New method of playing!

Hi I have been using a method of playing that I made up and I was wondering if anyone can tell me based on my evidence if my method would work for the long term or if there is any holes/inconsistencies in my statistics. Also how many hands would I need to play before I would know that my method would be successful? Here is my information:

I used the Blackjack simulator on this website
6 deck shoe
hands played: 8,073
bet size: $5-$30
win percentage: 43.8127%
total earnings: $2,342
Worst streak of shoes: -$830
Best streak of shoes: $1,586

best 10 shoes vs. worst 10 shoes
1. $650 1. -$251
2. $473 2. -$230
3. $303 3. -$215
4. $288 4. -$213
5. $268 5. -$198
6. $260 6. -$192
7. $248 7. -$162
8. $235 8. -$153
9. $210 9. -$150
10. $207 10. -$148

Hi I have been using a method of playing that I made up and I was wondering if anyone can tell me based on my evidence if my method would work for the long term or if there is any holes/inconsistencies in my statistics. Also how many hands would I need to play before I would know that my method would be successful? Here is my information:

I used the Blackjack simulator on this website
6 deck shoe
hands played: 8,073
bet size: $5-$30
win percentage: 43.8127%
total earnings: $2,342
Worst streak of shoes: -$830
Best streak of shoes: $1,586

best 10 shoes vs. worst 10 shoes
1. $650 1. -$251
2. $473 2. -$230
3. $303 3. -$215
4. $288 4. -$213
5. $268 5. -$198
6. $260 6. -$192
7. $248 7. -$162
8. $235 8. -$153
9. $210 9. -$150
10. $207 10. -$148

1) You didn't explain what you system is. That would save you and us a lot of time. Although possible, it is unlikely you've come up with something that we haven't already seen.

2) Comparing best 10 shoes vs worst 10 shoes is irrelevant because it's easy to skew the results by using a progression. Based on your results, I would guess you are using a negative progression like Martingale, and you didn't play sufficient hands to hit the inevitable losing streak that will wipe all your wins.

3) 8000 hands is nowhere near enough to evaluate the efficacy of a system in the long run. You need numbers in millions of hands to have reasonably accurate win rate. If you really need it to be accurate to a couple of decimal points, you need about billion hands.

Warning: if your system is a progression, please do yourself and us a favor by not starting a long thread trying to convince us that your system is viable. Such systems have already been disproven mathematically and insisting otherwise would result in nothing but disruption.

I previously posted a message requesting information regarding how many hands it takes in an online simulation or program to reach statistical significance.

Although I don't recall who posted the response, I was told that it was somewhere between 7,500 hands and 50,000 hands, depending upon the type of game being simulated.

You are now saying that a simulation is not statistically significant until it reaches into the millions of hands. Which is correct?

If you run a simulation of say 50,000 hands, and the results match the percentage results for wins (43+%), losses (48+%) and pushes (8+%), doesn't this reach statistical significance?

I am totally confused. Please advise.

I previously posted a message requesting information regarding how many hands it takes in an online simulation or program to reach statistical significance.

Although I don't recall who posted the response, I was told that it was somewhere between 7,500 hands and 50,000 hands, depending upon the type of game being simulated.

You are now saying that a simulation is not statistically significant until it reaches into the millions of hands. Which is correct?

If you run a simulation of say 50,000 hands, and the results match the percentage results for wins (43+%), losses (48+%) and pushes (8+%), doesn't this reach statistical significance?

I am totally confused. Please advise.

The problem is that your standard deviation / hand is high in relation to your initial expected value / hand. The standard deviation grows by square root of the number of hands simulated, while the EV grows linearly.

Consider the following example where the EV = 1%, the SD = 1.15 per hand, and the average bet is $10.

After 50,000 hands, the EV = 50,000 * 1% * $10 = $5,000, whereas the SD is 1.15 * sqrt (50,000) * $10 = $2,571. This means there is 68% chance that the simulation result will fall within 1 SD (between $2,429 and $7,571). There is a 95% chance for 2 SD and 99% for 3 SD.

For a 1,000,000 hands, the EV = $100,000, and the SD = $11,500.

For a 1,000,000,000 hands, the EV = $100,000,000 and the SD = $363,662. At this point, even if your simulation result is 3 SD from the real EV, your result will be off by 1%. In this case, your sim will result in an EV = 1.01% instead of the actual 1.00%. (For 50,000 hands the error for 3 SD is 146%, for 1 million hands, the error is 35%).

So, you can easily see that a huge number of samples is needed to have a reasonable assurance that the result is accurate.

I understand the large variation with only playing 8,000 hands, but isnt there some point when you would at least know this method is affective. I understand that for accuracy you must play a billion hands, but I am more interested if this method works or doesnt. I apologize if it seems obnoxious for me to not put my method up here, but it is not martingale or progressive. So then what Im really wondering is how many hands would I need to play just to know if my method would produce positive outcomes, for right now Im not as concerned with how specific those outcomes are.

I understand the large variation with only playing 8,000 hands, but isnt there some point when you would at least know this method is affective. I understand that for accuracy you must play a billion hands, but I am more interested if this method works or doesnt. I apologize if it seems obnoxious for me to not put my method up here, but it is not martingale or progressive. So then what Im really wondering is how many hands would I need to play just to know if my method would produce positive outcomes, for right now Im not as concerned with how specific those outcomes are.

The quick answer is about 1,000,000. That's the number I use when trying to determine whether or not a system worth further study.

Thanks for your thoughtful response. However, although I am a rabid blackjack player, I am not a mathematical person and have no head for it. So, your message sounded like Polish to me.

Is there a resource I can go to to study so that I can possibly understand what you are trying to tell me?

I really would like to understand. The resolution of this issue is very important to me.

