Full Wheel Guarantee ... Calculations for any full wheel

[Brad]

Does anyone know how to work out the prize guarantee a full wheel would get?

For example, playing all the possible combination of 15 numbers (full wheel) in say 6/49 ... FW15 ...

the required 5005 combinations will get:

if 3 matched> 220x 3
if 4 matched> 660x 3 + 55x 4
if 5 matched> 1,200x 3 + 225x 4 + 10x 5
if 6 matched> 1,680x 3 + 540x 4 + 54x 5 + 1x 6

Gail Howard's program has the stats for all Full Wheels up to FW32, I'm interested how to do the actual calculations ... I lost my notes on that, I 'knew' how at one time.

Maybe there is a link to this info?

Cheers


PS could extend the above to include 2+Bonus and 5+Bonus prizes as well




Note: I moved some posts here from another thread (and changed this one slightly to suit the move)

 

[Brad]

Brad are you referring to the % of prizes in this pool of 178,365 lines?

Hi Frank,

I'm referring to the actual number of prizes, not percentages, when playing all the possible combinations.

 

[Brad]

I have the number of combinations for each number for a full wheel, but not the prize guarantee. Would be nice to know in a different thread.

 

[Karnac]

The LS2004 program should give you what you want. Set it for 49 numbers , Check off check all combinations. Let it process the 13M+ combos then press the Lotto check, put in the winning numbers of choice and the breakdown is given ..... or is that not what you want.

 

[Brad]

See? All I had to do was ask!

Great stuff Karnac, now I have a reason to try the Wheeler. I just wonder how long it will take to generate ALL the ~14M combinations? ... I'll report back later on that.

I would still like to know how to do them calculations 'manually', just for my records.


Cheers

 

[Karnac]

I'm at 1.3 million now after 24 minutes...P4 1.8G 512K ram

You can even save it to say ya got it

 

[Brad]

Hey, I have identical specs, P4 1.8G 512K

But mine's getting about a Mil per 15 min, so at this rate I'm expecting 3.5 hrs to complete. And that's after I lowered the priority to 'below normal' in Task Manager ... otherwise the prog is a real memory hog (99%).

Quick observation, de-selecting 'row number' and setting the 'Font' on lowest (6) seems to speed things up ... that's just a visual take, didn't actually time it.

Now for saving it, any guess how big the file's gonna be? Will I need another HDD? I have 20GB left

 

[hot4]

let me see if I finish before your pentiums :

6 numbers : 1 line = 1 first prize
5+b : 6 lines = 6 second prizes
5 numbers : 252 lines = 252 third prizes
4 numbers : 13545 lines = 13545 fourth prizes
3 numbers : 246,820 lines = 246,820 fifth prizes

OK Brad now you calculate 2+b

 

[Brad]

Hrmphffffffff .....

It all started off swimmingly, then my lappy got slower and slower ... until it bogged down down to a crawl around the 11M mark or so. Took about 12 hrs but I decided to end the run then, saved the file ... 212MB.

So despite a valiant effort on my lappy's part to crunch the whole 14M enchilada I had to take pity on my electronic friend and give it a respite from the beastly task. Maybe another day I'll have a try again.

There must be an easier way to do this, a pencil/paper effort would accomplish this much faster, I'm still looking for a calc solution.

So Frank, you must have access to a Mother of all Computers, or a Cybernetic Speedy Gonzales to get them figures so fast, eh? ... either that or a sharp pencil

 

[PAB]

Hi Brad,

The Results hot4 have Given Above are for a 649 Lotto with a Bonus Number in Addition to the Match 5, these Results are Achieved with the Following Formulas :-

6 = COMBIN(6,6)*COMBIN(43,0) = 1 Combination
5 + = COMBIN(6,5)*COMBIN(43,0) = 6 Combinations
5 = COMBIN(6,5)*COMBIN(42,1) = 252 Combinations
4 = COMBIN(6,4)*COMBIN(43,2) = 13,545 Combinations
3 = COMBIN(6,3)*COMBIN(43,3) = 246,820 Combinations
Total Winning Combinations = 260,624 Combinations

2 = COMBIN(6,2)*COMBIN(43,4) = 1,851,150 Combinations
1 = COMBIN(6,1)*COMBIN(43,5) = 5,775,588 Combinations
0 = COMBIN(6,0)*COMBIN(43,6) = 6,096,454 Combinations
Total Losing Combinations = 13,723,192 Combinations

Total Winning Combinations = 260,624 Combinations
Total Losing Combinations = 13,723,192 Combinations
Total Combinations = 13,983,816 Combinations

Also take a Look at johnph77's Site ( Well Worth a Visit ). Here is the Link that will Show you the Actual Formulae for the Canadian BC 649 Lotto :-
http://www.johnph77.com/math/stlot.html#cndbc49

Hope this Helps.

All the Best.
PAB

 

[hot4]

Re: Hrmphffffffff .....

...<snip>
So Frank, you must have access to a Mother of all Computers, or a Cybernetic Speedy Gonzales to get them figures so fast, eh? ... either that or a sharp pencil

As PAB posted, using those formulas, CYBERNATICALLY with my Windows calculator!

Next step: how to calculate 2+b?

