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guido111
guido111
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October 27th, 2010 at 12:26:01 PM permalink
Quote: MathExtremist

Quote: guido111


This law does not imply that the absolute difference between
the numbers of heads and tails should oscillate close to zero. On the contrary.
For games of chance, such as coin-tossing, it is even typical, as we shall see, that
for long time periods, either heads or tails will remain constantly in the lead,
with the absolute difference between the numbers of heads and tails tending to
become larger and larger."



That is the most critical piece to understand if you want to overcome the typical intuitive misunderstanding that is the gambler's fallacy. As the number of trials grows, the difference between heads and tails also grows, even as the percentage of heads or tails converges on 50%. In actual numbers, the distribution becomes less likely to be exactly 50/50 over time, but more likely to be "close to it." (Edit: I'm not discussing the infinite random walk theorem that says it's 100% likely to reach every point on the line.)

Not understanding this aspect of randomness and betting in a way based on its opposite has led to the ruin of a great many gamblers. 98steps may not even be the latest.


Exactly ME.

The Gamblers Fallacy exists because people misunderstand what the Theory of Large Numbers or law of averages is all about.
Just a simple reading of any prob and stat book will point out the errors.

The percentages converge as the number of trials increase but the actual numbers do not and are more likely to get further and further away from each other as N increases.

Maybe 98steps will take a closer look at how he bets.
He does use a D'Alembert progression and that system only wins as the NUMBER of wins and NUMBER of losses are close to each other. So he must hope to win fast since the longer he plays the actual numbers can start getting further and further away from each other.

A formula for bankroll disaster!
goatcabin
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October 27th, 2010 at 4:19:25 PM permalink
Quote: 7winner

Not a nightmare if you noticed the streaks and trends against what you were betting and just bet the don't pass. It does the same as the Pass Line.
Then you could have waited until the Pass Line could prove to you in the short run it could win as expected.
More craps players I have seen lose more money betting against losing streaks and trends. Just a fact of the game.



This, of course, is the OTHER side of the Gambler's Fallacy: instead of assuming a trend in the past indicates a CHANGE in the future, assume it indicates MORE OF THE SAME. At no time does an observed trend give information about the next bet or series of bets, one way or the other.
Cheers,
Alan Shank
Woodland, CA
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
guido111
guido111
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October 28th, 2010 at 2:24:23 PM permalink
Update time?
#Date/Time/LocationDaySession HoursResult
1October 21. 7:45pm - 11:30pm. El Cortez Casino, Downtown. Gross Earnings $162Thurs3.75$162
2October 22. 9:30am - 4:15pm. Eastside Cannery, Boulder Highway. Gross Earnings $60.Fri6.75$60
3October 23. 1:30pm - 4:30pm. Eastside Cannery, Boulder Highway. Gross Earnings $153.Sat3$153
4October 23. 5:45pm - 5:30am. Boulder Station, Boulder Highway. Gross Earnings $175.Sat11.75$175
 October 24: I am taking Sunday OFFSun00
5October 25: 11am-11:30am. Main Street Station, Downtown. Gross Earnings +156Mon0.5$156
6October 25: 12:30pm - 2:15pm. Golden Gate Casino, Downtown. Gross Earnings +152Mon1.75$152
7October 25: 4pm - 2am. Stratosphere, STRIP, LOSS -2316Mon10($2,316)
 October 26: I am taking Tuesday OFFTues00
 October 27: No reportWed..
 October 28: No reportThurs..
 ....
 ....
 .Totals37.5($1,458)
98steps
98steps
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October 29th, 2010 at 11:24:41 AM permalink
Progres Update.......

Sorry for the delay in reporting.....the trials of having a 20 year old daughter are never ending. Thursday was a no action day. Wednesday was a good day. Three relatively easy sessiuons, with the table behaving exactly as it should.

10/27 11am - 2:30pm Boulder Station, Boulder Highway. Gross Earnings +154. Bankroll Low -132.
10/27 4pm - 6pm El Cortez, Downtown. Gross Earnings +151. Bankroll Low -89.
10/27 7pm - 12:30am Main Street Station, Downtown. Gross Earnings +163. Bankroll Low -211.
Ayecarumba
Ayecarumba
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October 29th, 2010 at 11:57:56 AM permalink
Quote: 98steps

Progres Update.......

Sorry for the delay in reporting.....the trials of having a 20 year old daughter are never ending. Thursday was a no action day. Wednesday was a good day. Three relatively easy sessiuons, with the table behaving exactly as it should.

10/27 11am - 2:30pm Boulder Station, Boulder Highway. Gross Earnings +154. Bankroll Low -132.
10/27 4pm - 6pm El Cortez, Downtown. Gross Earnings +151. Bankroll Low -89.
10/27 7pm - 12:30am Main Street Station, Downtown. Gross Earnings +163. Bankroll Low -211.



Thanks for the update 98steps. I am encouraged to hear that your family is coming before your, "work".

"table behaving exactly as it should"??? Careful... Maybe the table likes you, but the dice hate you with a passion...hehe.

Main Street seems to be good to you...

Please make sure everywhere rates your play. You owe it to your "investors" to reduce your overhead with comps for Room and Board.
Simplicity is the ultimate sophistication - Leonardo da Vinci
98steps
98steps
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October 29th, 2010 at 2:54:32 PM permalink
Progress Update.......

Nice Easy run today. Will be one more later. Boulder is quickly becoming a comfortable place to hang out. Don't anyone try to say anything different, this is HARD WORK.

10/29 Noon - 2:30pm Boulder Station, Boulder Highway. Gross Earnings +162. Low Bankroll -173.
Mosca
Mosca
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October 29th, 2010 at 4:07:35 PM permalink
Quote: 98steps

Progress Update.......

Nice Easy run today. Will be one more later. Boulder is quickly becoming a comfortable place to hang out. Don't anyone try to say anything different, this is HARD WORK.

10/29 Noon - 2:30pm Boulder Station, Boulder Highway. Gross Earnings +162. Low Bankroll -173.