Thanks in advance for the guidance.

Thanks for all your help. I would like to run my system through a simulation so that I can get that many hands, do you know how I could do that. or the formulas I would need.

Thanks for your thoughtful response. However, although I am a rabid blackjack player, I am not a mathematical person and have no head for it. So, your message sounded like Polish to me.

Is there a resource I can go to to study so that I can possibly understand what you are trying to tell me?

I really would like to understand. The resolution of this issue is very important to me.

Thanks in advance for the guidance.

This is will be difficult to do, as the concepts are difficult even for people who do understand mathematics.

First of all we have expected value. This is how much you expect your bet to make over the long run. For example, if you have a 10% advantage for a particular bet, over the long run, you will make $1 for every $10 you bet.

The problem is that you will rarely win exactly 10%. If you make 100 $10 bets, while you expect to win 100 * $10 * 10% = $100, most likely your actual result will fall + or - of that value. If you are running a simulation to calculate your advantage, you would not want to have a misleading number that resulted from a random error.

You are probably familiar with the bell curve. If you run a series of simulations to calculate your advantage and plotted the results in a histogram, you would expect the histogram to look like a bell curve, where the hump in the middle represents the true expected value. The results to the left are too low and the ones to right are too high. How confident are you that your simulated result is near the actual value?

This is where standard deviation comes in. For a given simulation, there is a standard deviation. If you were to look at the bell curve, the results that between EV-SD and EV+SD would comprise about 68% of all the results. Looking at this in reverse, this means a given result has 68% chance of being within 1 SD of the true value. Within 2 SD, it's 95%, and within 3 SD, it's 99%.

So the key here is reduce your SD relative the expected value. The way you do this is increase the number of trials in the simulation. This is because SD increases by the square root of the number of trials, while the expected value increases in direct proportion.

So, if you're making $10 bets with a 1% advantage and your SD is 1.15/hand, your EV/hand = $0.1 while your SD/hand = $11.50.

If you make a 100 bets, your EV=$10, and your SD = $11.50. Since 3 SD = $345, that means there is a 99% chance your result will be between -$335 and +$355. If you were to try to determine your advantage there is a 99% change it would be between -33.50% and + 35.50%. It would be very difficult to have any confidence in your result which such a large range.

If you make 10,000 bets, your EV=$1000 and your SD= $1150. In the case, your advantage has a 99% chance your result of being between -2.45% and +4.45%. Again, this sample is clearly too small to be "statically significant." It might be good for an opinion poll with a 3% margin of error*.

Following are the EV, SD, and 99% range for a given number of bets:

1 million: EV=$100,000, SD=$11,500, 99%=+0.66% to +1.35%
100 million: EV=$10 million, SD=$115,000, 99%=0.97% to 1.03%
10 billion: EV=$1 billion, SD=$1,150,000, 99%=1.00% to 1.00%.

As you can see, the more trials you have, the higher your confidence is that your simulated advantage falls near the actual advantage.

I hope this helps.

* Opinion polls are slightly different because they poll a sample from a limited population. In a blackjack simulation, the population size is infinite.

Thanks for all your help. I would like to run my system through a simulation so that I can get that many hands, do you know how I could do that. or the formulas I would need.

That would depend on the system. I'm kind of familiar with how CVCX and BJRM work. Both are good with coming up with the advantage and SCORE for systems that involve counting, but IMHO are weak with wonging in and out, as well as spreading between 1 and 2 hands. I don't think either will handle a progression system, but I could be wrong.

Personally, I either write my own program (as for calculating Lucky Ladies) or I use Sage Blackjack (registered version) available at www.s-a-g-e.com. Sage Blackjack has the capacity for wonging in and out and progressions, but does not calculate SCORE. I can use its statistics to come up with a SCORE value that is slightly less than the actual SCORE because it can't handle multiple indices for the same situation like hitting, standing, or surrending 16v10. It also treats split bets as single bets instead of combining them.

There are other choices available, but I'm don't know any well enough.

Panama Rick wrote:

So, if you're making $10 bets with a 1% advantage and your SD is 1.15/hand, your EV/hand = $0.1 while your SD/hand = $11.50.

If you make a 100 bets, your EV=$10, and your SD = $11.50. Since 3 SD = $345...

That last $11.50 should have been $115.00.

Despite this small flaw, a very informative answer, Panama Rick!

Dog Hand

Thanks for the informative response. I think I understand what you are saying. My high school math classes are starting to come back to me (horror of horrors!) However, you stated:

"This is where standard deviation comes in. For a given simulation, there is a standard deviation. If you were to look at the bell curve, the results that between EV-SD and EV+SD would comprise about 68% of all the results. Looking at this in reverse, this means a given result has 68% chance of being within 1 SD of the true value. Within 2 SD, it's 95%, and within 3 SD, it's 99%."

My stupid question is as follows: What constitutes one "standard deviation"? Graphically, as it relates to the bell curve, what does a standard deviation represent?

Thanks again in advance for the assistance. This is all starting to make some sense to me now.

It represents how much something deviated from what was the expected result. Sometimes you get results that are ahead of expectation, other times you gets results that are well behind expectation. The more you play (consistantly), the more likely the theoretical expectation will eventually happen. It's a temporary situation that swings back and forth.

Let me add my thanks to Panama Rick for his great explanation.

My stupid question is as follows: What constitutes one "standard deviation"? Graphically, as it relates to the bell curve, what does a standard deviation represent?

Standard deviation represents luck. When playing, negative SD represents bad luck, positive SD represents good luck. In the short term, your results are largely due to luck, either good or bad. In the long term, luck has very little to do with it.

Thanks again in advance for the assistance. This is all starting to make some sense to me now.

Glad I could be of help.