this VAR.
VAR is additive (just like EV), so the variance after n bets is just (n * VAR).
Standard deviation is just the square root of variance. So the standard deviation after n bets is sqrt(n*VAR). So, for any n, the EV of n bets is n*EV and 2x the standard deviation is 2*sqrt(n*VAR).
So, stop when you are at 2*sqrt(n*VAR)-(n*EDGE).
There is, of course, no guarantee that you will be ahead the first time that you reach this point.
Calculate (or look up) the house edge of a single bet. Call this EDGE
Calculate (or look up) the variance of a single bet. Call this VAR.
VAR is additive (just like EV), so the variance after n bets is just (n * VAR).
Standard deviation is just the square root of variance. So the standard deviation after n bets is sqrt(n*VAR). So, for any n, the EV of n bets is n*EV and 2x the standard deviation is 2*sqrt(n*VAR).
So, stop when you are at 2*sqrt(n*VAR)-(n*EDGE).
There is, of course, no guarantee that you will be ahead the first time that you reach this point.
December 28th, 2013 at 10:55:06 AM
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nice first question.Quote: PeteI know that when I stand at the craps table I am basically paying rent on my spot and I am happy with this.
However I would like some guidance on when to walk away ahead.
need more info
But first with the pass line bet, is this the bet you make every roll or does that mean a pass line and come bet every roll?
In 100 pass line bets resolved with no odds - what IS max odds anyways?,
this could be between 3 to 5 hours of play, maybe,
what happens to the 9.32% (93218 out of 1 million) of sessions that NEVER get ahead?
with pass and come bets every roll for 100 rolls that percentage could be smaller depending on the odds taken.
What do you play to when that happens? in other words,
I would think you would have some kind of 'loss limit' per session played - maybe all your starting bankroll.
the mean and standard deviation are advanced math concepts especially with casino bets and bankrolls involved.
to use that to determine when to walk away when you have a profit of 2SD is interesting.
I ask: Why 2SD?
Why not 1.5SD?
most just work with house edge
and maybe ev (expected value) and leave it at that.
as when to walk away, many will say when you are happy with how much you have won.
hard to define "happy" for everyone
what are your actual bets and parameters you wish to deal with?
for 100 rolls making pass and come every roll with full 2.5x odds, $1 bets
(so for $5 just times everything by 5 and $10 by 10 and so on)
you can see the mean and the sd
here is for 2sd
and 1.5sd
just read what you see
unless there are no photos
also to point out that ending at 2SD after 100 rolls is different from hitting 2SD somewhere before 100 rolls.
Both bust rates and target goals could be about 1.5x more likely
than the end point probability.
(so for $5 just times everything by 5 and $10 by 10 and so on)
you can see the mean and the sd
here is for 2sd
and 1.5sd
just read what you see
unless there are no photos
also to point out that ending at 2SD after 100 rolls is different from hitting 2SD somewhere before 100 rolls.
Both bust rates and target goals could be about 1.5x more likely
than the end point probability.
winsome johnny (not Win some johnny)
December 28th, 2013 at 1:23:56 PM
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Quote: PeteI know that when I stand at the craps table I am basically paying rent on my spot and I am happy with this. However I would like some guidance on when to walk away ahead.
Working on the assumption that I bet one unit on the line each role and take full odds if I wanted to walk away whenever my winnings were two standard deviations from the middle of the probability distribution when should I conclude I am 2 standard deviations up. i.e how many units after would I need to be up to achieve a 2SD outcome after say 30, 60, 90, 120, etc rolls?
Regards,
Pete
It's all very simple w/o the math: Walk away whenever you feel like it when you're up over your buy-in. Walk away when your loss limit is reached.
December 28th, 2013 at 1:45:52 PM
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with the math, or sim data, one can be more realistic in their goals.Quote: Sonny44It's all very simple w/o the math: Walk away whenever you feel like it when you're up over your buy-in. Walk away when your loss limit is reached.
example
$300 unit buy-in
1unit pass and come bets with full 2x odds
100 roll session
what % of 100 roll sessions NEVER show a profit?
0.1% (1 in 1000)
1% (1 in 100)
10% (1 in 10)
20% (1 in 5)
edit: this is with odds not working on the come-out roll
it is close to 7.2% or 72 out of 1000 never see a profit
with odds working on the come-out roll:
it is close to 7% or 7 out of 100 never see a profit
but almost all craps players will say you will always at some point be up in a session. always
excellent!
it is close to 7.2% or 72 out of 1000 never see a profit
with odds working on the come-out roll:
it is close to 7% or 7 out of 100 never see a profit
but almost all craps players will say you will always at some point be up in a session. always
excellent!
how about busting a 300 unit bankroll in 100 rolls trying to win just 1 unit
edit: this is with odds not working on the come-out roll
looks to be about 0%. but it can be bad.
about .06% lose at least 100 units
looks to be about 0%. but it can be bad.
about .06% lose at least 100 units
reality is what it is
reality playing craps = sh*t happens
winsome johnny (not Win some johnny)
