Roulette Mathematical Advantage
December 23rd, 2012 at 12:35:09 PM
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As strenuously as you object to my system, your frustration doesn't change anything. I have already repeated said that every spin has a negative expectation. However, by combining spins into bets, there is no negative expectation. If I suggested that you walk up and plunk a unit down on 2nd and 3rd for the next 3 hours, regardless of what happens, you would be completely correct that I'm doomed. I haven't suggested that, and I have no plans to. What I am saying is that if you walk up the casino and make exactly 1 bet, regardless of how many spins it takes to resolve that bet, with you quitting after a win or a loss but spinning as long as you get repeats, you have a positive expectation.
December 23rd, 2012 at 12:36:43 PM
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Quote: rdw4potusDude, seriously, NO. No amount of bankroll management does anything at all (even a little bit) to change the fact that the game has a negative expectation on every spin.
But it's not based on every spin. It's based on every bet :P
I know nothing!
December 23rd, 2012 at 12:37:27 PM
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Quote: colbsterAs strenuously as you object to my system, your frustration doesn't change anything. I have already repeated said that every spin has a negative expectation. However, by combining spins into bets, there is no negative expectation.
What you're saying, almost literally, is that -2.7+-2.7=>1. How am I - how is anyone - supposed to take you seriously?
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
December 23rd, 2012 at 12:40:12 PM
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So if the spins have a negative expectation, and your bet is based off of stringing spins together, then your bet also has negative expectation.
Because more than 1 spin just has a more negative expectation.
The only thing that can make any series of spins positive expectation is being the house (I guess wheel bias and wheel clocking, but let's assume that's not happening.)
Because more than 1 spin just has a more negative expectation.
The only thing that can make any series of spins positive expectation is being the house (I guess wheel bias and wheel clocking, but let's assume that's not happening.)
December 23rd, 2012 at 12:49:51 PM
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deleted
DUHHIIIIIIIII HEARD THAT!
December 23rd, 2012 at 12:54:16 PM
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Quote: PM from Colbster
I'm new, so it limits my responses. Please post a message online so everyone knows I am not stopping this line of discussion.
Take this example
1 -2
1 -2
1 -2
1 -2
1 -2
1 -2
1 -2
1 -2
1 -2
1 -2
1 -2
1 -2 (12 chances of -2)
2 then 1 -1
2 then 1 -1
2 then 1 -1
2 then 1 -1
2 then 2 then 1 0
2 then 2 then 2 3+
2 then 2 then 3 3
2 then 2 then 3 3
2 then 3 2
2 then 3 2
2 then 3 2
2 then 3 2
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
I have shown 36 spins with 1/3 in each dozen (12 x -2, 12 x +1, and then 12 repeats). The 12 repeats have a net of 13+ because we don't know how many repeats could appear. -24+12+13.xxx gives us a positive number.
The math doesn't lie!
and my response:
I'll post that, but...ummm...if the repeats don't result in a change in bet size, why do the repeats do anything at all other than result in a net win of 1? if there are 12 hits per dozen in 36 spins and you aren't changing your bet size, then you'll lose 24 from the unbet 12 hits, and win 24 from the bet 24 hits. that nets to 0, because the repeats don't affect your bet size or bet frequency or anything at all that would affect your return in the short term.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
December 23rd, 2012 at 1:38:46 PM
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Quote: colbsterWhat I am saying is that if you walk up the casino and make exactly 1 bet, regardless of how many spins it takes to resolve that bet, with you quitting after a win or a loss but spinning as long as you get repeats, you have a positive expectation.
You are wrong, of course. But 7 pages of trying to explain it to you have proven fruitless. As will any further attempts....
Please answer me this.... If you have a system that will win, why are you having this long winded internet diatribe? Why are you not just going to a casino and winning money, day after day, week after week, etc....
December 23rd, 2012 at 1:50:52 PM
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Quote: colbster
By extending the odds of each level out, this method gives a positive expectation of +3.xxx units over a single 0 table, better than +1.xxx on a 0/00 table, and better than +5.xxx on no-zero tables (if you are lucky enough to find them).
The method does not give you those. Your fuzzy math does. If you're trying to sell some kind of "winning method" on roullette, don't go into all the math mumbo-jumbo. The smart people will know that you don't have an understanding of probability theory. The dumb people will just get confused. Just say, "I made $1 million playing by this method, and so can you! (For a small fee)."
All the email scams about Nigerian princes asking for money is ridiculous for a reason. It's to weed out the smart people and to target the most vulnerable people:
http://www.npr.org/blogs/money/2012/06/22/155581764/those-nigerian-email-scams-are-ridiculous-for-a-reason
If you're not selling anything and you are sincerely pursuing the probability of roullette wheels, I apologize. I hope you find the answer.
December 23rd, 2012 at 1:57:13 PM
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Quote: colbsterWhat I am saying is that if you walk up the casino and make exactly 1 bet, regardless of how many spins it takes to resolve that bet, with you quitting after a win or a loss but spinning as long as you get repeats, you have a positive expectation.
Just a gem. In other words, if there is any possibility that you can be ahead, you have a positive expectation. By this definition, all casino games have positive expectations!!!
He should be a marketing director for casinos. New slogan, "playing the slots as long as you can someday be 1 cent over what you put in at some point, you have a positive expectation!"
December 23rd, 2012 at 1:58:07 PM
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Quote: colbsterAs strenuously as you object to my system, your frustration doesn't change anything. I have already repeated said that every spin has a negative expectation. However, by combining spins into bets, there is no negative expectation. If I suggested that you walk up and plunk a unit down on 2nd and 3rd for the next 3 hours, regardless of what happens, you would be completely correct that I'm doomed. I haven't suggested that, and I have no plans to. What I am saying is that if you walk up the casino and make exactly 1 bet, regardless of how many spins it takes to resolve that bet, with you quitting after a win or a loss but spinning as long as you get repeats, you have a positive expectation.
Ok, here's the thing. Expectation is additive. You can't change that. If your expectation on each spin is -$1, then your expectation on any set of 10 spins is -$10, and your expectation on any 100 spins is -$100. It doesn't matter how you group them, and it doesn't matter what you call them. This is a mathematical theorem. If you are saying that this is wrong, then you may as well say that 1+1 = 6 or that an odd number multiplied by an odd number is even. You can't be right, because there is a mathematical theorem that says you are wrong.
