
February 12th, 2008, 03:03 PM

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Join Date: Mar 2007
Location: southern US
Posts: 40


The Gambler's Fallacy
I have been a serious parttime counter for several years. I have given up counting for a while (for various reasons) and have been trying out a system that I have put a lot of thought into. I have been playing it for about 5 monthshave been very successfulbut I know with the few # of hands played (just over 11k) there is no reason to get excited. Here is my system:
I keep track of the number of hands lost vs. number won. I know, in the long run, the win/loss % is 47.5/52.5. I count on long losing streaks and then the math to take over and start bringing me back towards that 50/50 ratio. For example:
I start out betting 2 units. I count my wins and losses. Win = +1, Loss = 1. I bet 2 units until I reach a 6 count. At that point I ramp to 10 units. I continue to play untilt the count is even (I stop), or the count goes to 12 (I ramp up to 15 units. I continue to play until the count is 2 (I stop) or the count goes to 18 (I ramp up to 20 units). I continue to play until the count
reaches 5 (I stop) of goes to 25 (I ramp up to 25 units).
I have never gone beyond 28, and this only one time in 5 months.
I know this seems ridiculous to some of you. However, just as sure as the math says that the casino has a small edge over perfect basice strategy, it also says that my long term win loss ratio will approach 48/52.
I like to play 100 hand sessions. Occasionally, if the count is high, I will go up to 200 hands. Yes, I have losing sessions (about 1 in 6), but until now my wins have far exceeded my losses.
My heart wants to believe this will work long term, but my head tells me this has already been tried and there is a professional out there that can show me the error of my ways! I have learned a lot about blackjack and counting from this website and I would like to thank the pros who take the time to respond to questions like theses!

February 12th, 2008, 03:30 PM


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Location: Los Angeles, CA
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Quote:
Originally Posted by adventureboy
I count on long losing streaks and then the math to take over and start bringing me back towards that 50/50 ratio.

Your system is based on the Gambler’s Fallacy:
“If a fair coin is tossed repeatedly and tails comes up many times in a row, a gambler may believe, incorrectly, that heads is more likely on the following toss. This is an informal fallacy.”
http://en.wikipedia.org/wiki/Gambler%27s_fallacy
There is no reason to think that the wins and losses are going to immediately start evening out. In fact, it may take thousands or even millions of hands for the number to approach the expected ratio. What makes things worse is that even though the percentages are getting closer to what you would expect, the absolute differences will tend to get bigger!
For example, you would expect a fair coin flip to have a 50/50 distribution of heads and tails. But what happens when you bet your money on it? Let’s see.
You decide to bet $1 on tails and see how things go. After 10 flips there have been 8 heads and 2 tails. You have lost $6 so far. Using your logic you would continue betting on tails because you expect it to even out to 50/50. After 100 flips there have been 55 heads and 45 tails. That’s a little closer to 50/50, but now you’ve lost $10 in the process. After 1,000 flips there have been 515 heads and 485 tails. Still closer, but now you’re down $30. After a grueling 10,000 flips there have been 5050 heads and 4950 tails. Now we’ve got a 50.5/49.5 ratio, which is darn close to 50/50, but you’ve lost $100. Even though the percentages are getting closer to 50/50, the actual number of flips is getting farther away and you’re losing money along the way.
Listen to your head and ignore your heart. I know that you want this to work, but I can tell that you know better.
Sonny

February 12th, 2008, 09:40 PM


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Join Date: Nov 2005
Location: SoCal
Posts: 10,532


Quote:
Originally Posted by Sonny
Your system is based on the Gambler’s Fallacy:
“If a fair coin is tossed repeatedly and tails comes up many times in a row, a gambler may believe, incorrectly, that heads is more likely on the following toss. This is an informal fallacy.”
http://en.wikipedia.org/wiki/Gambler%27s_fallacy
There is no reason to think that the wins and losses are going to immediately start evening out. In fact, it may take thousands or even millions of hands for the number to approach the expected ratio. What makes things worse is that even though the percentages are getting closer to what you would expect, the absolute differences will tend to get bigger!
For example, you would expect a fair coin flip to have a 50/50 distribution of heads and tails. But what happens when you bet your money on it? Let’s see.
You decide to bet $1 on tails and see how things go. After 10 flips there have been 8 heads and 2 tails. You have lost $6 so far. Using your logic you would continue betting on tails because you expect it to even out to 50/50. After 100 flips there have been 55 heads and 45 tails. That’s a little closer to 50/50, but now you’ve lost $10 in the process. After 1,000 flips there have been 515 heads and 485 tails. Still closer, but now you’re down $30. After a grueling 10,000 flips there have been 5050 heads and 4950 tails. Now we’ve got a 50.5/49.5 ratio, which is darn close to 50/50, but you’ve lost $100. Even though the percentages are getting closer to 50/50, the actual number of flips is getting farther away and you’re losing money along the way.
Listen to your head and ignore your heart. I know that you want this to work, but I can tell that you know better.
Sonny

