http://mathworld.wolfram.com/BinomialDistribution.html

Spreadsheets like excel also have built in formulas for these type of calculations.

Quote:daveylbraHey guys, sorry I didn't mean to cause arguments.

I think we are ALL agreed, though, that a very large n flips of a coin (to simplify) will

result in a close proximity to 50% each.

Now, can we get to this stage-

Probability of < x% heads in n flips? Anyone know the formula for this?

then we might get to-

Probability of <34% reds in n spins. (we will have to consider that for 1 spin, probability is 48.65%, not 50%)

This will tell us the probability we won't win 1/3 of our bets in n spins, which would be a more practical use

of our knowledge. Can anyone help?

I'm not sure why you think winning 1/3 of your bets is going to produce a profit with the labouchere progression. I'm guessing it's because you add 1 number to the line on a loss, and subtract 2 numbers on a win. If you play the system, though, you would need to win 1/2 of your bets, not 1/3.

Just quickly if you started the line with...

1-2

you lose and add 3

1-2-3

you lose again add 4

1-2-3-4

That's 2 losses. So, in order to end the labouchere you would need 2 wins.

You bet 5 and win, subtract the 1 and 4, you're left with...

2-3

You bet 5 again and win, subtract the 2 and 3, and you've cleared the line.

The end result was 2 losses, and 2 wins or 50%.

So, for the labouchere progression you would still need the Law of Large Numbers, a legitimate LLN.

So, if your going to use a computer simulator, make sure that the RNG is not cheating the LLN. You can check at each "large number" intervals to make sure the percentage is getting closer to the mean. If the LLN is being broken then the whole simulation is worthless, but the Simulators won't check this for you, so you have to check it yourself.

OnceDear, please don't respond to my posts,, I've blocked you and tringlomane as well, for your horrific math.

Quote:JyBrd0403I'm not sure why you think winning 1/3 of your bets is going to produce a profit with the labouchere progression. I'm guessing it's because you add 1 number to the line on a loss, and subtract 2 numbers on a win. If you play the system, though, you would need to win 1/2 of your bets, not 1/3.

Just quickly if you started the line with...

1-2

you lose and add 3

1-2-3

you lose again add 4

1-2-3-4

That's 2 losses. So, in order to end the labouchere you would need 2 wins.

You bet 5 and win, subtract the 1 and 4, you're left with...

2-3

You bet 5 again and win, subtract the 2 and 3, and you've cleared the line.

The end result was 2 losses, and 2 wins or 50%.

So, for the labouchere progression you would still need the Law of Large Numbers, a legitimate LLN.

So, if your going to use a computer simulator, make sure that the RNG is not cheating the LLN. You can check at each "large number" intervals to make sure the percentage is getting closer to the mean. If the LLN is being broken then the whole simulation is worthless, but the Simulators won't check this for you, so you have to check it yourself.

OnceDear, please don't respond to my posts,, I've blocked you and tringlomane as well, for your horrific math.

I fully expect you will continue to get responses to your calculations whether you like them or not. This forum does not allow bad advice or information to go unchallenged. It's part of its basic purpose. So block anyone you like, preferably without making a public point of it, but don't think you have the right to stop them from commenting.

Uh oh, better watch out or JyBrd might block you for "horrific commenting."Quote:beachbumbabsI fully expect you will continue to get responses to your calculations whether you like them or not. This forum does not allow bad advice or information to go unchallenged. It's part of its basic purpose. So block anyone you like, preferably without making a public point of it, but don't think you have the right to stop them from commenting.

I wonder if he's blocked the Wizard yet...

Quote:beachbumbabsI fully expect you will continue to get responses to your calculations whether you like them or not. This forum does not allow bad advice or information to go unchallenged. It's part of its basic purpose. So block anyone you like, preferably without making a public point of it, but don't think you have the right to stop them from commenting.

Just letting them know that I will not be able to read their posts, so they are not directing their posts at me, as OnceDear had earlier.

Just like I'm blocking you now BBB, so you don't have to bother sending another posts directed at me, like the one above. I won't be reading it.

I thought it would be nice to let you know that, my bad.

Quote:MathExtremistUh oh, better watch out or JyBrd might block you for "horrific commenting."

Quote:JyBrd0403Just like I'm blocking you now BBB, so you don't have to bother sending another posts directed at me, like the one above. I won't be reading it.

Man, you can't make this up.

Quote:MathExtremistMan, you can't make this up.

Oh please..... Please Mike, Please wade in with your Wizardy Wisdom and show JyBrd403 some maths, any maths, just so we can get the spectacle of Wizard being blocked on his own forum.

From wikipedia, labouchere system - "Theoretically, because the player is cancelling out two numbers on the list for every win and adding only one number for every loss, the player needs to have his proposition come at least 33.34% to eventually complete the list. For example, if the list starts with seven numbers and the player wins five times and loses three (62.5% winning percentage) the list is completed and the player wins the desired amount, if the list starts with seven numbers and the player wins 43,600 times and loses 87,193 times (33.34% winning percentage) the list completes and the player wins."

Similarly, I understood Labouchere to require one third plus one bets, out of the total bets, to win.

BUT, suppose I start with 1,1,1,1,1. I lose the first 9 bets.

I have 1,1,1,1,1,2,3,4,5,6,7,8,9, 10. I have lost 54 units. (2+3+4+5+6+7+8+9+10)

I then win 6 bets. I have 3,4. I have won 52 units in those 6 bets. (11+10+9+8+7+7)

I have won 6 out of 15 bets. This is a third plus one. But I am still clearly down!

Can someone please explain?? Is there a certain number of total bets required before the one third plus one law 'kicks in?'

Very true. But what I've often wondered is this: Does a baseball team have a memory? If an average baseball team lost 8 in a row would it be more likely than usual to win one of the next 4 games? Assuming no super pitchers are involved. It would seem like they would want very badly and try very hard to have a winning game and end their losing streak. More so than their opposing team would want to keep their losing streak alive. I really don't know the answer to this. It would take an awful lot of data mining to answer the question. But if I had to express an opinion I would say that they are more likely than usual to win one of their next four games.

Quote:OnceDearOh please..... Please Mike, Please wade in with your Wizardy Wisdom and show JyBrd403 some maths, any maths, just so we can get the spectacle of Wizard being blocked on his own forum.

This would be hilarious.