Jeez, buddy. $150 a day x 5 days a week x 50 weeks a year = $37500. Give or take. Go drive a cab, sell cars, get an Amway distributorship. Become a medical transcriptionist, sell magazines over the phone. Anything has to pay better than that. With no risk of ruin.
A falling knife has no handle.
MichaelBluejay
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October 29th, 2010 at 7:30:07 PM permalink
Quote: Mosca

Jeez, buddy. $150 a day x 5 days a week x 50 weeks a year = $37500. Give or take. Go drive a cab, sell cars, get an Amway distributorship. Become a medical transcriptionist, sell magazines over the phone. Anything has to pay better than that. With no risk of ruin.



Are you kidding? $37,500 a year is nearly $18 an hour, more than *twice* the minimum wage. And I'm going to guess that *most* jobs in Vegas pay less than $37,500 a year. Cabbies certainly make less than $18 an hour these days.

Also, 98 would probably tell you that if the system were shown to be a winner, then he would simply make larger bets (once capitalized) and increase his hourly take.
Presidential Election polls and odds: https://2605.me/p
thecesspit
thecesspit
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October 29th, 2010 at 7:45:32 PM permalink
Quote: Mosca

Jeez, buddy. $150 a day x 5 days a week x 50 weeks a year = $37500. Give or take. Go drive a cab, sell cars, get an Amway distributorship. Become a medical transcriptionist, sell magazines over the phone. Anything has to pay better than that. With no risk of ruin.



Tax free!
"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
Mosca
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October 29th, 2010 at 8:18:38 PM permalink
Quote: MichaelBluejay

Are you kidding? $37,500 a year is nearly $18 an hour, more than *twice* the minimum wage. And I'm going to guess that *most* jobs in Vegas pay less than $37,500 a year. Cabbies certainly make less than $18 an hour these days.

Also, 98 would probably tell you that if the system were shown to be a winner, then he would simply make larger bets (once capitalized) and increase his hourly take.



Hehe. I know, that's why I threw in the Amway thing. But if he's going to complain about how much hard work it is, and there is the probability that he will go completely bust, then flipping burgers is a better return. Stealing money from his parents will give a better return. The $37500 would only be if his system would actually work, which it won't.
A falling knife has no handle.
soulhunt79
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October 29th, 2010 at 10:20:03 PM permalink
Quote: Mosca

Hehe. I know, that's why I threw in the Amway thing. But if he's going to complain about how much hard work it is, and there is the probability that he will go completely bust, then flipping burgers is a better return. Stealing money from his parents will give a better return. The $37500 would only be if his system would actually work, which it won't.



I think his win limit is lower than expected until he gets his entire backroll starting early november. The early trials I saw meant no stopping until +600.
mkl654321
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October 29th, 2010 at 11:03:14 PM permalink
Quote: Mosca

Hehe. I know, that's why I threw in the Amway thing. But if he's going to complain about how much hard work it is, and there is the probability that he will go completely bust, then flipping burgers is a better return. Stealing money from his parents will give a better return. The $37500 would only be if his system would actually work, which it won't.



We do all realize that even if 98steps manages to eke out a win over the next two or three weeks, it won't mean a damn thing as far as proving the efficiacy of his system, don't we?
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
98steps
98steps
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October 30th, 2010 at 1:33:43 AM permalink
Progress Update......

I really enjoy the atmosphere at the Cannery. The crew is always friendly and accomodating. They are the most generous with comps on Boulder Highway. If only they could get a keep a full game going it would be a daily location. Long grinding session, but never any danger.

10/29 7pm - 12:30am. Eastside Cannery, Boulder Highway. Gross Earnings +158. Low Bankroll -162.
98steps
98steps
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October 30th, 2010 at 7:40:58 AM permalink
Progress Update......

Couldn't really sleep, was up and down all morning. Decided to take a walk about 530am and amazingly there was an almost full game going. Everyone was hoottin and hollerin, at 530am.....so I jumped in. One thing I love about Vegas....the game is ALWAYS there, only have to play when it feels right.

10/30 5:30am - 7:15am. Boulder Station, Boulder Highway. Gross Earnings +153. Bankroll Low EVEN.
guido111
guido111
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October 30th, 2010 at 11:16:09 AM permalink
Quote: 98steps

Progress Update......


Nice
#Date/Time/LocationDaySession HoursResult
1October 21. 7:45pm - 11:30pm. El Cortez Casino, Downtown. Gross Earnings $162Thurs3.75$162
2October 22. 9:30am - 4:15pm. Eastside Cannery, Boulder Highway. Gross Earnings $60.Fri6.75$60
3October 23. 1:30pm - 4:30pm. Eastside Cannery, Boulder Highway. Gross Earnings $153.Sat3$153
4October 23. 5:45pm - 5:30am. Boulder Station, Boulder Highway. Gross Earnings $175.Sat11.75$175
5October 25: 11am-11:30am. Main Street Station, Downtown. Gross Earnings +156Mon0.5$156
6October 25: 12:30pm - 2:15pm. Golden Gate Casino, Downtown. Gross Earnings +152Mon1.75$152
7October 25: 4pm - 2am. Stratosphere, STRIP, LOSS -2316Mon10($2,316)
810/27 11am - 2:30pm Boulder Station, Boulder Highway. Gross Earnings +154. Bankroll Low -132.Wed3.5$154
910/27 4pm - 6pm El Cortez, Downtown. Gross Earnings +151. Bankroll Low -89.Wed2$151
1010/27 7pm - 12:30am Main Street Station, Downtown. Gross Earnings +163. Bankroll Low -211.Wed5.5$163
1110/29 7pm - 12:30am. Eastside Cannery, Boulder Highway. Gross Earnings +158. Low Bankroll -162.Fri5.5$158
1210/30 5:30am - 7:15am. Boulder Station, Boulder Highway. Gross Earnings +153. Bankroll Low EVEN.Sat1.75$153
 .Totals55.75($679)
teddys
teddys
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October 30th, 2010 at 2:21:39 PM permalink
98steps -- I really enjoy your account, nothwithstanding the merits of your system. You should give Joker's Wild on Boulder a try. The atmosphere is really nice and the limits can go as low as $1 with 10x odds. You should also check out Arizona Charlie's on Boulder, and maybe a couple of the other Stations like Sunset or the Fiesta (where you can say hi to Dan!)
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
98steps
98steps
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October 30th, 2010 at 3:18:18 PM permalink
Progress Update.....