FWIW, Buzz's comment about someone who sells every item at a loss but hopes to make it up in volume is spot on. That is exactly what you are doing. You are giving away 2.7% in expectation every spin (by your own admission) but hoping to make it up by grouping them into these multi-spin "bets". You might as well give me $100 every 5 minutes and hope to come out ahead by grouping the giveaways into "promotional periods". In fact, I'd much prefer if you did this.
In short:
1. Expectation is additive
2. Addition is associative. If you don't know what associative means, look here: http://en.wikipedia.org/wiki/Associative_property
So put those parentheses wherever you'd like; just keep those $100 bills flowing in my direction.
December 23rd, 2012 at 2:22:41 PM
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Quote: colbsterI have had some fair size losses and some fair size wins,.
And in the long run they will even out so you're
losing right at the house edge.
I so decree by the power vested in me by the
Roulette Council in ancient Gaul...
"It's not called gambling if the math is on your side."
December 23rd, 2012 at 2:50:15 PM
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Quote: colbsterNo, it is only -2.7 on the first spin. Once you have already taken the +1 from a repeat, your new payouts would be 13x-1, and 24x+2, meaning that once you have gotten a repeat, your spins expected value is +0.3.
And there's the flaw in your analysis.
The expected value is -2.7% on the first spin if you count the second 12 as +1. However, you are carrying it over to the next spin, so as far as that first spin is concerned, the second 12 pays +0 "on the first spin", making the expected value of the first spin (13 x -2 + 12 x 0 + 12 x +1) / 37 = -37.84%.
December 23rd, 2012 at 3:25:48 PM
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Let me get my terms all defined:
A "Spin" is pretty self explanatory.
A "Third" is a group of twelve numbers even though there are 37 numbers on a European wheel.
A "Bet" is a series of one or more spins where one unit is placed on the previously landed on third and another unit is placed on another third.
A bet is resolved when the ball lands in a third that is different than the previous third upon which it landed or the zero (what third do you bet on after a zero?).
The spin which eventually resolves the bet will either lose 2 or win 1.
So if the bet is resolved, which it must be, that spin will yield:
( 1 * 12/25 ) - ( 2 * 13/25 ) = -0.56
So can we get streaky enough to overcome that loss of 56 cents for every dollar bet?
Moving onto the next spin within a bet has a probability of 12 in 37 or 0.324..
Here are the calculated returns of the cumulative win at bet resolution:
I have this system losing 8 cents per dollar.
A "Spin" is pretty self explanatory.
A "Third" is a group of twelve numbers even though there are 37 numbers on a European wheel.
A "Bet" is a series of one or more spins where one unit is placed on the previously landed on third and another unit is placed on another third.
A bet is resolved when the ball lands in a third that is different than the previous third upon which it landed or the zero (what third do you bet on after a zero?).
The spin which eventually resolves the bet will either lose 2 or win 1.
So if the bet is resolved, which it must be, that spin will yield:
( 1 * 12/25 ) - ( 2 * 13/25 ) = -0.56
So can we get streaky enough to overcome that loss of 56 cents for every dollar bet?
Moving onto the next spin within a bet has a probability of 12 in 37 or 0.324..
Here are the calculated returns of the cumulative win at bet resolution:
| Spin | Result | Probability | Net |
|---|---|---|---|
| 1 | -2 | 0.351351351.. | -0.702702702.. |
| 1 | +1 | 0.324324324.. | +0.324324324.. |
| 2 | -1 | 0.1139517896 | -0.1139517896 |
| 2 | +2 | 0.1051862673 | +0.2103725347 |
| 3 | 0 | 0.0369573372 | 0.00 |
| 3 | +3 | 0.0341144651 | +0.1023433953 |
| 4 | +1 | 0.0119861634 | +0.0119861634 |
| 4 | +4 | 0.0110641508 | +0.0442566034 |
| 5 | +2 | 0.0038874043 | +0.0077748087 |
| 5 | +5 | 0.0035883732 | +0.0179418662 |
| 6 | +3 | 0.0012607798 | +0.0037823394 |
| 6 | +6 | 0.0011637967 | +0.0069827804 |
| 7 | +4 | 0.0004089016 | +0.0016356062 |
| 7 | +7 | 0.0003774476 | +0.0026421331 |
| 8 | +5 | 0.00013261672 | +0.0006630836 |
| 8 | +8 | 0.00012241543 | +0.0009793235 |
| 9 | +6 | 0.00004301083 | +0.0002580650 |
| 9 | +9 | 0.00003970230 | +0.0003573207 |
| 10 | +7 | 0.00001394946 | +0.0000976462 |
| 10 | +10 | 0.00001287642 | +0.0001287642 |
| Total: | 0.999987123 | -0.080127734 |
I have this system losing 8 cents per dollar.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
December 23rd, 2012 at 3:34:38 PM
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Quote: colbsterThe continuance of repeats makes this a very elegant method of beating the house advantage, which cannot possibly cost you more than 2 units while you are allowed to win as much as random wants to present you with.
Dude, this is just wrong. Unless you have a superior
bet selection which can accurately predict the next
spin, the house edge is written in stone. You yourself
don't understand how your system works or you'd be
able to explain how it works, which you can't. It looks
like you're playing all kinds of games with the math
and curve fitting it till you get an answer you like. Take
some money to the casino and see how they like your
system. And don't tell me you've been playing it for
years and won lots of money, thats what everybody
says who can't explain what they do. Like those are
credentials anybody believes.
"It's not called gambling if the math is on your side."
December 23rd, 2012 at 6:37:23 PM
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If anybody is interested, he proposed this system 2
years ago on another forum. A lot of thought has
gone into it. My question is that, 2 years later, how
come he still doesn't know if it works. Its
probably because it doesn't and he's here to find out
why not.
http://www.vlsroulette.com/index.php?topic=17692.0
years ago on another forum. A lot of thought has
gone into it. My question is that, 2 years later, how
come he still doesn't know if it works. Its
probably because it doesn't and he's here to find out
why not.
http://www.vlsroulette.com/index.php?topic=17692.0
"It's not called gambling if the math is on your side."
December 23rd, 2012 at 6:42:06 PM
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Once again, EvenBob is the voice of reason !
