dice testing

The best system for making a determination of dice control is smart craps. This a tough test and hard to pass. I have only
known of 1 player that passed it the first time he took it.

If we really want to check lets get 10 guys on here to complete 3000 rolls and enter them in smart craps, If you'
are honest it will show how you compare to random and if you have a demonstratable advantage, and what
that is per number.

Once we have all completed this there will be no question how we all relate in terms the effectiveness of our
throw. For good or bad there it is...

Time to get off the bench and play ball.


dicesitter

Quote: dicesitter

The best system for making a determination of dice control is smart craps. This a tough test and hard to pass. I have only
known of 1 player that passed it the first time he took it.

You mean the best software program to use is Smart Craps.
Agree.
The only software in the world to prove the DI skill level.

They even claim in their Help section that one can have verifiable proof of dice influence in as little as 100 dice rolls up to 500 rolls.
Excellent.

But that is not all
1. how to prove, with statistical certainty, that you are influencing the dice outcomes, using our powerful and new Pro Test© method.
2. the optimal dice sets and bets given your unique dice control skill.
3. your edge over the casino: how much money you can make playing craps. (yeah! Now we are talking!)

The Smart Craps program is slick and accurate.
http://www.deepnettech.com/SmartCraps.shtml

I think most DIs KNOW what their edge is and what numbers they are likely to roll with what sets they use.
They do not need a program to tell them that.
They do not need to track their rolls, they just know the actual skill level they have is from playing on real tables.
That is the bottom line.

Frank Scoblete, #1 best-selling gaming author in America, says:
"Dan Pronovost is a genius, there's no question about that.
His new software SMART CRAPS is truly revolutionary.
The concept of the software is to prove you have an edge and to show you how to increase that edge with "cutting edge" dice sets that you may not have even thought about.
What startled me was that my rolls were analyzed and while I had a good edge, the software recommended I change certain things about my dice sets at certain times.
This increased my edge by quite a bit."

Maybe you should start out and be first and show your dice rolls and results from the tests in SC.

Once there is a leader, there will be followers.

Isn't that software written for windows 3.1?

Quote: Ahigh

Isn't that software written for windows 3.1?

Smart Craps will work on any desktop computer running Windows 98 or higher (i.e. Windows 98 SE, Windows 2000, Windows ME, Windows XP, etc.).
15 megabytes of hard disk space is required.
800 by 600 screen resolution or higher is recommended.
Smart Craps does not run on Windows CE handheld operating systems (or Palm OS), since the computing capacity of these small devices is very minimal.

The unregistered shareware version of Smart Craps will let you fully explore the program and features.
But, it will only allow limited rounds during simulation runs, and will prompt you from time to time to purchase a registration ('nag' screens).

from their website

But not compatible with Windows 7, huh?

Quote: Ahigh

But not compatible with Windows 7, huh?

V 1.83, the newest, has fixed bugs related to windows 7.
I use it on windows xp and windows7 machines and have had no issues at all with it.

I really like the risk of ruin program and simulator in it.
Not really have I tried the Pro tests.

added: the Pro Tests works with Excel if you want to use it.
Cool.
And then you can go back to the program and see your edge and dice set suggestions.
I had 3007 of my rolls from last year entered.
More later

" They even claim in their Help section that one can have verifiable proof of dice influence in as little as 100 dice rolls "

ROFLMAO ! ! !

Quote: Buzzard

" They even claim in their Help section that one can have verifiable proof of dice influence in as little as 100 dice rolls "

ROFLMAO ! ! !

yes really!
The mathematical tests are 100% accurate up to 1000 dice rolls with a 99% degree of certainty.
One can take that to the bank!

Bottom of page 37. The help pdf is a free document.

Here is what it reads

"In tests with actual practicing dice setters,
skilled shooters are capable of passing the Pro 1 Test in 100 to 500 rolls, in controlled test conditions.

Measuring actual throws in a live casino is not advised, since the shooter most likely will employ dice sets that make recording Pro Test passes difficult.
In all pro Tests, the shooter must use the hardway set, and should record the actual throw as well as the Pro Test pass/failures"

My 3007 actual dice rolls did not use the hardway set.
I guess I have to do my rolls all over again even tho I did pass tests 1 and 3.

I am math illiterate, but even I know 100 rolls will not prove a F***ing thing.

Quote: Buzzard

I am math illiterate, but even I know 100 rolls will not prove a F***ing thing.