You big spoil sport  now he'll start losing because you smashed his delicate belief system! zg

February 13th, 2008, 08:14 AM


Executive Member


Join Date: Apr 2006
Posts: 5,141


elegant attempt adventure boy! but no cigar
IMHO your thought process is first rate just applied against a hidden factor summarized by the capricious gambler's fallacy wherein our gift of recognizing patterns leads us astray when up against phenomenon shrouded by the confusion of dependent and independent events. the law of averages may be valid but alas anything can and will happen in the short term and with the odds stacked against us from the get go the short term can end up an eternity of hell
beware of smoke and mirrors
hopefully i can take my own advice lol cause this is a tough one for me as well.

February 13th, 2008, 06:03 PM

Member


Join Date: Mar 2007
Location: southern US
Posts: 40


Quote:
Originally Posted by Sonny
Your system is based on the Gambler’s Fallacy:
“If a fair coin is tossed repeatedly and tails comes up many times in a row, a gambler may believe, incorrectly, that heads is more likely on the following toss. This is an informal fallacy.”
http://en.wikipedia.org/wiki/Gambler%27s_fallacy
There is no reason to think that the wins and losses are going to immediately start evening out. In fact, it may take thousands or even millions of hands for the number to approach the expected ratio. What makes things worse is that even though the percentages are getting closer to what you would expect, the absolute differences will tend to get bigger!
For example, you would expect a fair coin flip to have a 50/50 distribution of heads and tails. But what happens when you bet your money on it? Let’s see.
You decide to bet $1 on tails and see how things go. After 10 flips there have been 8 heads and 2 tails. You have lost $6 so far. Using your logic you would continue betting on tails because you expect it to even out to 50/50. After 100 flips there have been 55 heads and 45 tails. That’s a little closer to 50/50, but now you’ve lost $10 in the process. After 1,000 flips there have been 515 heads and 485 tails. Still closer, but now you’re down $30. After a grueling 10,000 flips there have been 5050 heads and 4950 tails. Now we’ve got a 50.5/49.5 ratio, which is darn close to 50/50, but you’ve lost $100. Even though the percentages are getting closer to 50/50, the actual number of flips is getting farther away and you’re losing money along the way.
Listen to your head and ignore your heart. I know that you want this to work, but I can tell that you know better.
Sonny

Well, I certainly would not predict when a winning hand is comming. I know I may lose 1020 hands in a row at any given time. However, I do not believe that I can lose 100 hands in a row. As losses continue to rise and draw me away from the 48% win expectaion, I do believe it becomes more likley that the trend will reverse and start back toward expectation. The question is, how far can it go....and can my bankroll withstand it? To that end, I pose the following question:
In a game of 1000 hands, what is the most hands one could lose playing perfect basic strategy? We would "expect" to win 480. How far could we go below that? 380, 280, 180? I am not sure how to go about answering that question. It seems to me that if we go into a game knowing the minimum number of wins possible that you could curve fit a system to break even (or keep losses manageable) in the event that the worst happened.
Of course, I could be wrong....and probably am!

February 13th, 2008, 07:54 PM

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Join Date: May 2006
Location: NYC
Posts: 6,696


If you were to come up with a betting system that promised a profit if you win only any 28% of your hands in the long run,you would be on to something,provided you had the BR to back your play. Basing a system on winning 48% is a sure fire way to go broke.

February 14th, 2008, 09:31 AM


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Join Date: Mar 2006
Location: Los Angeles, CA
Posts: 4,748


Quote:
Originally Posted by adventureboy
I know I may lose 1020 hands in a row at any given time. However, I do not believe that I can lose 100 hands in a row.

It is rare, but it can happen. Just because something is unlikely doesn’t mean it is impossible. It’s safe to say that it probably won’t happen to you in your lifetime, but you can’t rule it out. It's going to happen to somebody eventually.
And besides, you don’t have to lose them all in a row. Most of the time your losing streaks will have a few wins and pushed mixed in. Your system is based on the total number of wins and losses so it doesn’t matter if they are consecutive or not.
Quote:
Originally Posted by adventureboy
As losses continue to rise and draw me away from the 48% win expectaion, I do believe it becomes more likley that the trend will reverse and start back toward expectation.