Change of Venue today. Boulder strip all booked up for holiday weekend. Only Room in town i could get comped was at Texas Station, on Rancho. So, whole new area to explore. And now that my shift is over, it is Football Time for a few Hours.

10/30 11:30am - 2:45pm Texas Station, Rancho. Gross Earnings +150. Low Bankroll -328.
98steps
98steps
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October 30th, 2010 at 5:51:31 PM permalink
Quote: Ayecarumba

Thanks for the update 98steps. I am encouraged to hear that your family is coming before your, "work".

"table behaving exactly as it should"??? Careful... Maybe the table likes you, but the dice hate you with a passion...hehe.

Main Street seems to be good to you...

Please make sure everywhere rates your play. You owe it to your "investors" to reduce your overhead with comps for Room and Board.



I absolutely make sure they rate me for every session. Overhead though is not a factor to my investors. Any costs associated with my tenure in Vegas come exclusively out of my pocket.
superrick
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November 2nd, 2010 at 11:15:35 AM permalink
98steps

I don’t believe in systems, because every system might work some times but will not work every time. I think I was at Boulder Station on the 10/30 but it might have been on the day before about the time you said you were playing.

Here is one of the problems I would have with your system without even seeing it played, and that’s your $2, 316 lose, and what you are winning on your sessions. Take your one on the 22 of Oct, you made $60 for almost 7 hours of work. I don’t know what your buy-in is, but it seems like you are just wasting you time if that is all you are walking out the door with and are willing to risk $2, 316!

I don’t know if you are a local, and I am not interested in buying into your system, but I could meet up with you and see what I think about what you are doing!

You can get a hold of me over on a different board that I am on, it’s a free board then Just PM me there. I can play almost any morning, and when I do play it’s always in the mornings from 5am till 7am.

Here is the link; http://procraps4u2.myfanforum.org

LOL

superrick




Quote: guido111

Nice

#Date/Time/LocationDaySession HoursResult
1October 21. 7:45pm - 11:30pm. El Cortez Casino, Downtown. Gross Earnings $162Thurs3.75$162
2October 22. 9:30am - 4:15pm. Eastside Cannery, Boulder Highway. Gross Earnings $60.Fri6.75$60
3October 23. 1:30pm - 4:30pm. Eastside Cannery, Boulder Highway. Gross Earnings $153.Sat3$153
4October 23. 5:45pm - 5:30am. Boulder Station, Boulder Highway. Gross Earnings $175.Sat11.75$175
5October 25: 11am-11:30am. Main Street Station, Downtown. Gross Earnings +156Mon0.5$156
6October 25: 12:30pm - 2:15pm. Golden Gate Casino, Downtown. Gross Earnings +152Mon1.75$152
7October 25: 4pm - 2am. Stratosphere, STRIP, LOSS -2316Mon10($2,316)
810/27 11am - 2:30pm Boulder Station, Boulder Highway. Gross Earnings +154. Bankroll Low -132.Wed3.5$154
910/27 4pm - 6pm El Cortez, Downtown. Gross Earnings +151. Bankroll Low -89.Wed2$151
1010/27 7pm - 12:30am Main Street Station, Downtown. Gross Earnings +163. Bankroll Low -211.Wed5.5$163
1110/29 7pm - 12:30am. Eastside Cannery, Boulder Highway. Gross Earnings +158. Low Bankroll -162.Fri5.5$158
1210/30 5:30am - 7:15am. Boulder Station, Boulder Highway. Gross Earnings +153. Bankroll Low EVEN.Sat1.75$153
 .Totals55.75($679)

Note, all my post start with this is just my opinion...! You do good brada ..! superrick Winning comes from knowledge and skill when your betting and not reading fiction http://procraps4u2.myfanforum.org/index.php ...
guido111
guido111
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November 2nd, 2010 at 11:40:36 AM permalink
Nov 2

#Date/Time/LocationDaySession HoursResult
1October 21. 7:45pm - 11:30pm. El Cortez Casino, Downtown. Gross Earnings $162Thurs3.75$162
2October 22. 9:30am - 4:15pm. Eastside Cannery, Boulder Highway. Gross Earnings $60.Fri6.75$60
3October 23. 1:30pm - 4:30pm. Eastside Cannery, Boulder Highway. Gross Earnings $153.Sat3$153
4October 23. 5:45pm - 5:30am. Boulder Station, Boulder Highway. Gross Earnings $175.Sat11.75$175
5October 25: 11am-11:30am. Main Street Station, Downtown. Gross Earnings +156Mon0.5$156
6October 25: 12:30pm - 2:15pm. Golden Gate Casino, Downtown. Gross Earnings +152Mon1.75$152
7October 25: 4pm - 2am. Stratosphere, STRIP, LOSS -2316Mon10($2,316)
810/27 11am - 2:30pm Boulder Station, Boulder Highway. Gross Earnings +154. Bankroll Low -132.Wed3.5$154
910/27 4pm - 6pm El Cortez, Downtown. Gross Earnings +151. Bankroll Low -89.Wed2$151
1010/27 7pm - 12:30am Main Sroweet Station, Downtown. Gross Earnings +163. Bankroll Low -211.Wed5.5$163
1110/29 7pm - 12:30am. Eastside Cannery, Boulder Highway. Gross Earnings +158. Low Bankroll -162.Fri5.5$158
1210/30 5:30am - 7:15am. Boulder Station, Boulder Highway. Gross Earnings +153. Bankroll Low EVEN.Sat1.75$153
1310/30 11:30am - 2:45pm Texas Station, Rancho. Gross Earnings +150. Low Bankroll -328.Sat3.25$150
..Totals59($529)


Now the real bankroll, bets and fun can begin.
mkl654321
mkl654321
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November 2nd, 2010 at 12:21:05 PM permalink
Quote: guido111

Now the real bankroll, bets and fun can begin.



Actually, it looks like 98steps' system is behaving EXACTLY as a Martingale (which his system is a derivative of) should: lots of small wins, and the occasional ghastly loss, which outweighs all the small wins combined. The system looks its best just before the next big loss, and its worst just after such a loss.