Shed not for her
the bitter tear
Nor give the heart
to vain regret
Tis but the casket
that lies here,
The gem that filled it
Sparkles yet
December 23rd, 2012 at 8:21:32 PM
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Shared this: https://docs.google.com/spreadsheet/ccc?key=0AlRSxZ2plqHPdGE2ZDNIUzZCY0JISjViQWtHaGZld3c
Looks to me like this system has 0 EV on a no-0 wheel. Color me not surprised...
Looks to me like this system has 0 EV on a no-0 wheel. Color me not surprised...
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
December 23rd, 2012 at 9:55:06 PM
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It's especially interesting to read the last page (page 7) of that thread.Quote: EvenBobIf anybody is interested, he proposed this system 2
years ago on another forum. A lot of thought has
gone into it. My question is that, 2 years later, how
come he still doesn't know if it works. Its
probably because it doesn't and he's here to find out
why not.
http://www.vlsroulette.com/index.php?topic=17692.0
Climate Casino: https://climatecasino.net/climate-casino/
December 23rd, 2012 at 11:10:06 PM
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I just read that. Seems that the OP has scammed some people there into trying his system, found that the average loss was exactly equal to the house edge times the number of spins (stop the presses!!!) and has moved over here?
Also, I wasn't aware that there were entire communities of people trying to come up with systems to beat roulette. It would never have occurred to me to look for that sort of thing. It's a little hilarious and a little sad at the same time.
Also, I wasn't aware that there were entire communities of people trying to come up with systems to beat roulette. It would never have occurred to me to look for that sort of thing. It's a little hilarious and a little sad at the same time.
December 24th, 2012 at 12:19:34 AM
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Quote: AxiomOfChoiceIt would never have occurred to me to look for that sort of thing. It's a little hilarious and a little sad at the same time.
Lots of roulette forums. Its their life's work, they're
obsessed with it. On some of those forums you get
banned for expressing a negative opinion about
somebody's system. I'm not joking.
"It's not called gambling if the math is on your side."
December 24th, 2012 at 1:28:48 AM
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FYP = "Roulette Mathematical Advantage For The House"
December 24th, 2012 at 3:40:41 AM
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Glad to have a new days worth of posting limits, although work forces me just this one right now. First, let me move back a couple pages and address some issues.
@AxiomofChoice: I understand what associative means. I appreciate your inclusion of a Wikipedia link to dumb it down for me, because I clearly am a mook with no grasp of the English language. A positive expectation is also additive and associative. The bets have a positive expectation.
@DebitnCredit: No, I'm not selling anything. I have nothing to sell - I have already freely given my contribution. I am as sincere and honest about this as anyone could be. If your hedged apology if this was the case was actual, it is gladly accepted with my wishes to you of a Merry Christmas.
@EvenBob: Where does it look like I am questioning if this works? From my first post, I have stated definitively that this works. I have also stated that it is an abstract that I struggle to apply to a bet selection because bet selections have built in weaknesses that can offset the slim advantage I have identified. I'm not looking why this doesn't work because it does. I am posting this in the same spirit as a theorist who posts in a peer-reviewed journal. I have something to share with the community. You can't prove something is correct, but you can prove it is incorrect. Nowhere in this thread have I seen a legitimate proof that actually addresses my system. All I have seen is the old 2.7 arguments and personal attacks. Read what I have written and you will see that this is different than what we have done in the past.
Finally, yes, there are lots of roulette forums and they contain a lot of laughable materials. There is a lot of hocus-pocus, numerology, Martingales and the like. Some of looser than others, but there are also some serious students of the game. I find it amusing that EvenBob states that its "their life's work, they obsessed with it" as if he is above it all. He admits that he frequents the same boards that I do, which he would not do if he were not hoping to find something that he hasn't found yet.
I love roulette. I look at it like many people consider chess. You can play a whole lifetime and still have something to learn. My enjoyment comes from the challenge of "beating" roulette and I enjoy coming up with new angles. I have proposed several over the years, but this one that I have posted here is my baby. I know it works. The math doesn't lie.
@AxiomofChoice: I understand what associative means. I appreciate your inclusion of a Wikipedia link to dumb it down for me, because I clearly am a mook with no grasp of the English language. A positive expectation is also additive and associative. The bets have a positive expectation.
@DebitnCredit: No, I'm not selling anything. I have nothing to sell - I have already freely given my contribution. I am as sincere and honest about this as anyone could be. If your hedged apology if this was the case was actual, it is gladly accepted with my wishes to you of a Merry Christmas.
@EvenBob: Where does it look like I am questioning if this works? From my first post, I have stated definitively that this works. I have also stated that it is an abstract that I struggle to apply to a bet selection because bet selections have built in weaknesses that can offset the slim advantage I have identified. I'm not looking why this doesn't work because it does. I am posting this in the same spirit as a theorist who posts in a peer-reviewed journal. I have something to share with the community. You can't prove something is correct, but you can prove it is incorrect. Nowhere in this thread have I seen a legitimate proof that actually addresses my system. All I have seen is the old 2.7 arguments and personal attacks. Read what I have written and you will see that this is different than what we have done in the past.
Finally, yes, there are lots of roulette forums and they contain a lot of laughable materials. There is a lot of hocus-pocus, numerology, Martingales and the like. Some of looser than others, but there are also some serious students of the game. I find it amusing that EvenBob states that its "their life's work, they obsessed with it" as if he is above it all. He admits that he frequents the same boards that I do, which he would not do if he were not hoping to find something that he hasn't found yet.
I love roulette. I look at it like many people consider chess. You can play a whole lifetime and still have something to learn. My enjoyment comes from the challenge of "beating" roulette and I enjoy coming up with new angles. I have proposed several over the years, but this one that I have posted here is my baby. I know it works. The math doesn't lie.
December 24th, 2012 at 4:53:46 AM
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Quote: colbster
I love roulette. I look at it like many people consider chess. You can play a whole lifetime and still have something to learn. My enjoyment comes from the challenge of "beating" roulette and I enjoy coming up with new angles. I have proposed several over the years, but this one that I have posted here is my baby. I know it works. The math doesn't lie.
You would get the same result from this system as you would from flipping 2 coins and using the result to bet dozens. 2 heads and you bet D1+2, two tails you bet D2+3, one head one tail you bet D1+3.
