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#1
October 30th, 2009, 04:34 PM
 Dopple Executive Member Join Date: Jul 2007 Posts: 461
I am due for luck

I knew that would get some attention.

Although it is unprediictable is you have been in a negative variance it is true you should expect at some time to have a positive variance so this title does have an element of truth I would think.

The main idea I have causing me thought is that is all periods to which a standard deviation can defined are independent of each other so if I play 100 hours and come out at 1sd below my EV why would I not then again have the same likelyhood of once again being 1sd below my EV. The cards dont remember that I had a bad variance so why am I due a good variance.

I know this is somewhat childish thinking but it is just bugging me.

Flame if you must, I suppose I deserve it.
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cuts-you-up
#2
October 30th, 2009, 04:55 PM
 Jack_Black Executive Member Join Date: Aug 2009 Location: Planet Earth Posts: 504

warming up the flame thrower. LOL.

anyway, 100 hours is not enough. there is a probability that you will be ahead, but you might still be down after 100 hours. Remember, if you're only counting, you have at best 2% edge over the house. think like the house, they never stress when someone wins big at a slot machine with a 98% payout. they know that over time, they will be keeping 2% of what comes in.
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Part of the \$10 million I spent on gambling, part on booze and part on women. The rest I spent foolishly. -George Raft-
#3
October 30th, 2009, 05:36 PM
 FLASH1296 Executive Member Join Date: Oct 2007 Location: East Coast, U S A Posts: 2,748

Apparently you do not have a working definition off "long run"
__________________

"Part of the \$10 million I spent on gambling, part on booze and part on
women. The rest I spent foolishly."

. . . George Raft, actor

"I have approximate answers and possible beliefs and different degrees of

. . . Richard Feynman, 1965 Nobel Laureate

"Anyone can win or lose, but those whose play is efficacious,
merit credit for good news, and find the adverse less vexatious."
#4
October 30th, 2009, 06:44 PM
 ExhibitCAA Senior Member Join Date: Mar 2009 Location: Carthe Lodge Posts: 63

"The main idea I have causing me thought is that is all periods to which a standard deviation can defined are independent of each other so if I play 100 hours and come out at 1sd below my EV why would I not then again have the same likelyhood of once again being 1sd below my EV."

You DO have exactly the same likelihood of once again being 1sd below your EV.

"The cards dont remember that I had a bad variance so why am I due a good variance."

You are NOT "due" a good variance.

Let's say you're betting on Heads in a coin-flip game. Say you flip 100 times and get 45 Heads. With H=45 and N=100, we have H/N=0.45. In the next 100 flips, your chance of bad luck (i.e., being 5 Heads short of the expected number) is the same as it was before. You are not "supposed" to get 55 Heads in the next 100. It does NOT balance out in that way. But look what happens if you get the expected number of Heads (50) out of the next 100 flips. Your totals now become 95/200 = 0.475. You have gotten closer to the expected fraction, with only "normal" luck, NOT with "good variance."

Notice that the fraction is "correcting itself" through the DENOMINATOR, not the numerator. As N grows, any surplus or deficit of Heads gets diluted, so that your fraction H/N will get closer to 0.5 even if you never have any "good variance." You just have to not have CONSISTENT "bad variance," and you won't, provided you aren't cursed.
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"Occupy yourselves--play some cards."
#5
October 30th, 2009, 08:46 PM
 Jack_Black Executive Member Join Date: Aug 2009 Location: Planet Earth Posts: 504

Wow, my head kinda swam around a sec on that explanation, thanks CAA. But yes, do you expect getting exactly 50 heads and 50 tails when you flip a coin 100 times? Let's say you flip it 1,000,000 times. The theory of “law of large numbers” shows that your expectation of heads showing up 50% of the time will manifest itself the more trials you have. So if your EV is 2% in your favor, and you have a 100 sided dice(I've seen one, RPG dorks use them) and you get paid even money if you hit 1-52, but lose on 53-100, do you expect to be ahead after 100 rolls? 200? 400?

I think you also are looking at SD as something that is “due” for you. You're EV is due for you, variance is just what comes along with the territory. So after a billion hands, your EV will be given to you. During your time playing a billion hands, you will see negative variance and positive variance.

variance is a mathematical term for luck.
__________________
Part of the \$10 million I spent on gambling, part on booze and part on women. The rest I spent foolishly. -George Raft-
#6
October 30th, 2009, 08:51 PM
 Canceler Executive Member Join Date: Apr 2005 Location: Minnesota Posts: 1,112
So as not to let you down...