If I hit box cars 99 times out of 100, I think I might be proving something. So it would be possible to prove extreme dice influence in 100 rolls. The more rabid would probably say if I hit an on axis roll 99 times out of 100, I'd be golden, but I'm not so sure about that.

If 100 rolls don't proving a thing, why ask for 3:1 lays on proving expert versus novice? Hmm? :)

If you think 100 rolls proves something, what is a fair line for an expert dice setter versus me. 1 to 1 is an admission dice setting is not a skill.

Quote: thecesspit

So it would be possible to prove extreme dice influence in 100 rolls.

The Pro Tests in Smart Craps looks to be all about z-axis control, pitches and double-pitches.

I guess if one die actually does a 360 degree turn and ends up as it begun, the Test says it passed and stayed on axis.

Got to love the end justifies the means.

Great stuff to learn in just 100 to 500 dice rolls.
Time is money.

added: Wong also has an excel spreadsheet out on the net that does about the same thing.
I have not looked at in a few years.

'The Pro Tests in Smart Craps looks to be all about z-axis control, pitches and double-pitches."

Silly me, I thought it would have something to do with rolling a desired number.

Quote: Buzzard

'The Pro Tests in Smart Craps looks to be all about z-axis control, pitches and double-pitches."

Silly me, I thought it would have something to do with rolling a desired number.

It is.

The theory is if you can keep the dice on axis and paired, you will only roll either 2 or 4 possible numbers. If you can keep them on axis at all, you only roll 16 out of 36 possible numbers. Those, with the right betting pattern, would give you an advantage. But unless you are hitting a perfect roll a lot of the time, you'll need many more than 100 rolls to prove that you have anything special going on. Heavy posted on here his "books" of 720 rolls. Those were kinda data mining, if you ask me.

I'll leave it as an exercise to the crowd to decide if this theory is worth more than a pile of fetid dingo kidneys. I think I know several people's opinions already.

Quote: Buzzard

'The Pro Tests in Smart Craps looks to be all about z-axis control, pitches and double-pitches."

Silly me, I thought it would have something to do with rolling a desired number.

I'm not a believer in DI, but if a shooter could use a hardway set (which I do), could keep the dice in a position as if they were fused together (which I cannot), with the result being that they always (or extremely frequently) roll a hard 4, 6, 8, or 10, then their gambling results should be outstanding, even though they would not have one specific number that they were trying to roll.

" with the result being that they always (or extremely frequently) roll a hard 4, 6, 8, or 10" and I will take 3 to 1 they will not do this more frequently than me in 100 rolls.

I mean , isn't that a fair comparison. Dice setters always talk about it being a skill, like golf. Any of them willing to take 3 to 1 against Tiger Woods? Of course not, Tiger has an actual skill.

I love reading all this.

On the subject of small numbers of samples, I took the improperly balanced die from the last show and did random rolls on it.

535522413441435156155431145
152334542624425652554114653
542611115664116611345445454
621142534364266535414456263
514654553324616314261223226
636

111111111111111111111111
222222222222222222
33333333333333333
44444444444444444444444444444
5555555555555555555555555555
6666666666666666666666

1 - 24 - 17.39% (+0.73%)
2 - 18 - 13.04% (-3.62%)
3 - 17 - 12.32% (-4.34%)
4 - 29 - 21.01% (+4.34%)
5 - 28 - 20.28% (+3.61%)
6 - 22 - 15.94% (-0.73%)

So the only one that was biased more heavily on the smaller numbers (opposite the heavy corner of the die) is the 6, and it was only biased by a tiny amount.

The other numbers came up more frequently with the heavier side of the die up.

But as it pertains to this discussion, with this few number of samples, none of this means much at all, and it all seems within the tolerance of random even without doing any tests.

Quote: Buzzard

" with the result being that they always (or extremely frequently) roll a hard 4, 6, 8, or 10" and I will take 3 to 1 they will not do this more frequently than me in 100 rolls.

I mean , isn't that a fair comparison. Dice setters always talk about it being a skill, like golf. Any of them willing to take 3 to 1 against Tiger Woods? Of course not, Tiger has an actual skill.

I -think- you are over estimating the amount of skill the setter could possibly have. I only think. Let me run some numbers this week and see what 3:1 fair line would mean.

Well, any skill should be measurable. Unless it exists only in the mind of deluded dice setters.

Quote: Buzzard

Well, any skill should be measurable. Unless it exists only in the mind of deluded dice setters.