[This space is intentionally left blank]
December 24th, 2012 at 5:08:33 AM
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Quote: colbsterI have proposed several over the years, but this one that I have posted here is my baby. I know it works. The math doesn't lie.
You haven't answered my question. If you 'know' this system has a positive expectation, why are you not playing it? Why are you writing about it?
December 24th, 2012 at 7:24:02 AM
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Quote: colbsterAll I have seen is the old 2.7 arguments and personal attacks....The math doesn't lie.
Look harder.
Quote: my PM
OK, so after the 2nd dozen hits the first time, here's what to expect:
12 times, the 1st dozen hits and you lose 2
12 times the 3rd dozen hits and you win 1
4 times, the 2nd dozen hits once, and then the 1st dozen hits and you lose 1 (+1, -2, -1 net)
4 times, the 2nd dozen hits once, and then the 3rd dozen hits and you win 2 (+1, +1, +2 net)
1.33 times, the 2nd dozen hits once, and then hits again, and then the first dozen hits and you win 0 (+1, +1, -2, 0 net)
1.33 times, the 2nd dozen hits once, and then hits again, and then the 3rd dozen hits and you win 3 (+1, +1, +1, +3 net)
1.33 times, the 2nd dozen hits once, and then hits again, and then hits again and you win at least 1 (+1, +1, +1, -2, +1 net worst-case outcome)
-24+12-4+8+0+4+(1.33+x) = -2.67+x, where x is the remaining value of the unresolved 3 repeat sequence.
And the spreadsheet expanding considerably on the value of x, which it turns out is 2.67...https://docs.google.com/spreadsheet/ccc?key=0AlRSxZ2plqHPdGE2ZDNIUzZCY0JISjViQWtHaGZld3c
You're right, the math doesn't lie......
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
December 24th, 2012 at 7:38:30 AM
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deleted
DUHHIIIIIIIII HEARD THAT!
December 24th, 2012 at 7:59:57 AM
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....... " I am posting this in the same spirit as a theorist who posts in a peer-reviewed journal." .......
Then it should be posted in a " IQ below 70 " journal.
Then it should be posted in a " IQ below 70 " journal.
Shed not for her
the bitter tear
Nor give the heart
to vain regret
Tis but the casket
that lies here,
The gem that filled it
Sparkles yet
December 24th, 2012 at 12:19:46 PM
permalink
Quote: colbsterNo, adding the 0s in makes every "spin" have a negative expectation. I have explained that this deals with "bets", not "spins". When "bets" can contain a number of "spins", you no longer have the negative expectation.
So the mathematical principle you are relying on in the "system" is something like this:
Spin #1 = EV of -2.7
Spin #2 = EV of -2.7
Spin #3 = EV of -2.7
Spin #4 = EV of -2.7
Spin #5 = EV of -2.7
Spin #6 = EV of -2.7
Spin #7 = EV of -2.7
However when you sum the results of Spins #1 through #4 and call that a "bet" it has a positive EV. Furthermore, when you sum the results of Spins #5 through #7 and call that a second "bet" it also has a positive EV.
Just curious how the sign (negative) of the individual parts you are summing together changes to a positive in the addition process......answer = it doesn't and your system is nothing more than a progression/martigale systemt that has been around forever.
Enough time wasted here!
December 24th, 2012 at 12:22:00 PM
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Quote: colbster
I find it amusing that EvenBob states that its "their life's work, they obsessed with it" as if he is above it all. He admits that he frequents the same boards that I do, which he would not do if he were not hoping to find something that he hasn't found yet.
.
I have thousands of posts on roulette forums, over 20,000,
actually. I look at forums now, but I rarely post about roulette.
There are some very bright math people here and you can't
get one of them to agree with you. Why is that?
What you're doing is called curve fitting. You're taking you're
results and making them do what you want on paper, to show
you what you want to see. You're here because what you do
doesn't work in simulations or in a real casino, and you're
puzzled as to why. Oldest story in the roulette systems book.
"It's not called gambling if the math is on your side."
December 24th, 2012 at 8:11:52 PM
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I'm reposting this calculation because the first attempt was muddled. This new and improved version has a table!!
----
Let me get my terms all defined:
A "Spin" is pretty self explanatory.
A "Third" is a group of twelve numbers even though there are 37 numbers on a European wheel.
A "Bet" is a series of one or more spins where one unit is placed on the previously landed on third and another unit is placed on another third.
A bet is resolved when the ball lands in a third that is different than the previous third upon which it landed or the zero (what third do you bet on after a zero?).
The spin which eventually resolves the bet will either lose 2 or win 1.
So if the bet is resolved, which it must be, that spin will yield:
( 1 * 12/25 ) - ( 2 * 13/25 ) = -0.56
So can we get streaky enough to overcome that loss of 56 cents for every dollar bet?
Moving onto the next spin within a bet has a probability of 12 in 37 or 0.324..
Here are the calculated returns of the cumulative win at bet resolution:
I projected this out to 20 spins in an excel spreadsheet and this system approaches a loss of 8 cents per dollar with each iteration.
The math doesn't lie.
----
Let me get my terms all defined:
A "Spin" is pretty self explanatory.
A "Third" is a group of twelve numbers even though there are 37 numbers on a European wheel.
A "Bet" is a series of one or more spins where one unit is placed on the previously landed on third and another unit is placed on another third.
A bet is resolved when the ball lands in a third that is different than the previous third upon which it landed or the zero (what third do you bet on after a zero?).
The spin which eventually resolves the bet will either lose 2 or win 1.
So if the bet is resolved, which it must be, that spin will yield:
( 1 * 12/25 ) - ( 2 * 13/25 ) = -0.56
So can we get streaky enough to overcome that loss of 56 cents for every dollar bet?
Moving onto the next spin within a bet has a probability of 12 in 37 or 0.324..