We can thank 98steps' rigid methodology and faithful reporting for this. I actually hope, for his sake, that the big losses continue to come as often as they "should", and that those losses continue to wipe out his wins: that would be the superior outcome. It would NOT be good for either him or his investors if he was lucky enough to avoid the big losses; that would create the illusion that the system was effective. The long-term effect of that would more than offset any profit made from the system test.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
superrick
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November 2nd, 2010 at 4:27:06 PM permalink
mkl654321

Some times I wonder why they keep trying to find a system that will work, when you have small profits and big losses, you are just going to take a beating. Now I will be the first guy to tell everybody on this board I am not a math guy, nor a system players. I get a good laugh out of some of the guys that buy into some of these systems. The only thing I can say is what a great job the guy did that sold them the system, he made money, but will the guy that bought it ever make money? I don't think so unless they just get lucky.

Your buy-in and bank roll dictates your ability to win at craps, small buy-in and bank roll the harder it is to win, because to have to leave your money at risk longer, or press-up your bets! This all depends on your win goal, some players would just be happy to make $50 a day while others are looking for a lot more every time they play, I fall into the this category!

The one thing I found out a long time ago is you need the buy-in to make the money.
Small buy-ins just hurts your chances of winnings.
Where with a good buy-in you can regress your bets down after getting paid off on one of your bets, get your money off the table if you want to do that, then press and spread, with what you just won on one good-sized bet!

I have seen a lot of systems being played by players, and the one thing I have found out is most players will stop playing them because they lost over time!
Note, all my post start with this is just my opinion...! You do good brada ..! superrick Winning comes from knowledge and skill when your betting and not reading fiction http://procraps4u2.myfanforum.org/index.php ...
mkl654321
mkl654321
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November 2nd, 2010 at 4:32:34 PM permalink
Quote: superrick

The one thing I found out a long time ago is you need the buy-in to make the money.
Small buy-ins just hurts your chances of winnings.



On the other hand, a small buyin reduces the size of your potential loss (assuming that if you lose your buyin, you're done), but your possible win is still infinite.

What matters is not how much you buy in for, but the total amount of your bets. The more you bet, the more you will lose (odds bets excluded).
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
goatcabin
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November 2nd, 2010 at 5:20:35 PM permalink
Quote: mkl654321

On the other hand, a small buyin reduces the size of your potential loss (assuming that if you lose your buyin, you're done), but your possible win is still infinite.

What matters is not how much you buy in for, but the total amount of your bets. The more you bet, the more you will lose (odds bets excluded).



Once again, this is NOT true. The more you bet (odds excluded) the more is your EXPECTED loss. The ev is not RESULTS. The ev does not determine the shape of the graph, nor does it determine one's chance of winning.

Actually, the biggest determinant of whether a bettor will reach some win goal for a session is the degree of variance in the bet strategy.
Cheers,
Alan Shank
Woodland, CA
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
mkl654321
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November 2nd, 2010 at 8:57:59 PM permalink
Quote: goatcabin

Once again, this is NOT true. The more you bet (odds excluded) the more is your EXPECTED loss. The ev is not RESULTS. The ev does not determine the shape of the graph, nor does it determine one's chance of winning.

Actually, the biggest determinant of whether a bettor will reach some win goal for a session is the degree of variance in the bet strategy.
Cheers,
Alan Shank
Woodland, CA



That's mere semantics. In the long run, actual results approach expected results. The more you bet, the greater your expected loss. The greater your expected loss, the more you will lose. This, of course, refers to the long run--but the long run is all that is meaningful in evaluating a betting strategy. I realize, of course, that the Law of Large Numbers means that the graph of results will be asymptotic--nearing, but never touching, expected results.

In point of fact, EV IS results, in the larger scheme of things. Casinos structure their games on the basis of EV, and they expect their results to average to EV, because they book so many decisions. If they cared about RESULTS in the short term, they'd burn all the crap tables when they lost money, and build more tables when they won. This isn't a fruitful outlook for the casino, and the analogous attitude for the player would be to sell his house and move to Vegas if he won, but swear on a stack of Bibles never to come to Vegas again if he lost.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
goatcabin
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November 2nd, 2010 at 10:42:51 PM permalink
Quote: mkl654321

That's mere semantics. In the long run, actual results approach expected results. The more you bet, the greater your expected loss. The greater your expected loss, the more you will lose. This, of course, refers to the long run--but the long run is all that is meaningful in evaluating a betting strategy.



But no player is in it for the long run; no one can bet that long or that much.

Quote: mkl654321

In point of fact, EV IS results, in the larger scheme of things. Casinos structure their games on the basis of EV, and they expect their results to average to EV, because they book so many decisions.



That is true for the casino, and it's true for the players, taken as an aggregate, but it is NOT true for any given player, and you know that.

If they cared about RESULTS in the short term, they'd burn all the crap tables when they lost money, and build more tables when they won. This isn't a fruitful outlook for the casino, and the analogous attitude for the player would be to sell his house and move to Vegas if he won, but swear on a stack of Bibles never to come to Vegas again if he lost.



The player is not a casino and he/she is not ALL the players. Every player has a chance to come out ahead, and intelligent players know that, but also know that that chance diminishes the more they play. You seem to have blinders on when it comes to variance and skew, although you understand the terms. It is virtually certain that some players will be lifetime winners, not because they have figured out some way to defeat the house edge, but just due to positive variance (luck).
Cheers,
Alan Shank
Woodland, Ca
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
mkl654321
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November 2nd, 2010 at 11:38:40 PM permalink
Quote: goatcabin

But no player is in it for the long run; no one can bet that long or that much.
You seem to have blinders on when it comes to variance and skew, although you understand the terms. It is virtually certain that some players will be lifetime winners, not because they have figured out some way to defeat the house edge, but just due to positive variance (luck).
Cheers,
Alan Shank
Woodland, Ca



Oddly enough, YOU seem to have blinders on when I talk about the "long term", even though I'm sure you understand the term. Long term does not mean a billion billion outcomes. It means enough outcomes to smooth out the effects of variance, with the goal of approaching expected value. For me, that may mean 1000 hours, or 800,000 hands, of video poker. When I say I regard only the long term as meaningful, it means I will NOT stop and assess my results before I reach that long term perspective--I will not Singerize, and stop and assess my results every 400 hands.