Sure. Not disagreeing with you there. I only disagree that 3:1 over 100 rolls will give you a bet that a DI would take with a measureable skill. 100 rolls is probably not enough to prove anything, right?

Even huge numbers don't prove anything.

Some chick won 17 million here a while back.

That doesn't even prove she's lucky! Some people believe in the "curse."

3000 rolls is a good number, if you throw 100 rolls a night it will take you 30 days. I think to do it right that is
to many rolls, I think taking 50 good rolls a night over 60 days will give you the best indication of your
influence over the dice or lack thereof.

If you are a random thrower 60 days also makes sure you cant get lucky enough to tilt the test.

I am certainly not afraid to reveal my results to anyone.

Dicesitter

Quote: thecesspit

Sure. Not disagreeing with you there. I only disagree that 3:1 over 100 rolls will give you a bet that a DI would take with a measureable skill. 100 rolls is probably not enough to prove anything, right?

We can do series of 100 trials, till the dice setter is tapped out.

The result are meaningless without a financial incentive. I want the dice setter motivated.

Quote: Buzzard

We can do series of 100 trials, till the dice setter is tapped out.

I have betting strategies that easily last 100,000 rolls that don't depend on anything but random rolling.

They are pretty boring, and don't make much money, but they last a long damn time without losing!

You sound pretty certain about 100 trials tapping out a shooter.

No I think trials of 100 will prove dice setters are no better than an untalented fool, namely me.

I don't think there's any proof in any of this. If anyone is overcoming the combined house edge, the finger snappers are losing enough extra money that nobody cares.

The proof part is the hardest part of all of this.

But it's reasonable in my mind that someone could muster up an edge with a legal shot.

It's not reasonable to me that anybody cares as long as the casino in question is still making enough money.

If the Wynn doesn't care if I might have an advantage throw while their table is dumping tens of thousands of dollars while I am shooting, and they let me keep shooting, then nobody generally cares because it still comes out in the wash when some drunk guy is making horn bets just giving it all away!

I'm pretty sure there is a threshold when they will care though. I'm not sure what it would be.

But the whole back and forth about prove this and that is sort of meaningless.

If you want the truth, you can find it just going in and seeing what happens!

All these bets between friends mean nothing towards proof. Especially with so low numbers of rolls and such small edges on either side.

The non-existent rush of dice setters to challenge me speaks volumes.

Maybe people are just ignoring you? IE: maybe it's you?

Quote: Ahigh

Maybe people are just ignoring you? IE: maybe it's you?

You are so right!!
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Quote: dicesitter

3000 rolls is a good number, if you throw 100 rolls a night it will take you 30 days. I think to do it right that is
to many rolls, I think taking 50 good rolls a night over 60 days will give you the best indication of your
influence over the dice or lack thereof.

If you are a random thrower 60 days also makes sure you cant get lucky enough to tilt the test.

I am certainly not afraid to reveal my results to anyone.

Dicesitter

The idea is to enter rolls into the software program.

It will tell you if you are controlling the outcomes, by how much and what sets to use to make the highest edge possible.

Start with 100 and see what the results are.
The program says that if you are controlling the dice over 100 rolls, it will be easier the more rolls you do and add to the program.

Where are YOUR rolls?
That is all that is needed.
I can enter them into the program or just have my 8 year old grandson do it.
Ain't hard at all to do.

Remember the rules are you have to use the hardway set or the test results are useless.

Be the leader and show your rolls.
Enter them into the Smart Craps program and show your results.

I can not be on a craps table until Saturday and I will start my rolls at that point.
I think I can even get my friend who owns 6 craps tables to log his rolls too.

I ain't no DI, but I can easily test a software program.

IMO, Ahigh appears to me to not be interested in trying the Smart Craps program.
I do not know why, it is free to have and use to see results and the results can even be verified in Excel
to make sure the program is doing all the math right.
A no-brainer IMO

Dicesitter, where are your dice rolls??

Ahigh why would they pay any attention to you when you are shooting, they see random rollers making the tables dump there all the time?

Quote:

If the Wynn doesn't care if I might have an advantage throw while their table is dumping tens of thousands of dollars while I am shooting, and they let me keep shooting, then nobody generally cares because it still comes out in the wash when some drunk guy is making horn bets just giving it all away!

I'm pretty sure there is a threshold when they will care though. I'm not sure what it would be.