Here are the calculated returns of the cumulative win at bet resolution:
| Spin | Result | Probability | Net |
|---|---|---|---|
| 1 | -2 | 0.351351351.. | -0.702702702.. |
| 1 | +1 | 0.324324324.. | +0.324324324.. |
| 2 | -1 | 0.1139517896 | -0.1139517896 |
| 2 | +2 | 0.1051862673 | +0.2103725347 |
| 3 | 0 | 0.0369573372 | 0.00 |
| 3 | +3 | 0.0341144651 | +0.1023433953 |
| 4 | +1 | 0.0119861634 | +0.0119861634 |
| 4 | +4 | 0.0110641508 | +0.0442566034 |
| 5 | +2 | 0.0038874043 | +0.0077748087 |
| 5 | +5 | 0.0035883732 | +0.0179418662 |
| 6 | +3 | 0.0012607798 | +0.0037823394 |
| 6 | +6 | 0.0011637967 | +0.0069827804 |
| 7 | +4 | 0.0004089016 | +0.0016356062 |
| 7 | +7 | 0.0003774476 | +0.0026421331 |
| 8 | +5 | 0.00013261672 | +0.0006630836 |
| 8 | +8 | 0.00012241543 | +0.0009793235 |
| 9 | +6 | 0.00004301083 | +0.0002580650 |
| 9 | +9 | 0.00003970230 | +0.0003573207 |
| 10 | +7 | 0.00001394946 | +0.0000976462 |
| 10 | +10 | 0.00001287642 | +0.0001287642 |
| Total: | 0.999987123 | -0.080127734 |
I projected this out to 20 spins in an excel spreadsheet and this system approaches a loss of 8 cents per dollar with each iteration.
The math doesn't lie.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
December 24th, 2012 at 11:38:32 PM
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Quote: EvenBobI have thousands of posts on roulette forums, over 20,000,
actually. I look at forums now, but I rarely post about roulette.
If you don't mind me asking, what method do you use that you have had the most luck with while playing roulette?
December 26th, 2012 at 3:07:04 AM
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Quote: EvenBobI have thousands of posts on roulette forums, over 20,000,
actually. I look at forums now, but I rarely post about roulette.
There are some very bright math people here and you can't
get one of them to agree with you. Why is that?
What you're doing is called curve fitting. You're taking you're
results and making them do what you want on paper, to show
you what you want to see. You're here because what you do
doesn't work in simulations or in a real casino, and you're
puzzled as to why. Oldest story in the roulette systems book.
Evenbob, no crime to try to dig deeper where others did not succed.
Curve fitting is a way of "Gambler´s Falacy" where you find the proper bet to each situation to win.
The question is the following: supose(for this exersiice) Colbster would have a winning system, he has been curve fitting his results and found he won most of the sessions, and his hit have gone to the +3 st dev level or more. You can curvefit for some time but sooner or later it sinks whatever you do.
Supose Colbster could curvefit his results for doulble time period math says.
We know his system cannot avoid the -2.7%, but, he started saying that he picked a dozen as an example. To succed, we must make predicctions to cope with the -2.7% and get a +3 to 10% edge.
December 26th, 2012 at 2:18:36 PM
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The following is from a PM I sent regarding a theoretical 36 spins. Hope this may be clearer for some:
We can agree that 12 losses at -2 give us -24 and 12 wins at +1 give us +12, netting -12 before considering the repeats.
When we get repeats, the new 12-spin average is +1 (-1/2/2) which covers the -12 evenly, meaning we have EV of 0.
BUT, 1/3 of those twelve will move up to the next level which averages +2 (0/3/3). This new 1/3 of 12 adds 4 units to our equation, meaning we are at -24/16/12, or +4
BUT, 1/3 of those 4 move up to the next level which average +3 (1/4/4). This new 1/3 of 4 adds 1.333 units, meaning we are at -24/17.333/12, or +5.333
BUT, 1/3 of those 1.333 move up to the next level which average +4 (2/5/5). This new 1/3 of 1.333 adds 0.443 units, meaning we are at -24/17.776/12, or +5.776
BUT, 1/3 of those 0.443 units move up to the next level which average +5 (3/6/6). This new 1/3 of 0.443 adds 0.148 units, meaning we are at -24/17.924/12, or 5.924.
This continues on until the 2nd dozen (the repeats) approach, but don't reach, 18, meaning we expect slightly less than EV of 6 per 36 spins on a no-zero table. Obviously, 36 bets is too small for these fractions, but expanded over a larger quantity of bets with normal distribution, the math holds up. If we considered, 2187 spins instead of 36 spins, it is more evident, but the numbers remain exactly the same throughout.
We can agree that 12 losses at -2 give us -24 and 12 wins at +1 give us +12, netting -12 before considering the repeats.
When we get repeats, the new 12-spin average is +1 (-1/2/2) which covers the -12 evenly, meaning we have EV of 0.
BUT, 1/3 of those twelve will move up to the next level which averages +2 (0/3/3). This new 1/3 of 12 adds 4 units to our equation, meaning we are at -24/16/12, or +4
BUT, 1/3 of those 4 move up to the next level which average +3 (1/4/4). This new 1/3 of 4 adds 1.333 units, meaning we are at -24/17.333/12, or +5.333
BUT, 1/3 of those 1.333 move up to the next level which average +4 (2/5/5). This new 1/3 of 1.333 adds 0.443 units, meaning we are at -24/17.776/12, or +5.776
BUT, 1/3 of those 0.443 units move up to the next level which average +5 (3/6/6). This new 1/3 of 0.443 adds 0.148 units, meaning we are at -24/17.924/12, or 5.924.
This continues on until the 2nd dozen (the repeats) approach, but don't reach, 18, meaning we expect slightly less than EV of 6 per 36 spins on a no-zero table. Obviously, 36 bets is too small for these fractions, but expanded over a larger quantity of bets with normal distribution, the math holds up. If we considered, 2187 spins instead of 36 spins, it is more evident, but the numbers remain exactly the same throughout.
December 26th, 2012 at 2:20:22 PM
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Quote: CroupierYou would get the same result from this system as you would from flipping 2 coins and using the result to bet dozens. 2 heads and you bet D1+2, two tails you bet D2+3, one head one tail you bet D1+3.
Also, I am amused that everyone wants to jump on my system but nobody mentions the incredibly faulty logic of this comment. Croupier, using your method, you would bet D1+3 50% of the time and 25% each D1+2 and D2+3. I understand your point, but it is mathematically incorrect.
December 26th, 2012 at 2:34:23 PM
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deleted
DUHHIIIIIIIII HEARD THAT!
December 26th, 2012 at 2:42:09 PM
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Colbster, nobody here will tell you that you have a
winning system. You don't. Nobody here will give
you permission to go the casino and lose your house,
you have to make that decision on your own.
winning system. You don't. Nobody here will give
you permission to go the casino and lose your house,
you have to make that decision on your own.