Another thing you're not considering is that for most people, myself included, "long term" is somewhat subjective. For the casino, or for anyone making +EV bets (which might include stock market or bond investors), the long term is a not sharply defined, but nonetheless meaningful concept. It means we won't attach undue importance to what happens today, or this week.

I'm sure there's a mathematical expression of the long term, in that an increasing number of trials causes results to converge on the mean to such an extent that the mean is, for all intents and purposes, reached--it's not unlike the sum of an infinite series approaching 1. Of course I understand that those results are virtually certain to not fall ON the mean, but as a practical matter, for casinos and APs, close is good enough.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
Mosca
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November 3rd, 2010 at 6:17:22 AM permalink
Although the lottery is completely -EV, everyone who has won is a lifetime winner.
A falling knife has no handle.
weaselman
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November 3rd, 2010 at 6:46:07 AM permalink
Quote: mkl654321

T I realize, of course, that the Law of Large Numbers means that the graph of results will be asymptotic--nearing, but never touching, expected results.



Not that it matters much for anything, but it's not assymptotic. It fluctuates around the expected value, crossing it many times back and forth. As the number of experiments grows, the amplitude of fluctuations becomes lower.
"When two people always agree one of them is unnecessary"
weaselman
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November 3rd, 2010 at 6:54:52 AM permalink
Quote: goatcabin

But no player is in it for the long run; no one can bet that long or that much.


If a hundred thousand players make a hundred thousand bets, that's your "long run".
What you are missing is that your "long run" does not have to be constructed only of bets, made by you. If that large devastating loss is supposed to happen "in the long run" when you use martingale, there is no reason it won't happen to you on your very first bet.


Quote:

That is true for the casino, and it's true for the players, taken as an aggregate, but it is NOT true for any given player, and you know that.


A given player may get lucky for some period of time. Or he may get unlucky. There is no way to tell for sure which way your luck will swing, but because it is a -EV game, the distribution is shifted to the left, meaning it is more likely, that you'll get unlucky than that you'll get lucky.

The simple truth is that, long run or not, you are more likely to lose than to win, and the longer you play the more likely you are to lose, and the larger bets you are making, the more is the amount you are likely to lose.
"When two people always agree one of them is unnecessary"
goatcabin
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November 3rd, 2010 at 8:59:11 AM permalink
Quote: weaselman

If a hundred thousand players make a hundred thousand bets, that's your "long run".
What you are missing is that your "long run" does not have to be constructed only of bets, made by you. If that large devastating loss is supposed to happen "in the long run" when you use martingale, there is no reason it won't happen to you on your very first bet.



What you are missing is that I am talking about individual players. As I said, the casinos and the players, taken as aggregates, play in the "long run"; individual players do not. I am not advocating progress-on-a-loss betting, by any means. And I have pointed out exactly that same fact -- that the big loss can occur at any time.

Quote: weaselman

A given player may get lucky for some period of time. Or he may get unlucky. There is no way to tell for sure which way your luck will swing, but because it is a -EV game, the distribution is shifted to the left, meaning it is more likely, that you'll get unlucky than that you'll get lucky.



That's not true -- a player is just as likely to experience positive variance as negative variance; it's just that the mean of the distribution is on the losing side of the zero point. So, for any given degree of variance, the losses are greater than the wins.

Quote: weaselman

The simple truth is that, long run or not, you are more likely to lose than to win, and the longer you play the more likely you are to lose, and the larger bets you are making, the more is the amount you are likely to lose.



That's the simple truth, all right, but it is too simple for my tastes. It needs to be supplemented with more information about likely outcomes. What I have been objecting to is mkl's repeated incorrect statements that "the more you bet, the more you WILL lose" (emphasis mine).

There is no specific definition of "long run", but we can define different degrees of likelihood that a player will be ahead after different numbers of bets. I did a post a while back about where the ev equals the standard deviation, which means a player needs to have experienced one standard deviation's worth of positive variance in order to offset the expected loss. The probability of this is about .16. When enough bets have been made that the SD is half the ev in magnitude, then the probability of a player breaking even or better is down to less than .03. However, let's take your 100,000 players; at the point where |ev| = 2 SD, we'd still expect over 2000 of them to be even or ahead.
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Alan Shank
Woodland, CA
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
mkl654321
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November 3rd, 2010 at 9:18:10 AM permalink
Quote: weaselman

Not that it matters much for anything, but it's not assymptotic. It fluctuates around the expected value, crossing it many times back and forth. As the number of experiments grows, the amplitude of fluctuations becomes lower.



As an absolute number, I meant, since whether it is positive or negative in relation to the mean at any one point is irrelevant.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
goatcabin
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November 3rd, 2010 at 9:20:15 AM permalink
Quote: mkl654321

Oddly enough, YOU seem to have blinders on when I talk about the "long term", even though I'm sure you understand the term. Long term does not mean a billion billion outcomes. It means enough outcomes to smooth out the effects of variance, with the goal of approaching expected value.



For craps players, approaching expected value is certainly not a "goal". You claim to be a +EV player, presumably not in craps; that is a different story entirely, since the ev is on the plus side. Most craps players do not play enough over their lifetimes to "smooth out the effects of variance" to the extent of having almost no chance of being even or ahead.

Quote: mkl654321

For me, that may mean 1000 hours, or 800,000 hands, of video poker. When I say I regard only the long term as meaningful, it means I will NOT stop and assess my results before I reach that long term perspective--I will not Singerize, and stop and assess my results every 400 hands.



Why not? How would that hurt you? Your results for the first 400 hands are "in the books"; the expectation going forward for the next 799,600 hands does not change, unless you believe, as many do, in the "cosmic rubber band" pulling your results back toward the mean. Here again, you seem to assume that if someone assesses his/her results, that means he/she doesn't understand what they mean and don't mean. If I plan to flip a coin 1000 times, and the first 10 flips are all heads, those ten heads are "in the bank", and my expectation for the entire 1000 is now 505 total heads, not 500.