But the whole back and forth about prove this and that is sort of meaningless.

If you want the truth, you can find it just going in and seeing what happens!

Will everybody please show up at the Wynn so Ahigh can put on a show for everybody. Make sure you tell all your high rolling buddies so they can make big bucks, off his excellent baised shooting.

Please Ahigh tell everybody when your next show will happen at the Wynn.

Show at the Wynn? Really? What the hell are you talking about.

Listen, I'm going to go to the Wynn more often. Anybody who wants to meet me there, let's go!

You can get $100 private table any time of day pretty much.

Maybe you and me can go and play against each other. I'll bet the don't pass on your roll you and you on mine.

Let's go tough guy!

If you're better than me, show me don't tell me.

Quote: DeMango

You are so right!!
[ A post by Buzzard has been blocked due to your settings | Show it to me anyway | View members I have blocked ]

He used to be somewhat funny but of late just hate and garbage, adds absolutely zero to any discussion. Really improved the signal-to-noise ratio now that he's blocked.

Well i said we should do that, and i will, I am going to retire this Friday

I will start recording a new set of data next Tueday evening. 60 days, 3000 rolls. I have no idea what the final data
will indicate. I have entered thousands over time in several segments. At times i have passed all 3 plus SRR and at
times only 1 & 3 plus SRR.... i am excited to see what my results will be

Dicesitter

Quote: dicesitter

Well i said we should do that, and i will, I am going to retire this Friday

I will start recording a new set of data next Tueday evening. 60 days, 3000 rolls. I have no idea what the final data
will indicate. I have entered thousands over time in several segments. At times i have passed all 3 plus SRR and at
times only 1 & 3 plus SRR.... i am excited to see what my results will be

Dicesitter

What is your seven to rolls ratio? (Or Rolls to Sevens Ratio)?

Just curious, based on another thread... or is it just more complex than that?

well that varies over time it was 7.92, anything over 6. 1 gives you slight advantage and on up. The srr is only important if you throw
box numbers and stay on axis. if your are all over with lots of crap numbers it does not mean much.


And i had a very clear advantage over the 6/8/ and 4.

But it is vital not to get to caught up in very high throw totals becasue you need to know what your present numbers look
like. What you did 6 months ago is not relevant. I like to start over every 3000 rolls or so. When young it is not so bad
but when you get to be close to 65 your hands and feel are not what they were

If you find you have 3-4% advantage over the 6 and 8 you bet those, if you have a 3% advantage over the 5 or 9 you dont bet
those because the house advantage is higher than that. Same with 4 or 10 your advantage must be high enough to out pace
the house advantage.

dicesitter

I don't see why anyone needs to pay $90 for some program to analyze dice results. The test is not that difficult. Suppose you're testing for on-axis results: the expectation is 16/36 = .44444 if the results are random. The standard deviation is (pqn)^.5, where p and q are the percentages and n is the number of rolls. Then, when you take your sample, the "Critical Ratio" is:

CR = r - .5 - pn / SD

where r is the sample number of on-axis-appearing outcomes.

The "Critical Ratio" is the number of standard deviations away from the expected result. A CR of 3 means that there is only a .0013 probability that the result is due to chance alone, so that's .9987.

Let's put in some numbers. What if we take a sample of 200 rolls. SD = (pqn)^.5 = (.4444444 * .5555556 * 200)^.5 = 7.027

We can solve for a CR of 3 thus:

3 = (r - .5 - (.4444444 * 200) ) / 7.027
We multiply both sides of the equation by 7.027, and get
21.081 = r -.5 - 88.888
r = 110.4698

Let's check our work:

CR = (111 - .5 - 88.89) / 7.027 = 3.076

This does NOT mean that 200 rolls are sufficient to convince us that something non-random is going on for just anyone. The farther from expectation a sample result is, the smaller the sample that is significant. In the above example, 55.5% of the rolls were "on-axis", but a result closer to expectation could still be significant if sustained over a larger number of rolls.

The closer p and q are to each other, the higher the SD for a given number of rolls. If we test for a particular outcome, like seven, the SD would be:

(.166667 * .8333333 * 200)^.5 = 5.27

So, let's take the alleged 7.92 SRR, which is equivalent to reducing the probability of a seven from .166667 to .12626, right? At that rate, in 200 rolls, dicesitter would be expected to roll only 25 or 26 sevens, instead of 33 or 34.