"It's not called gambling if the math is on your side."
December 26th, 2012 at 5:00:34 PM
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If and when someone finds a surefire way to beat roulette (and they may have already done with biased wheels, pocket computers combined with very late bets etc) they will not post it on an internet forum.
Anyone that posts a "system" that relies on beating roulette using maths is either naive, a scammer, or retarded. Every spin gives the house its 2.7% edge (or more on 00). It is physically impossible to overcome this on a random roulette wheel.
I am sick of reading the bullshit systems people keep wasting internet ink on this forum with GRRRRRRRRRRRRRRR
Anyone that posts a "system" that relies on beating roulette using maths is either naive, a scammer, or retarded. Every spin gives the house its 2.7% edge (or more on 00). It is physically impossible to overcome this on a random roulette wheel.
I am sick of reading the bullshit systems people keep wasting internet ink on this forum with GRRRRRRRRRRRRRRR
December 26th, 2012 at 5:10:31 PM
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You didn't look at my chart, did you? Your system actually increases the house edge to exactly 8%.Quote: colbster..but expanded over a larger quantity of bets with normal distribution, the math holds up. If we considered, 2187 spins instead of 36 spins, it is more evident, but the numbers remain exactly the same throughout.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
December 26th, 2012 at 5:27:04 PM
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Your math should be just as scrutinized as my own. My system overcomes the house edge, it doesn't fundamentally alter it. I looked at your chart but couldn't follow your reasoning. However, your suggestion that my simple bet manages to alter the 2.7% is not feasible. You appear to not understand my explanation, as you cannot possibly lose at the 2.7% level except at the first spin of a bet. As soon as there is a win or a loss, the bet is reset as is the 2.7% house edge. Considering your signature about the current administration, I want more than anyone to be on your side. Regrettably, I think Pelosi might be helping you with your math!
December 26th, 2012 at 6:16:20 PM
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" Regrettably, I think Pelosi might be helping you with your math! "
Perhaps the ghost of Ronald Raegan could help you with your Voodoo Mathematics ?
Perhaps the ghost of Ronald Raegan could help you with your Voodoo Mathematics ?
Shed not for her
the bitter tear
Nor give the heart
to vain regret
Tis but the casket
that lies here,
The gem that filled it
Sparkles yet
December 26th, 2012 at 6:58:31 PM
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Since you couldn't understand the chart, let me repost it and I'll try to explain it in as simple terms as I can muster:Quote: colbsterYour math should be just as scrutinized as my own. My system overcomes the house edge, it doesn't fundamentally alter it. I looked at your chart but couldn't follow your reasoning. However, your suggestion that my simple bet manages to alter the 2.7% is not feasible. You appear to not understand my explanation, as you cannot possibly lose at the 2.7% level except at the first spin of a bet. As soon as there is a win or a loss, the bet is reset as is the 2.7% house edge. Considering your signature about the current administration, I want more than anyone to be on your side. Regrettably, I think Pelosi might be helping you with your math!
| Spin | Result | Probability | Net |
|---|---|---|---|
| 1 | -2 | 0.351351351.. | -0.702702702.. |
| 1 | +1 | 0.324324324.. | +0.324324324.. |
| 2 | -1 | 0.1139517896 | -0.1139517896 |
| 2 | +2 | 0.1051862673 | +0.2103725347 |
| 3 | 0 | 0.0369573372 | 0.00 |
| 3 | +3 | 0.0341144651 | +0.1023433953 |
| 4 | +1 | 0.0119861634 | +0.0119861634 |
| 4 | +4 | 0.0110641508 | +0.0442566034 |
| 5 | +2 | 0.0038874043 | +0.0077748087 |
| 5 | +5 | 0.0035883732 | +0.0179418662 |
| 6 | +3 | 0.0012607798 | +0.0037823394 |
| 6 | +6 | 0.0011637967 | +0.0069827804 |
| 7 | +4 | 0.0004089016 | +0.0016356062 |
| 7 | +7 | 0.0003774476 | +0.0026421331 |
| 8 | +5 | 0.00013261672 | +0.0006630836 |
| 8 | +8 | 0.00012241543 | +0.0009793235 |
| 9 | +6 | 0.00004301083 | +0.0002580650 |
| 9 | +9 | 0.00003970230 | +0.0003573207 |
| 10 | +7 | 0.00001394946 | +0.0000976462 |
| 10 | +10 | 0.00001287642 | +0.0001287642 |
| Total: | 0.999987123 | -0.080127734 |
The column labeled 'Result' is the outcome of the bet, -2 units, +1 unit etc..
The column labeled 'Probability' is the relative probability of that bet resolution occurring, posted as a fraction of 1.
The column labeled 'Net' is the 'Result' times the 'Probability'. This calculates the expected return over an infinite number of trials.
The Wizard uses a variation of this method to calculate the house edge
in Jacks-or-better video poker as seen here.
Getting back to our example,
if the bet resolves on the first spin, it can resolve in one of two ways, it can lose (row 1) or it can win (row 2).
There is a slightly greater than one in three chance that the bet will resolve as a loser.
There is a slightly less than one in three chance that the bet will resolve as a winner.
All of the other rows in the table consist of what does NOT happen in the first two rows.
Rows three and four show you what happens when you get past rows one and two.
If the bet resolves on the second spin, rows three and four show you the expected return.
Notice that the returns are much smaller because the probability of getting there is also much smaller.
If the bet does not resolve on the second spin, we move on to the fifth and sixth rows.
Notice how the results get even tinier, this is because the probability is getting smaller much
more quickly than the result of the bet is getting larger.
After only 10 spins, the probability of going on is so tiny as to not matter much anymore.
As you can see, with almost all the probability accounted for, the expected loss
for the listed outcomes is eight cents per 'bet' which is even worse than the
expected loss on a single spin.
The math doesn't lie.
Let me prove it to you with a simple thought exercise.Quote: colbsterHowever, your suggestion that my simple bet manages to alter the 2.7% is not feasible.
Your system places a unit on two of the three thirds and leaving the last third and the zero empty.
If you win, you get 2 to 1 and lose the other bet.
Let's take it to the absurd:
If you bet all three thirds what would happen?
You would get paid 2 to 1 on the winner and lose the other two bets for a net of zero.