Quote: mkl654321


I'm sure there's a mathematical expression of the long term, in that an increasing number of trials causes results to converge on the mean to such an extent that the mean is, for all intents and purposes, reached--it's not unlike the sum of an infinite series approaching 1. Of course I understand that those results are virtually certain to not fall ON the mean, but as a practical matter, for casinos and APs, close is good enough.



I am not talking about casinos and APs, as I have pointed out several times. "Long term" as far as I'm aware does not have any specific definition, mathematical or not, but a degree of "long termness" can be defined by the ratio of the ev to the standard deviation, as I have suggested on this or another thread.
Cheers,
Alan Shank
Woodland, CA
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
weaselman
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November 3rd, 2010 at 9:35:49 AM permalink
Quote: goatcabin

I am not advocating progress-on-a-loss betting, by any means. And I have pointed out exactly that same fact -- that the big loss can occur at any time.


What's your point then?

Quote:

That's not true -- a player is just as likely to experience positive variance as negative variance; it's just that the mean of the distribution is on the losing side of the zero point. So, for any given degree of variance, the losses are greater than the wins.



What's "not true"? You said the same thing I did.
A small correction is that the losses are not only greater than the wins, but also more frequent, since you are correct that "positive variance" is as likely as "negative variance", but some of the former is still a loss, because EV is negative.


Quote:


That's the simple truth, all right, but it is too simple for my tastes. It needs to be supplemented with more information about likely outcomes.



Well, the EV of the game gives you that information, yet you keep objecting to it being looked at.

Quote:

There is no specific definition of "long run", but we can define different degrees of likelihood that a player will be ahead after different numbers of bets.


Yes, and the more bets you make, the less that likelihood is. That's exactly mkl's point.

Once again, you seem to be making a point, and disputing it at the same time.
"When two people always agree one of them is unnecessary"
goatcabin
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November 3rd, 2010 at 10:00:14 AM permalink
Quote: weaselman

What's your point then?



I am objecting to mkl's assertion that "you will lose". Here is his statement: "The more you bet, the more you will lose (odds bets excluded)."
That is clearly incorrect.



Quote: weaselman

What's "not true"? You said the same thing I did.
A small correction is that the losses are not only greater than the wins, but also more frequent, since you are correct that "positive variance" is as likely as "negative variance", but some of the former is still a loss, because EV is negative.



No, I didn't say the same thing. Again, quoting will clarify: "There is no way to tell for sure which way your luck will swing, but because it is a -EV game, the distribution is shifted to the left, meaning it is more likely, that you'll get unlucky than that you'll get lucky."

You now say yourself that positive variance is just as likely as negative variance, and that was my point. I equate "getting lucky" with "experiencing positive variance", not necessarily with being ahead.




Quote: weaselman

Well, the EV of the game gives you that information, yet you keep objecting to it being looked at.



Not at all. It is an important piece of information, but it is not the only one. The variance (standard deviation) is equally important in determining what chance a player has of coming out ahead for any given number of bets. It's the ratio of ev/SD that tells you how lucky you have to be (i.e. what degree of positive variance you have to experience) in order to overcome the expected loss. I have NEVER objected to the ev "being looked at".


Quote: weaselman

Yes, and the more bets you make, the less that likelihood is. That's exactly mkl's point..



No, it is not. Read his post again, please. It's an absolute statement "you will lose", not couched in terms like "the longer you play, the higher the probability you will lose". That is what I have been objecting to, on this and other threads.
Cheers,
Alan Shank
Woodland, CA
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
Doc
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November 3rd, 2010 at 10:47:17 AM permalink
Quote: goatcabin

... I equate "getting lucky" with "experiencing positive variance", not necessarily with being ahead..

That just might be a key point of disagreement. Do you often hear people say, " I was really lucky in the casino today; I (a) lost money, (b) lost less than I expected to, (c) lost less than I did yesterday." I suspect most people would describe that session as just not being as unlucky as it might have been.

I tend to agree that positive deviation from expectation is an indication of better than normal luck, even if a loss is involved, but I think this may be a point of disagreement in many cases.

As a side matter, I see that you use an expression that I formerly used and decided was incorrect: "experiencing positive variance". Isn't variance by definition a positive number? I now try to refer to positive deviation -- is there an issue of correctness here? I'm not really sure.
goatcabin
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November 3rd, 2010 at 11:02:24 AM permalink
Quote: Doc

That just might be a key point of disagreement. Do you often hear people say, " I was really lucky in the casino today; I (a) lost money, (b) lost less than I expected to, (c) lost less than I did yesterday." I suspect most people would describe that session as just not being as unlucky as it might have been.

I tend to agree that positive deviation from expectation is an indication of better than normal luck, even if a loss is involved, but I think this may be a point of disagreement in many cases.

As a side matter, I see that you use an expression that I formerly used and decided was incorrect: "experiencing positive variance". Isn't variance by definition a positive number? I now try to refer to positive deviation -- is there an issue of correctness here? I'm not really sure.



By "positive" I mean in the direction advantageous to the player. Yes, variance is always positive in the mathematical sense, since the differences are all squared, which is just a way to get an absolute value, or magnitude, of differences from the mean. Also, I often use the term "variance" not in its formal meaning but as a general term for a degree of volatility. "Positive deviation" sounds good, too -- less chance of confusion. Thanks.
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Alan Shank
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weaselman
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November 3rd, 2010 at 11:40:31 AM permalink
Quote: goatcabin

I am objecting to mkl's assertion that "you will lose". Here is his statement: "The more you bet, the more you will lose (odds bets excluded)."
That is clearly incorrect.



If he added "likely" after will, would that be all?


Quote:


No, I didn't say the same thing. Again, quoting will clarify: "There is no way to tell for sure which way your luck will swing, but because it is a -EV game, the distribution is shifted to the left, meaning it is more likely, that you'll get unlucky than that you'll get lucky."

You now say yourself that positive variance is just as likely as negative variance, and that was my point. I equate "getting lucky" with "experiencing positive variance", not necessarily with being ahead.



So, that's where we disagree then.





Not at all. It is an important piece of information, but it is not the only one. The variance (standard deviation) is equally important in determining what chance a player has of coming out ahead for any given number of bets. It's the ratio of ev/SD that tells you how lucky you have to be (i.e. what degree of positive variance you have to experience) in order to overcome the expected loss. I have NEVER objected to the ev "being looked at".




