DeMango
Joined: Feb 2, 2010
• Posts: 2601
July 5th, 2011 at 8:49:18 AM permalink
I found this formula on another board : "Long term play is officially achieved at the point where there is a 99% expectation of being within .5% of the EV of a particular game." So if this is true how many hands do we play before we hit the "long term" in craps or black jack?
When a rock is thrown into a pack of dogs, the one that yells the loudest is the one who got hit.
s2dbaker
Joined: Jun 10, 2010
• Posts: 3259
July 5th, 2011 at 8:58:28 AM permalink
Quote: DeMango

I found this formula on another board : "Long term play is officially achieved at the point where there is a 99% expectation of being within .5% of the EV of a particular game." So if this is true how many hands do we play before we hit the "long term" in craps or black jack?

looks like they're shooting for three standard deviations. I would guess that pass line and BJ are about the same but betting EC or hardways makes a bit of difference. I can't even guess at the moment since i'm on a Cell Phone.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
PapaChubby
Joined: Mar 29, 2010
• Posts: 494
July 5th, 2011 at 1:04:13 PM permalink
Assumptions:
standard deviation = 1 betting unit
house edge = 1%
99% confidence is essentially 3 standard deviations

The answer is (3 x 100 x 200) squared = 3.6 billion hands.

This seems to me to be a criteria for accurately calculating the house edge of a game based on random results. But it's way too conservative with regards to arriving at the point where "the house always wins".
CrystalMath
Joined: May 10, 2011
• Posts: 1866
July 5th, 2011 at 2:39:35 PM permalink
For betting the don't pass line only, I calculate that you need to play 257,975 games to be within +- 0.5% of the actual return with a 99% confidence.

If the game had a standard deviation of exactly 1 (craps pass/don't pass is very close), then you would need to play 265,396 games.

As for the definition of long term play, this seems arbitrary.
I heart Crystal Math.
PapaChubby
Joined: Mar 29, 2010
• Posts: 494
July 5th, 2011 at 5:25:56 PM permalink
It appears I may have misunderstood the problem. I calculated for an accuracy of 0.5% of HE, rather than HE +/- 0.5%. Your way makes more sense.
DeMango
Joined: Feb 2, 2010
• Posts: 2601
July 5th, 2011 at 6:50:06 PM permalink
Unfortunately these answers only give ammunition to the crowd that says the long term does not apply to them. Bet the horn, play bad rules bj, double zero roulette, etc., the long run doesn't apply to me......... anything can happen....... Oh well.
When a rock is thrown into a pack of dogs, the one that yells the loudest is the one who got hit.
FleaStiff
Joined: Oct 19, 2009
• Posts: 14484
July 5th, 2011 at 7:30:19 PM permalink
Quote: DeMango

Unfortunately these answers only give ammunition to the crowd that says the long term does not apply to them. Bet the horn, play bad rules bj, double zero roulette, etc., the long run doesn't apply to me......... anything can happen....... Oh well.

In a certain sense, the long term does not apply to anyone. Consider roulette: the long term on a five dollar even money bet is twenty-six cents. Yet that long term will in fact never take place because the next roll is either going to Lose Five Dollars or Win Five Dollars. That next roll will never be a twenty-six cent loss for the player.

Of course for some of these roulette players they seem to remind me of the "who taught you math" scene in Kiss Kiss Bang Bang wherein in an attempt to elicit information the questioner inserts one live round into a six gun and is amazed that the first pull of the trigger blows the suspects brains out.

That guy who walked into Benny Binions place with a quarter million for the PassLine knew math. Benny Binion said "book it" because he knew math too.
EvenBob
Joined: Jul 18, 2010
• Posts: 24291
July 5th, 2011 at 7:55:34 PM permalink
As soon as you start playing any game, you're in the long term immediately, because the game is in the long term. What you really want to know is where you are in the long term. You can figure that out with math, you don't actually have to see it physically manifest itself before you know. All you need to know is your edge, be it positive or negative.
"It's not enough to succeed, your friends must fail." Gore Vidal
thecesspit
Joined: Apr 19, 2010
• Posts: 5936
July 5th, 2011 at 9:39:53 PM permalink
Quote: CrystalMath

For betting the don't pass line only, I calculate that you need to play 257,975 games to be within +- 0.5% of the actual return with a 99% confidence.

If the game had a standard deviation of exactly 1 (craps pass/don't pass is very close), then you would need to play 265,396 games.

As for the definition of long term play, this seems arbitrary.

Well, yes, any line between "long term" and "short term" is kinda arbitary.

With the EV AND the variance we can say what sort of range of results a player may have in the time they get to play (you might even need the distribution of pay outs for games like VP), the EV giving you the central marker and the variance the pattern either side. As the number of trials grows the spread becomes much more well defined, and results start to tend towards the EV (as a percentage variation).
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
odiousgambit
Joined: Nov 9, 2009