CR = (26 - .5 - 33.333) / 5.27 = -1.486
Not even close to 3 (or, in this case -3). At that rate, how many (few) sevens would yield a CR of -3?

Again solving for CR, we get: 18.02.

Anyway, it's much easier to set up a spreadsheet to do this.

BTW, an SRR of 7.92 is about the same as having perfect on-axis performance without any pitch control. Anybody who had that kind of control would have a HUGE advantage over the house. I ran a quick sim in WinCraps Pro using custom probability files and betting $10 pass with double odds, $200 starting bankroll and 100-bet sessions. The probability files were set up such that each die stayed on axis 100% of the time, but the 16 remaining outcomes were equiprobable. For the comeout, both dice eliminated the 6/1 axis, for points of 4 or 10 I used 6/1 4/3 and for other points I used 6/1 5/2. Of 1000 sessions, 895 came out ahead, with a mean result of $522 and a standard deviation of $359. Over half the sessions won $500 or more.
Cheers,
Alan Shank

Alan, thanks for clearing that up. I can probably now just do the calculations in my head.
petro

Hasn't anyone heard of BoneTracker? Google it and it's free.

Quote: goatcabin

I don't see why anyone needs to pay $90 for some program to analyze dice results. The test is not that difficult. Suppose you're testing for on-axis results: the expectation is 16/36 = .44444 if the results are random. The standard deviation is (pqn)^.5, where p and q are the percentages and n is the number of rolls. Then, when you take your sample, the "Critical Ratio" is:

CR = r - .5 - pn / SD

where r is the sample number of on-axis-appearing outcomes.

The "Critical Ratio" is the number of standard deviations away from the expected result. A CR of 3 means that there is only a .0013 probability that the result is due to chance alone, so that's .9987.

Let's put in some numbers. What if we take a sample of 200 rolls. SD = (pqn)^.5 = (.4444444 * .5555556 * 200)^.5 = 7.027

We can solve for a CR of 3 thus:

3 = (r - .5 - (.4444444 * 200) ) / 7.027
We multiply both sides of the equation by 7.027, and get
21.081 = r -.5 - 88.888
r = 110.4698

Let's check our work:

CR = (111 - .5 - 88.89) / 7.027 = 3.076

This does NOT mean that 200 rolls are sufficient to convince us that something non-random is going on for just anyone. The farther from expectation a sample result is, the smaller the sample that is significant. In the above example, 55.5% of the rolls were "on-axis", but a result closer to expectation could still be significant if sustained over a larger number of rolls.

The closer p and q are to each other, the higher the SD for a given number of rolls. If we test for a particular outcome, like seven, the SD would be:

(.166667 * .8333333 * 200)^.5 = 5.27

So, let's take the alleged 7.92 SRR, which is equivalent to reducing the probability of a seven from .166667 to .12626, right? At that rate, in 200 rolls, dicesitter would be expected to roll only 25 or 26 sevens, instead of 33 or 34.

CR = (26 - .5 - 33.333) / 5.27 = -1.486
Not even close to 3 (or, in this case -3). At that rate, how many (few) sevens would yield a CR of -3?

Again solving for CR, we get: 18.02.

Anyway, it's much easier to set up a spreadsheet to do this.

BTW, an SRR of 7.92 is about the same as having perfect on-axis performance without any pitch control. Anybody who had that kind of control would have a HUGE advantage over the house. I ran a quick sim in WinCraps Pro using custom probability files and betting $10 pass with double odds, $200 starting bankroll and 100-bet sessions. The probability files were set up such that each die stayed on axis 100% of the time, but the 16 remaining outcomes were equiprobable. For the comeout, both dice eliminated the 6/1 axis, for points of 4 or 10 I used 6/1 4/3 and for other points I used 6/1 5/2. Of 1000 sessions, 895 came out ahead, with a mean result of $522 and a standard deviation of $359. Over half the sessions won $500 or more.
Cheers,
Alan Shank

What?

Quote: treetopbuddy

What?

Elementary, my dear Watson, elementary.

as i indicated Next Tuesday I will start my new 3000 roll set. What ever the numbers are , they are.


Today i took off my past 1500 rolls... they indicated in the past 1500 rolls i had 16.06% more 6's, 20% more
8's and 15.3% less 7's than would be expected in a random test. I passed 3 of the 4 parts of of smart
craps which included the SRR... i failed the hardways with a 6.85% total and you need 1% or less to pass.