 

[PAB]

Sorry Brad,

I Forgot to Include the Formulas if the Bonus was Also Relevant with a Match 2. I think these are the Correct Formulas ( I am Sure Someone will Correct me if I am Wrong ) :-

2 + = COMBIN(6,2)*COMBIN(42,3) = 172,200 Combinations
2 = COMBIN(6,2)*COMBIN(42,4) = 1,678,950 Combinations

All the Best.
PAB

 

[Karnac]

Re: Hrmphffffffff .....

It all started off swimmingly, then my lappy got slower and slower ... until it bogged down down to a crawl around the 11M mark or so. Took about 12 hrs but I decided to end the run then, saved the file ... 212MB.

So despite a valiant effort on my lappy's part to crunch the whole 14M enchilada I had to take pity on my electronic friend and give it a respite from the beastly task. Maybe another day I'll have a try again.

There must be an easier way to do this, a pencil/paper effort would accomplish this much faster, I'm still looking for a calc solution.

So Frank, you must have access to a Mother of all Computers, or a Cybernetic Speedy Gonzales to get them figures so fast, eh? ... either that or a sharp pencil

I had to bail too Brad....things got so slow everything started to freeze...I only got a little over half done and then I started to wonder if it was all that necessary.

 

[Brad]

Same here, Karnac ... I was curiosity driven

I did it just to see if I could, to see how my laptop would fare ...
The text file with all the combos, I'm guesstimating, would be about 250MB ... so not as big as I thought, not that I'd save it anyway.

Thanks Pab and Frank for your input. John's site is very good, I kinda forgot he had all the info.


Cheers



curiosity did not kill the Cat ... but almost smoked the lappy

 

[Brad]

Frank ... re: 2+B for 6/49

((6!/4!)/(2!))x((43!/39!)/(4!))x(4/43) = 172,200 possibilities, with 1:81 odds .... eh?

 

[PAB]

Hi Brad,

250MB for ALL 13,983,816 Combinations of a 649 Lotto Sounds about Right. I did Produce them ALL ( One Combination Per Cell ) to an Excel Spreadsheet Once, and from what I can Remember it was Something Around that Number .

All the Best.
PAB

 

[BushHappy]

I used the LottoGenius Full Wheels Generator ( which can be downloaded for free from http://www.lottogenius.com/Download/default ) to create the Full Wheel in 3 hours. The program worked in the background and did not slow any other processes down.

The size of the text file created was 410Mb - zips down to 68Mb (Still too big to send to anyone). The text file includes the line number - if the programmer had not included this the file would have been much smaller.

It took about 2 minutes to open the file using the text editor - 'Programmer's File Editor'

Cheers,
BushHappy

 

[Brad]

Thanks BushHappy,

LottoGenius FWGen is certainly a lot faster, it'll be in handy for those who need a Full Wheel. I did it only to see if I could (can you say bored? ).

However, I did find the calcs needed for working out the prize guarantee for full wheels, which was the original intent of this thread. Just have to adapt the formula from FW49 to an FW, for any Full Wheel now.


PAB,

re-check these lines in your posts:

-->2 = COMBIN(6,2)*COMBIN(42,4) = 1,678,950 Combinations
-->2 = COMBIN(6,2)*COMBIN(43,4) = 1,851,150 Combinations

I'm not fluent in Excel Speak, but this is what I get with good old factorials:

((6!/4!)/(2!))x((43!/39!)/(4!)) = 1,851,150

so it looks like your bottom line is it.



Cheers

 

[lottoarchitect]

I'm at 1.3 million now after 24 minutes...P4 1.8G 512K ram

You can even save it to say ya got it

Unbelievable... Do you really wait that much to generate all possible combinations to a text file? I just tried my system and saved the full 6/49 combinations in 1 minute and 20 secs... The file is only... 386.7MB lol

 

[PAB]

Hi Brad,

Your ...

((6!/4!)/(2!))x((43!/39!)/(4!)) = 1,851,150 Combinations

... is Correct for a Match 2.

You Asked what the Result would be if the Bonus Ball was ALSO Relevant with the Match 2.
Therefore you have to Take this into Account when Calculating for the Match 2. The Formulas and Resulting Combinations are as Follows :-

2 + Bonus = COMBIN(6,2)*COMBIN(42,3) = 172,200 Combinations
2 = COMBIN(6,2)*COMBIN(42,4) = 1,678,950 Combinations

That Makes the Full Table with the Bonus Relevant for Match 5 & Match 2 as Follows :-

6 = COMBIN(6,6)*COMBIN(43,0) = 1 Combination
5 + Bonus = COMBIN(6,5)*COMBIN(43,0) = 6 Combinations
5 = COMBIN(6,5)*COMBIN(42,1) = 252 Combinations
4 = COMBIN(6,4)*COMBIN(43,2) = 13,545 Combinations
3 = COMBIN(6,3)*COMBIN(43,3) = 246,820 Combinations
2 + Bonus = COMBIN(6,2)*COMBIN(42,3) = 172,200 Combinations
Total Winning Combinations = 432,824 Combinations

2 = COMBIN(6,2)*COMBIN(43,4) = 1,678,950 Combinations
1 = COMBIN(6,1)*COMBIN(43,5) = 5,775,588 Combinations
0 = COMBIN(6,0)*COMBIN(43,6) = 6,096,454 Combinations
Total Losing Combinations = 13,550,992 Combinations

Total Winning Combinations = 432,824 Combinations
Total Losing Combinations = 13,550,992 Combinations
Total Combinations = 13,983,816 Combinations

Hope this Helps.
All the Best.
PAB