Take this, Dopple:

Actually, you pretty much got everything right. You need to post something a lot dumber than that to draw serious flaming.
#7
October 31st, 2009, 03:11 AM
 Martin Gayle Senior Member Join Date: Oct 2008 Posts: 175

Quote:
 Originally Posted by Dopple I knew that would get some attention. Although it is unprediictable is you have been in a negative variance it is true you should expect at some time to have a positive variance so this title does have an element of truth I would think. The main idea I have causing me thought is that is all periods to which a standard deviation can defined are independent of each other so if I play 100 hours and come out at 1sd below my EV why would I not then again have the same likelyhood of once again being 1sd below my EV. The cards dont remember that I had a bad variance so why am I due a good variance. I know this is somewhat childish thinking but it is just bugging me. Flame if you must, I suppose I deserve it.
Think of it in terms of a baseball player. If a player is a career .300 hitter and he gets off to a terrible start in the season. After a month in he is hitting say .150. For the other 5 months of the season do you expect him to hit better than .300 to make up for the bad start? No. Do you expect him to continue to hit .150? No. You expect him to hit .300 from then on.

Similarly if he gets off to a blazing start and is hitting .410 a month in you cannot expect him to maintain that.

It would be rare to measure any block of the season and find him hitting .300 but in the long run he will maintain a .300 average.

I think alot of would-be AP's get hurt by getting out of the gates in a slump. I know when I went beyond being a hobbyplayer I was "lucky" enough not to get crushed by neg variance and infact had a great bout of pos variance.
#8
October 31st, 2009, 06:09 AM
 ExhibitCAA Senior Member Join Date: Mar 2009 Location: Carthe Lodge Posts: 63

Jack_Black: "But yes, do you expect getting exactly 50 heads and 50 tails when you flip a coin 100 times?"

No, I expect the number of heads to follow a binomial distribution as explained on p. 598 of CAA. I used the exact number 50 out of 100 as an illustration to show that the H/N fraction can converge to 0.5 even without getting a surplus of Heads following a deficit of Heads in the first 100 flips. Even with an even number of Heads in the next 100 flips, the fraction goes from 0.45 to 0.475.

Jack_Black: "I think you also are looking at SD as something that is “due” for you."

I have no idea what you mean here.

Jack_Black: "[in a] billion hands, you will see negative variance and positive variance."

Yes, but given that you have just witnessed negative variance, you are not more likely to now have positive variance. You don't need the system to "compensate" you for the bad variance. Henceforth you could get "balanced variance," but you will still see the H/N fraction approach 0.5, because the negative variance you observed is basically just a one-time shock that gets drowned out as N goes to infinity.

The baseball analogy is a good one. If a typically 0.300 hitter goes 0 for 4 in his first game, it doesn't mean he will now go 4 for 8 in his next eight at-bats. If he bats 0.300 from now on, then by the end of the season, he will be close to 0.300 overall, because the one bad game has been diluted.

If you experience repeated "bad variance," then it means you are not playing with the edge you think you have.
__________________
"Occupy yourselves--play some cards."
#9
October 31st, 2009, 02:21 PM
 Jack_Black Executive Member Join Date: Aug 2009 Location: Planet Earth Posts: 504

Quote:
 Originally Posted by ExhibitCAA Jack_Black: "But yes, do you expect getting exactly 50 heads and 50 tails when you flip a coin 100 times?" No, I expect the number of heads to follow a binomial distribution as explained on p. 598 of CAA. I used the exact number 50 out of 100 as an illustration to show that the H/N fraction can converge to 0.5 even without getting a surplus of Heads following a deficit of Heads in the first 100 flips. Even with an even number of Heads in the next 100 flips, the fraction goes from 0.45 to 0.475.
I was actually talking to Dopple, reiterating what you said in more of layman's terms for me and Dopple, using the most elementary example found in any intro to prob. and stats textbook.

Quote:
 Originally Posted by ExhibitCAA Jack_Black: "I think you also are looking at SD as something that is “due” for you." I have no idea what you mean here.
Early on for me, and I would think most beginners, we assume that counting cards will give us positive variance. We confuse EV and +SD as the same thing. It sounded as though Dopple was having the same problem, and I wanted to clarify that AP guarantees +EV, not +SD.

Quote:
 Originally Posted by ExhibitCAA Yes, but given that you have just witnessed negative variance, you are not more likely to now have positive variance. You don't need the system to "compensate" you for the bad variance. Henceforth you could get "balanced variance," but you will still see the H/N fraction approach 0.5, because the negative variance you observed is basically just a one-time shock that gets drowned out as N goes to infinity.
Thanks for another headspin, but I already knew that, albeit in more lame man's terms.
__________________
Part of the \$10 million I spent on gambling, part on booze and part on women. The rest I spent foolishly. -George Raft-
#10
October 31st, 2009, 04:00 PM
 Dopple Executive Member Join Date: Jul 2007 Posts: 461

Thanks again for all the great feedback. I have alot of fun here and learn from even the most simple questions.

I think it is hard to not have that mindset after a losing streak that your good days will be coming soon.

I think I read something about the government coming out with some new bailout package for AP players suffering prolonged negative variances.
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cuts-you-up

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