If the green-zero comes up, you lose all three, house edge there is 100%
By forcing one bet to lose, you are increasing the house edge. As the Wizard says, "Thou Shalt Not Hedge".
The math doesn't lie.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
December 26th, 2012 at 8:01:55 PM
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When PaigowDan calls you a thief, criminal, purse snatcher, etc.; then maybe I'll believe you have an edge.
"I am a man devoured by the passion for gambling." --Dostoevsky, 1871
December 26th, 2012 at 9:12:16 PM
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nvm..
December 26th, 2012 at 11:25:16 PM
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From what I understand, you pick 2 dozens. If the bet hits the third dozen, you consider that a win and the "bet" is done. If it hits the first dozen, you consider that bet a "loss" and the bet is done. I assume this also includes the 0. If it hits the 2nd dozen, you consider the bet "continued".
Your error is calculating the EV advantage on the first throw, which is *not* -1/37. It is -2/37. (13*-2 + 24*1)/37
Fine. Let's see how this fares. keep in mind that your "Bet" is not resolved until you say it is, which is when it lands on any other number but the 2nd dozen.
Your bet resolves to exactly an 1/37 house advantage on a single zero wheel, and here's why:
You are resolving a BET. You can't claim that the HA is -1/37 on the first roll, because your bet is not resolved on the first spin. You let it ride.
On the first roll, you lose 2 units 13/37 of the time, win 1 unit 12/37 of the time, and let it ride 12/37 of the time. If the bet is resolved on the first spin, on average, your expected loss is -.25566, not -1/37, BECAUSE YOU CAN'T ACCOUNT FOR THE 12/37 THAT YOU LET IT RIDE AS PART OF THE EXPECTED LOSS FOR THE FIRST BET.
On the second roll, you lose 1 unit 13/37 of the time, win 2 units 12/37 of the time, and let it ride 12/37 of the time. The bet will resolve itself on the 2nd spin on (12/37)*(25/37) and indeed, your expected win is .29729 units but it only hits 21.9138% of the time.
On the third roll, you break even 13/37 of the time, win 3 units 12/37 of the time, and let it ride 12/37 of the time. The bet will resolve itself on the 3rd spin on only 7.1072% of the time, and therefore even though your expected win is .97297 units, you only get this win 7.1072% of the time.
When you add it all up, here's what you get:
Resolved on 1st spin: EV = -.25566
Resolved on 2nd spin: EV = .065149
Resolved on 3rd spin: EV = .069151
Resolved on 4th spin: EV = .038002
Resolved on 5th spin: EV = .017376
Resolved on 6th spin: EV = .007274
Resolved on 7th spin: EV = .00289
Resolved on 8th spin: EV = .00111
Resolved on 9th spin: EV = .000416
Resolved on 10th spin: EV = .00015
Resolved on 11th spin: EV = .00006
Resolved on 12th spin: EV = .00002
Total EV = -.05405 = -2/37.
Your error is calculating the EV advantage on the first throw, which is *not* -1/37. It is -2/37. (13*-2 + 24*1)/37
Fine. Let's see how this fares. keep in mind that your "Bet" is not resolved until you say it is, which is when it lands on any other number but the 2nd dozen.
Your bet resolves to exactly an 1/37 house advantage on a single zero wheel, and here's why:
You are resolving a BET. You can't claim that the HA is -1/37 on the first roll, because your bet is not resolved on the first spin. You let it ride.
On the first roll, you lose 2 units 13/37 of the time, win 1 unit 12/37 of the time, and let it ride 12/37 of the time. If the bet is resolved on the first spin, on average, your expected loss is -.25566, not -1/37, BECAUSE YOU CAN'T ACCOUNT FOR THE 12/37 THAT YOU LET IT RIDE AS PART OF THE EXPECTED LOSS FOR THE FIRST BET.
On the second roll, you lose 1 unit 13/37 of the time, win 2 units 12/37 of the time, and let it ride 12/37 of the time. The bet will resolve itself on the 2nd spin on (12/37)*(25/37) and indeed, your expected win is .29729 units but it only hits 21.9138% of the time.
On the third roll, you break even 13/37 of the time, win 3 units 12/37 of the time, and let it ride 12/37 of the time. The bet will resolve itself on the 3rd spin on only 7.1072% of the time, and therefore even though your expected win is .97297 units, you only get this win 7.1072% of the time.
When you add it all up, here's what you get:
Resolved on 1st spin: EV = -.25566
Resolved on 2nd spin: EV = .065149
Resolved on 3rd spin: EV = .069151
Resolved on 4th spin: EV = .038002
Resolved on 5th spin: EV = .017376
Resolved on 6th spin: EV = .007274
Resolved on 7th spin: EV = .00289
Resolved on 8th spin: EV = .00111
Resolved on 9th spin: EV = .000416
Resolved on 10th spin: EV = .00015
Resolved on 11th spin: EV = .00006
Resolved on 12th spin: EV = .00002
Total EV = -.05405 = -2/37.
-----
You want the truth! You can't handle the truth!
December 26th, 2012 at 11:31:21 PM
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S2BAKER, I made the same error that you did when i did the calculation. I originally got 8% to be my HA as well. But your first two rows are wrong. The EV on the first spin has to be multiplied by 25/37.
-----
You want the truth! You can't handle the truth!