There are three problems with that approach. First, you have no idea when the trend will reverse. The losing streak may continue for another 100 hands, or 1,000 or 10,000 before the results begin to shift back. As I said before, you have no reason to think that the reversal will happen now. The losses don’t have to be consecutive either, so the probability of a gradual losing streak is much higher than that of an uninterrupted losing streak.
But the trend doesn’t even matter. As I showed, the number of hands that you lose is likely to get larger even though the percentages are approaching the expected 48%. You are losing more money even though the results are slowly regressing. Even when your system works you are still losing money.
Lastly, the house still has the advantage over you. It doesn’t matter how many hands you lose, you are always more likely to lose the next one. Remember that the house gets its edge from the fact that you have to play your hand first. If you bust then you automatically lose even if the dealer busts too. That asymmetry is what makes the percentages unbeatable. It doesn’t matter if you lose 100 hands in a row, you still have to play your hand first so you are still a 48% underdog on every single hand that you play. If you include pushed then you are always a 43% underdog. In short, the trends can’t help you when the game is designed to favor your opponent on every single hand.
Quote:
Originally Posted by adventureboy
In a game of 1000 hands, what is the most hands one could lose playing perfect basic strategy?

Well, you could lose all 1,000 couldn’t you? In fact, if you factor in splits and doubles then you could end up losing up to 8,000 bets in 1,000 hands. Obviously that would be very unlikely, but you still have to consider it.
Quote:
Originally Posted by adventureboy
We would "expect" to win 480. How far could we go below that? 380, 280, 180? I am not sure how to go about answering that question.

What you are describing is the standard deviation from the mean. In this case the mean, or average result, would be 480. The standard deviation will tell you what sort of results to expect in the short term. It will give you an idea of how far above or below your results might be from the average. For example, it may tell you that for 1,000 hands you would expect a result of 480 wins plus or minus 36 hands. Here is a good introduction to standard deviation:
http://www.blackjackforumonline.com/...g_And_Risk.htm
That should explain how to find the numbers you are looking for. Feel free to ask any questions.
Sonny
Last edited by Sonny; February 14th, 2008 at 09:36 AM.

February 14th, 2008, 11:06 AM


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Join Date: Apr 2005
Location: Minnesota
Posts: 1,625


Feeling free to ask a question...
Quote:
Originally Posted by Sonny

Maybe I’m gonna have a breakthrough in understanding here!
I understand everything about the chart in that article, except where the SD% comes from. For example, that chart is based on 60 hands per hour. If I wanted to make a chart like that for 80 hph, where would I get the new SD% numbers from? If someone could explain that (as if to a small child, please), it would be wonderful.

February 14th, 2008, 11:54 AM


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Join Date: Mar 2006
Location: Los Angeles, CA
Posts: 4,748


Quote:
Originally Posted by Canceler
If I wanted to make a chart like that for 80 hph, where would I get the new SD% numbers from?

Here’s a little more detail about what Snyder is doing in that article:
The standard deviation for one hand of BJ is about 1.15 units (I believe Snyder’s article uses 1.1 so we’ll stick with that for now). This is because of splits, doubles, blackjacks, and other things that skew the results. In order to find the SD for any number of hands, all you have to do is multiply 1.1 by the square root of the number of hands. In that article Snyder assumes 60 hands per hour so the SD for 1 hour of play is 1.1 * sqrt(60) = 8.52 units. Now we know that we will expect to be at –0.32 units plus or minus 8.52 units 68% of the time, and plus or minus 17.04 units 95% of the time.
If you want to use 80 hands per hour instead, just substitute 80 for 60 in the formula above. So for 1 hour of play your SD = 1.1 * sqrt(80) = 9.84 units.
Quote:
Originally Posted by Canceler
I understand everything about the chart in that article, except where the SD% comes from.

The SD% is just the SD (in units) divided by the number of hands per hour (or action). At $80 per hour with a SD of 9.84 units your SD% = 9.84 / 80 = 12.3%.
Sonny

February 14th, 2008, 01:20 PM


Executive Member


Join Date: Apr 2005
Location: Minnesota
Posts: 1,625


It works!
Thank you, Sonny! Now I'm finally getting it.
(The worst part is that in college I got a 4.0 in Statistics, but that was 30 years ago.)

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