My srr was only 7.09 which is not a good as usual, but thats life.

Now i can sit back and wait for BUzzard to call be a liar.


Dicesitter

Well, where is this log from? Were the rolls in a casino? Why would I call you a liar ? ? ?

My comments in the past have been to inquire what the edge is. Or stated in a way that angers SOOPPO, how much better are you than me, a classic random roller? I am math illiterate. So exactly how many 7 did you roll in 1500 rolls ?

I mean in bowling I don't care about the percentage of spares made on the 7 pins, how many times you got tapped and left the 10
pin. I just wanna know the final score say 235 or 153. or you average for x number of games.

In a contest where we were trying to roll less 7's or more 7's,your choice, in 1000 rolls, how many more or less than me would you roll ?

I should think that should be easy to approximate. Or most 7's is sets of 100, how many sets should you win out of 20 sets.

Yes, LUCK is always involved. In Bowling, horseshoes, whatever. But SKILL is easily displayed by superior results.

On 14-1 pocket billiards , even a casual observer can see who the better player is in most instances. Luck is a greater factor in 9 ball
than straight pool. but skill reigns even more is that genre.

As for dice setters and schools on the web, I judge them as I do people in life. By the friends they keep. When on their web sites they also sell systems to beat the slots or pow gai poker, I assume they are scumbags.


I have respect for what you are attempting to do. Let me rephrase, for what you can do. My question is how much better can you do it better than an unskilled player like me.

Quote: dicesitter

as i indicated Next Tuesday I will start my new 3000 roll set. What ever the numbers are , they are.


Today i took off my past 1500 rolls... they indicated in the past 1500 rolls i had 16.06% more 6's, 20% more
8's and 15.3% less 7's than would be expected in a random test. I passed 3 of the 4 parts of of smart
craps which included the SRR... i failed the hardways with a 6.85% total and you need 1% or less to pass.

My srr was only 7.09 which is not a good as usual, but thats life.

Now i can sit back and wait for BUzzard to call be a liar.


Dicesitter

Mr. Sitter.... if you can reliably have an SRR of 7.09 then you should be a multimillionaire. Just passline randomly then full odds with your set is a giant house edge. Not a tiny one, a giant one. It looks like you roll more 6's than 7's, and more 8's than 7's, so you can also easily bet the 6 and 8 after your comeout roll to speed yourself along to riches. Oh wait, you usually do better than 7.09 SRR, so I underestimated your path to wealth. Seriously, I assume you do this craps thing for a living, and don't waste time with a job. And have millions saved up.... Or have I missed something?

To elaborate with an SRR of 7.09, with all other numbers being equal, the theoretical player advantage is as follows:

Place 4/10: 5.98%
5/9: 7.54%
6/8: 9.14%

PL with 3/4/5 odds: 11.03%!

Mind you, at and SRR 7.09 you can't overcome the HA on the horn bets.

dicesitter should be a millionaire with that kind of odds in his favor.

Quote: boymimbo

To elaborate with an SRR of 7.09, with all other numbers being equal, the theoretical player advantage is as follows:

Place 4/10: 5.98%
5/9: 7.54%
6/8: 9.14%

PL with 3/4/5 odds: 11.03%!

Mind you, at and SRR 7.09 you can't overcome the HA on the horn bets.

dicesitter should be a millionaire with that kind of odds in his favor.

Mr. Sitter also claims a huge increase in 6's and 8's, so you are WAY underestimating his advantage!

Quote: SOOPOO

Or have I missed something?

Just the math.

Quote: tupp

Just the math.

Not at all. Your terse answer says nothing, adds nothing, and is well.. worth nothing. His claim is so astounding as to be a casino crusher... Boymimbo gave some examples, which are actually lower than Mr. Sitter's claims.

Since the only known is the SRR, I estimate the frequency of all of the other numbers via an even distribution.

Take a look at the SRR of 7. The 7 comes up 1/7th of the time. That leaves the other 30 numbers to come up 6/7th of the time. Therefore, the odds of throwing a 2 would be 1/30*6/7 = 6/210 = 1/35. The odds of throwing a 6 or 8 is 5/35.

Therefore, the odds are quite straight forward: the place 6/8 has a PA of 7/6 (1/2) - (1/2) = 1/12 = 8.33%; the place 5/9 has a PA of 7/5 (4/35) - 4/35 = 1/15 and the place 4/10 has a PA of 9/5 (3/35) - 5/35 = 5%