December 27th, 2012 at 3:27:20 AM
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I thought I was already doing that but I'll program a simulation later and we'll see what it comes out to in practice. Are you sure that you're not multiplying by 25/37 twice?Quote: boymimboS2BAKER, I made the same error that you did when i did the calculation. I originally got 8% to be my HA as well. But your first two rows are wrong. The EV on the first spin has to be multiplied by 25/37.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
December 27th, 2012 at 3:29:25 AM
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Quote: s2dbaker:
Spin Result Probability Net 1 -2 0.351351351.. -0.702702702.. 1 +1 0.324324324.. +0.324324324.. 2 -1 0.1139517896 -0.1139517896 2 +2 0.1051862673 +0.2103725347 3 0 0.0369573372 0.00 3 +3 0.0341144651 +0.1023433953 4 +1 0.0119861634 +0.0119861634 4 +4 0.0110641508 +0.0442566034 5 +2 0.0038874043 +0.0077748087 5 +5 0.0035883732 +0.0179418662 6 +3 0.0012607798 +0.0037823394 6 +6 0.0011637967 +0.0069827804 7 +4 0.0004089016 +0.0016356062 7 +7 0.0003774476 +0.0026421331 8 +5 0.00013261672 +0.0006630836 8 +8 0.00012241543 +0.0009793235 9 +6 0.00004301083 +0.0002580650 9 +9 0.00003970230 +0.0003573207 10 +7 0.00001394946 +0.0000976462 10 +10 0.00001287642 +0.0001287642 Total: 0.999987123 -0.080127734
I understand your chart now, thank you. I also commend you on one of the most reasoned responses against my system that I have seen, but it is quite incorrect for one reason. The construct of the chart is the actual downfall of the chart. This sort of breakdown is inapplicable to my own system for this reason:
Poker, after the hand is over, has a resolution that is fixed. The way you have set up your chart, my bet could never be resolved. It continues on forever, with a less probable but increasing payout on ongoing repeats. You have forgotten to include the stored value of the ongoing repeats. This is similar to attempting to apply the chart to a jackpot-style video poker system. We can easily see what the odds are, but until the bet is resolved, we don't know what the payout will be. Until a Royal Flush is hit, the jackpot continues to grow. If we have a 4000-to-1 payout on a RF, we know what the EV will be. However, it cannot be calculated with a jackpot until the jackpot is paid to a winner. Until then, we have just prospected EV.
Your chart suffers the same weakness. Reality will always conclude my bet to one side or the other - it will not increase infinitely to obscurity. The bet will win or lose at some lower level, similar to my explanation on page 9, which clearly has an edge.
December 27th, 2012 at 3:52:47 AM
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No, with calculus, you can resolve this, even to infinity. As the total probability approaches 1, the total loss approaches 8 cents.Quote: colbsterThe way you have set up your chart, my bet could never be resolved. It continues on forever, with a less probable but increasing payout on ongoing repeats. You have forgotten to include the stored value of the ongoing repeats.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
December 27th, 2012 at 3:56:08 AM
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Wow this show is great.
First it is mathematical proven that any system is subject to the house edge.
You claim no-one understands your system well enough, that it won't fall into the "any system" category, because your system is "special".
Then someone takes his precious time and makes an almost complete breakdown of all probabilities - which you later (after a private lesson of probability calculus) agree, and then you complain that there is a 0.0012% probability measure left which has not yet been calculated.
Do you really believe that all people here are that ignorant, not seeing your brilliant system (where you can't even explain your mechanism of edge).
And then suddenly you believe that your edge is somewhere hidden in the 0.0012% missing probability ?
If you can't spot the idiot in the room when entering, chances are you are the one.
All but your claims stated in this thread are correct. If you really understand the (very generously given ) probability table, it is now your job to complete it.
Maybe then you might learn something about your system or the game of roulette itself.
First it is mathematical proven that any system is subject to the house edge.
You claim no-one understands your system well enough, that it won't fall into the "any system" category, because your system is "special".
Then someone takes his precious time and makes an almost complete breakdown of all probabilities - which you later (after a private lesson of probability calculus) agree, and then you complain that there is a 0.0012% probability measure left which has not yet been calculated.
Do you really believe that all people here are that ignorant, not seeing your brilliant system (where you can't even explain your mechanism of edge).
And then suddenly you believe that your edge is somewhere hidden in the 0.0012% missing probability ?
If you can't spot the idiot in the room when entering, chances are you are the one.
All but your claims stated in this thread are correct. If you really understand the (very generously given ) probability table, it is now your job to complete it.
Maybe then you might learn something about your system or the game of roulette itself.
December 27th, 2012 at 4:02:26 AM
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Provided without formatting out to 30 repeats:
1 (2) 0.3513513514 (0.7027027027)
1 1 0.3243243243 0.3243243243
2 (1) 0.1139517896 (0.1139517896)
2 2 0.1051862673 0.2103725347
3 0 0.0369573372 0.0000000000
3 3 0.0341144651 0.1023433953
4 1 0.0119861634 0.0119861634
4 4 0.0110641508 0.0442566034
5 2 0.0038874043 0.0077748087
5 5 0.0035883732 0.0179418662
6 3 0.0012607798 0.0037823394
6 6 0.0011637967 0.0069827804
7 4 0.0004089016 0.0016356062
7 7 0.0003774476 0.0026421331
8 5 0.0001326167 0.0006630836
8 8 0.0001224154 0.0009793235
9 6 0.0000430108 0.0002580650
9 9 0.0000397023 0.0003573207
10 7 0.0000139495 0.0000976462
10 10 0.0000128764 0.0001287642
11 8 0.0000045241 0.0000361932
11 11 0.0000041761 0.0000459375
12 9 0.0000014673 0.0000132056
12 12 0.0000013544 0.0000162531
13 10 0.0000004759 0.0000047588
13 13 0.0000004393 0.0000057105
14 11 0.0000001543 0.0000016977
14 14 0.0000001425 0.0000019945
15 12 0.0000000501 0.0000006007
15 15 0.0000000462 0.0000006931
16 13 0.0000000162 0.0000002110
16 16 0.0000000150 0.0000002398
17 14 0.0000000053 0.0000000737
17 17 0.0000000049 0.0000000826
18 15 0.0000000017 0.0000000256
18 18 0.0000000016 0.0000000284
19 16 0.0000000006 0.0000000089
19 19 0.0000000005 0.0000000097
20 17 0.0000000002 0.0000000031
20 20 0.0000000002 0.0000000033
21 18 0.0000000001 0.0000000010
21 21 0.0000000001 0.0000000011
22 19 0.0000000000 0.0000000004
22 22 0.0000000000 0.0000000004
23 20 0.0000000000 0.0000000001
23 23 0.0000000000 0.0000000001
24 21 0.0000000000 0.0000000000
24 24 0.0000000000 0.0000000000
25 22 0.0000000000 0.0000000000
25 25 0.0000000000 0.0000000000
26 23 0.0000000000 0.0000000000
26 26 0.0000000000 0.0000000000
27 24 0.0000000000 0.0000000000
27 27 0.0000000000 0.0000000000
28 25 0.0000000000 0.0000000000
28 28 0.0000000000 0.0000000000
29 26 0.0000000000 0.0000000000
29 29 0.0000000000 0.0000000000
30 27 0.0000000000 0.0000000000
30 30 0.0000000000 0.0000000000
1.0000000000 (0.0800000000)
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