No, it is not. Read his post again, please. It's an absolute statement "you will lose", not couched in terms like "the longer you play, the higher the probability you will lose". That is what I have been objecting to, on this and other threads.
Cheers,
Alan Shank
Woodland, CA

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thecesspit
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November 3rd, 2010 at 11:43:29 AM permalink
Quote: mkl654321

As an absolute number, I meant, since whether it is positive or negative in relation to the mean at any one point is irrelevant.



it's still not asymptotic by the meaning of the word.
"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
weaselman
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November 3rd, 2010 at 11:52:41 AM permalink
Quote: goatcabin

I am objecting to mkl's assertion that "you will lose". Here is his statement: "The more you bet, the more you will lose (odds bets excluded)."
That is clearly incorrect.


so, if he added "likely" after "will", you would agree then?


Quote:


No, I didn't say the same thing. Again, quoting will clarify "There is no way to tell for sure which way your luck will swing, but because it is a -EV game, the distribution is shifted to the left, meaning it is more likely, that you'll get unlucky than that you'll get lucky."

You now say yourself that positive variance is just as likely as negative variance, and that was my point. I equate "getting lucky" with "experiencing positive variance", not necessarily with being ahead.



That's simple misunderstanding then. I used "get lucky" as a synonym to "win". If I lose, I don't consider myself lucky even if I lost less than EV.
With this correction, do you agree that we are saying the same thing now?


Quote:

Not at all. It is an important piece of information, but it is not the only one. The variance (standard deviation) is equally important in determining what chance a player has of coming out ahead for any given number of bets.



Not really. If the distribution is symmetric, increasing SD raises your chances of winning as much (actually, slightly less) as your chances of loosing. Yes with a huge SD you can win a lot, but you can lose a lot as well, so on average, it's the same.

Quote:

It's the ratio of ev/SD that tells you how lucky you have to be (i.e. what degree of positive variance you have to experience) in order to overcome the expected loss.



It's misleading though for the reason I mentioned above. If SD is large, you may not need as much "luck" to win, but at the same time it doesn't take much "lack of luck" to go bankrupt either. If you consider both possibilities, you'll have to conclude that you need about the same total amount of luck.

Put it another way, consider a single bet with extremely large SD. You can win a lot with relatively higher probability, that's correct. But at the same time, you can lose even more with even higher probability. And, if that happens, you are going to need to make many more subsequent bets to dig you out of the hole (again, risking to lose even more on each of them). You may need only a little bit of luck to win one bet, but overall you need a lot of it to come out ahead.
"When two people always agree one of them is unnecessary"
weaselman
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November 3rd, 2010 at 11:56:15 AM permalink
Quote: Doc

Isn't variance by definition a positive number? I now try to refer to positive deviation -- is there an issue of correctness here? I'm not really sure.



Deviation is a positive number too :)
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November 3rd, 2010 at 12:04:05 PM permalink
Quote: weaselman

Deviation is a positive number too :)

I didn't think that was necessarily so. If I am considering numbers within a distribution of mean µ, then an individual observation x would have a deviation from the mean equal to x-µ, which could be either positive or negative. In computing variance and standard deviation, these individual deviations are squared before they are added, so that both variance and standard deviation are positive numbers, but not individual deviations necessarily. Positive deviation implies an observation higher than the mean, which in the context of a gambling session suggests winning money or losing less money than expected on average.
mkl654321
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November 3rd, 2010 at 12:45:59 PM permalink
Quote: goatcabin

I am objecting to mkl's assertion that "you will lose". Here is his statement: "The more you bet, the more you will lose (odds bets excluded)."
That is clearly incorrect.



Semantics again, Alan. As you approach certainty, there becomes no meaningful distinction between absolute (mathematical) certainty and practical certainty. A 99.99999% chance of winning (or losing) is good enough for me.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
mkl654321
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November 3rd, 2010 at 12:48:03 PM permalink
Quote: goatcabin

Why not? How would that hurt you?



It would hurt me to stop and assess my results every 400 hands because I would be wasting my time gathering useless information. It's the same reason why the casino doesn't halt all play and count all the money every thirty minutes.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
MathExtremist
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November 3rd, 2010 at 1:00:36 PM permalink
Quote: Doc

I didn't think that was necessarily so. If I am considering numbers within a distribution of mean µ, then an individual observation x would have a deviation from the mean equal to x-µ, which could be either positive or negative. In computing variance and standard deviation, these individual deviations are squared before they are added, so that both variance and standard deviation are positive numbers, but not individual deviations necessarily. Positive deviation implies an observation higher than the mean, which in the context of a gambling session suggests winning money or losing less money than expected on average.



Right - *standard deviation* is a positive number since it's defined as the square root of variance (and not vice-versa), but any specific deviation of an outcome from the mean can be negative. Since we're talking about specific outcomes, that all makes sense. However, there's still a difference between what people think of as "good luck" and what is technically a positive deviation. For example, after playing $10,000 in handle on the passline, you're down $40. That's a positive deviation (the mean is -$141) but most people wouldn't think losing $40 in craps is "good luck".
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
Doc
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November 3rd, 2010 at 1:30:22 PM permalink
I think that is almost the exact message (with different words) I posted in the middle of page 49 of this thread. So...you get no argument from me.
goatcabin
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November 3rd, 2010 at 1:32:31 PM permalink
Quote: weaselman

so, if he added "likely" after "will", you would agree then?



No, the word "will" is inappropriate, as is "the more you bet" without distinguishing between betting more, once, and betting many times. If I bet $1000 on the pass line, my probability of winning is .4929. OTOH, if I bet $10 100 times, my probability of coming out ahead is more like .44. etc. etc. This is because the standard deviation goes up more slowly than the expected loss, as I'm sure you, and mkl, are aware. "You will lose" means zero probability of not losing.




Quote: weaselman

That's simple misunderstanding then. I used "get lucky" as a synonym to "win". If I lose, I don't consider myself lucky even if I lost less than EV.
With this correction, do you agree that we are saying the same thing now?



Yes, I believe so.

Quote: weaselman

Not really. If the distribution is symmetric, increasing SD raises your chances of winning as much (actually, slightly less) as your chances of loosing. Yes with a huge SD you can win a lot, but you can lose a lot as well, so on average, it's the same.



Yes, really. Compare betting the pass line for $5 with single odds against 3, 4, 5X odds. With the higher SD, same ev, the probability of a winning or breakeven session is increased. For 100 bets, the ev's are -$7.07, but the SD's are $98 and $246, so a smaller degree of "positive deviation", to use Doc's term, is required to overcome the expected loss. That is all I am saying. We all know that variance works both ways, and I am constantly pointing that out -- high variance spreads the graph out, but it doesn't change the mean. That doesn't make it "the same". High variance means that more players using that strategy will be ahead at any point in time. It's almost like insurance, in a weird way. The players at -1 SD are losing more than low-variance players at -1 SD, balancing the fact that the +1 SD high-variance players are ahead, while the + 1 SD low-variance players are not.


Quote: weaselman

It's misleading though for the reason I mentioned above. If SD is large, you may not need as much "luck" to win, but at the same time it doesn't take much "lack of luck" to go bankrupt either. If you consider both possibilities, you'll have to conclude that you need about the same total amount of luck.



The same total amount of luck for what? All I am saying is that a larger SD requires less luck to come out ahead. Of course it increases "risk of ruin"; of course the same degree of bad luck results in larger losses than with low variance. The fact that it works both ways does not change the fact that high variance increases one's chance of winning.

Quote: weaselman

Put it another way, consider a single bet with extremely large SD. You can win a lot with relatively higher probability, that's correct. But at the same time, you can lose even more with even higher probability. And, if that happens, you are going to need to make many more subsequent bets to dig you out of the hole (again, risking to lose even more on each of them). You may need only a little bit of luck to win one bet, but overall you need a lot of it to come out ahead.



What do you mean by "overall"? What is "a lot" of luck? The amount of luck you need to come out ahead, as I've stated over and over, is a function of ev/SD; the ev increases directly with the number of bets, the SD with the square root thereof, which is exactly why it becomes less likely to win the more you play a negative ev game. A gambler needs to understand what he/she is gambling for: minimizing loss rate to stay at the table? - low variance; willing to risk losing the bankroll for the chance for a big win - high variance -- both may have the same ev. 98 Steps' method introduces a high measure of skew - lots of winning sessions, risk of a big loss, but nobody except Krebs himself believes that this produces a positive expectation.
Cheers,
Alan Shank
Woodland, CA
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
goatcabin
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November 3rd, 2010 at 1:36:07 PM permalink
Quote: mkl654321

Semantics again, Alan. As you approach certainty, there becomes no meaningful distinction between absolute (mathematical) certainty and practical certainty. A 99.99999% chance of winning (or losing) is good enough for me.



But I don't think any individual player ever plays enough to approach certainty. It's not just semantics; I think there is an important, material difference between saying:

You can't beat craps.
AND
You can't win at craps.

You can't beat craps, in the sense of achieving a positive expectation by making different bets in different amounts at different times.
You can win at craps, even over a lifetime's play, but the more you play the less likely that is.
Cheers,
Alan Shank
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weaselman
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November 3rd, 2010 at 2:30:22 PM permalink
Quote: goatcabin


The amount of luck you need to come out ahead, as I've stated over and over, is a function of ev/SD



Well, I just have to say it again, that you seem to have a very unconventional definition of luck.


Suppose you bet $100 on a number in roulette. You expectation is about -$5.26, and SD is ~$576.
By your definition, the "amount of luck" you need to win is 0.00913.

Now consider betting $100 on black. The expectation is still -$5.26, but the SD is only $100. By your definition, this bet requires 0.0526 of luck to get ahead - almost 6 times more than the other one!

Yet, as we all know, you will (yes, will :) ) win a lot more often betting on red, then on a number (about 18 times more often to be precise - 47% of time vs. 2.6%).
"When two people always agree one of them is unnecessary"
goatcabin
goatcabin
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Joined: Feb 13, 2010
November 3rd, 2010 at 4:26:39 PM permalink
Quote: weaselman

Well, I just have to say it again, that you seem to have a very unconventional definition of luck.


Suppose you bet $100 on a number in roulette. You expectation is about -$5.26, and SD is ~$576.
By your definition, the "amount of luck" you need to win is 0.00913.

Now consider betting $100 on black. The expectation is still -$5.26, but the SD is only $100. By your definition, this bet requires 0.0526 of luck to get ahead - almost 6 times more than the other one!

Yet, as we all know, you will (yes, will :) ) win a lot more often betting on red, then on a number (about 18 times more often to be precise - 47% of time vs. 2.6%).



Oh, please, weaselman, when you are talking about one bet, neither the ev nor the standard deviation has any meaning. You cannot lose $5.26, and your results cannot vary by $576, or $100. On the one hand, you win $3500 or you lose $100, a difference of $3600; on the other, you win $100 or lose $100, a difference of $200. Also, you know full well that I am not talking about the probability of winning a single bet.

Let's compare 100 $10 bets for each. They each have an ev of -$52.63, while the standard deviations are about $100 for the black vs. about $576 for the single number. So, the black has an ev/SD of about .53, while the single number's is about .09. I ran a quick simulation of 10,000 sessions of each. For the black, there were 2784 winning sessions, 448 broke even and 6768 lost. For the single number, 4968 sessions won, none broke even and 5032 lost. Those figures are quite close to what the ev/SD ratios indicate -- .53 SD associates with a probability of .298, while the single-number set came out considerably better than the .464 for .09 SD. Let's say that those 10,000 sessions were by 10,000 different players - about 28% of the "black" players came out ahead, while almost half of the single-number players did. OTOH, if you look at it from the point of view of one player of each type playing 10,000 sessions, at the end of the 10,000 sessions they are going to be about equal.

What I'm getting at here is that individual players are not "doomed" to lose at craps, although the players, taken as an aggregate, are.
Cheers,
Alan Shank
Woodland, CA
Cheers, Alan Shank "How's that for a squabble, Pugh?" Peter Boyle as Mister Moon in "Yellowbeard"
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