# Odds and Total Combinations for a 649 Lotto

#### PAB

##### Member
Hi Everyone,

Has anyone got the following Odds and Total Combinations for a 649 Lotto please :-

Match 6 Main Numbers & 0 Bonus Number
Match 5 Main Numbers & 1 Bonus Number
Match 5 Main Numbers & 0 Bonus Number
Match 4 Main Numbers & 1 Bonus Number
Match 4 Main Numbers & 0 Bonus Number
Match 3 Main Numbers & 1 Bonus Number
Match 3 Main Numbers & 0 Bonus Number
Match 2 Main Numbers & 1 Bonus Number
Match 2 Main Numbers & 0 Bonus Number
Match 1 Main Numbers & 1 Bonus Number
Match 1 Main Numbers & 0 Bonus Number
Match 0 Main Numbers & 1 Bonus Number
Match 0 Main Numbers & 0 Bonus Number

Best Regards.
PAB

#### johnph77

##### Member
Beaker -

Thank you, kind sir!

PAB:

If there is a specific lottery using this format and the payout percentages are not listed on that page please either direct me to a site where I may obtain appropriate information or Email/Private Message me with same and I'll be happy to calculate, update and include.

gl

johnph77

#### johnph77

##### Member
Incomplete response, even on the linked page - sorry for any inconvenience.

Draw 6 from 49 with Bonus
• Hit 6 - 1 possibility, odds - 1::13,983,816.00
• Hit 5 + Bonus - 6 possibilities, odds - 1::2,330,636.00
• Hit 5 - 252 possibilities, odds - 1::55,491.33
• Hit 4 + Bonus - 630 possibilities, odds - 1::22,196.33
• Hit 4 - 12,915 possibilities, odds - 1::1,082.76
• Hit 3 + Bonus - 17,220 possibilities, odds - 1::812.07
• Hit 3 - 229,600 possibilities, odds - 60.91
• Hit 2 + Bonus - 172,200 possibilities, odds - 1::81.21
• Hit 2 - 1,678,950 possiblities, odds - 1::8.33
• Hit 1 + Bonus - 671,580 possibilities, odds - 1::20.82
• Hit 1 - 5,104,008 possibilities, odds - 1::2.74
• Hit 0 + Bonus - 850,668 possibilities, odds - 1::16.44
• Hit 0 - 5,245,786 possibilities, odds - 1::2.67

13.983,816 total possibilities.

Sorry for the poor formatting, would look much better in a table.....

#### peter

##### Member
Great information johnph77.
Welcome to the forum. I look forward to your posts.

#### PAB

##### Member
Thanks for the Replies.

This site is great and very Comprehensive :-
http://www.johnph77.com/math/stlot.html

johnph77 :-
Thanks very much for the Statistics, most appreciated.
It was not for a specific Lotto, it was just for my personal interest.

All the Best
PAB

#### johnph77

##### Member
PAB -

yqw

All -

tya for the kind words and warm welcome. If I can help on the math end let me know - I'll do what I can.

gl

john

#### PAB

##### Member
Hi John,

The post of the results to my initial question was exactly what I wanted.
Out of curiosity could you possibly help with the following statistics. In the UK we have a Lotto called "HOTPICKS", it is basically a Draw of 6 Numbers from 49 ( which you have Data on your site for the 2,3 and 4 ) and you must either Match 2,3 or 4 Numbers out of the 6 Numbers Drawn. Is it possible for you to ( in the same format you listed previously in this post ) provide the the other Odds and Combinations for Match 6 Main Numbers, Match 5 Main Numbers, Match 1 Main Number and Match 0 Main Numbers.

All the Very Best
PAB

#### johnph77

##### Member
PAB -

Well, you got my attention! First or all, the game formula is wrong - it should be the standard formula for 6/49, but the number of possibilities is correct - I'll correct that, and thanks for bringing it to my attention. Secondly, I'm coming up with numbers I'm not entirely happy with at this time, but here goes.

6 of 6 drawn from 49 - 1 possibility, odds - 1::13,983,816.00
5 of 6 drawn from 49 - 44 possibilities, odds - 1::317,814.00
4 of 6 drawn from 49 - 990 possibilities, odds - 1::14,125.07
3 of 6 drawn from 49 - 15,180 possibilities, odds - 1::921.20
2 of 6 drawn from 49 - 178,365 possibilities, odds - 1::78.40
1 of 6 drawn from 49 - 1,712,304 possibilities, odds - 1::8.17
0 of 6 drawn from 49 - 12,076,932 possibilities, odds - 1::1.16

Total possibilities - 13,983,816

I'm probably being paranoid about this - the numbers look good, and the posted percentages for the existing games are in line with normal payouts. If I find anything down the road yielding different results I'll let you know. In the meantime, if you're playing this game on a regular basis and coming up with a different pattern than what I've shown, let me know and I'll take it all back to the drawing board.

gl

john

#### PAB

##### Member
Hi John,

Have you had any luck yet.
I have played it only several times but with no success
The Formula for Combinations of a Standard 649 Lotto are :-

6 Numbers = COMBIN(6,6)*COMBIN(43,0)
5 Numbers = COMBIN(6,5)*COMBIN(43,1)
4 Numbers = COMBIN(6,4)*COMBIN(43,2)
3 Numbers = COMBIN(6,3)*COMBIN(43,3)
2 Numbers = COMBIN(6,2)*COMBIN(43,4)
1 Numbers = COMBIN(6,1)*COMBIN(43,5)
0 Numbers = COMBIN(6,0)*COMBIN(43,6)

Total Combinations 13,983,816.

Hope this helps.
All the Best
PAB

#### johnph77

##### Member

The above posted possibilities and odds are correct with one exception.

0 of 6 drawn from 49 - 6,096,454 possibilities, odds - 1::2.29

Now, you say, the possibilities don't add up to the total game possibilities, and you are correct. They don't. But, in this case, given the restrictions imposed, they can't. Each of the conditions (any number drawn of 6 from 49) is an independent game separate from any other, requiring an independent calcuation. For instance, when you draw 5 of 6 from 49, you only play 5 numbers, not 6. The 44 possibilities will include the 6th number drawn in the 6/49 game as well as the other 43 numbers that weren't drawn.

gl

#### PAB

##### Member
Hi John,

Thank you for your explanation. As you say, this game has different criteria to most standard Lotto games.
I have used these Formulas in Excel to come up with the Total Combinations for the Lotto HotPicks game.

6 Numbers = COMBIN(6,6)*COMBIN(43,0) = 1 Combination
5 Numbers = COMBIN(5,5)*COMBIN(44,1) = 44 Combinations
4 Numbers = COMBIN(4,4)*COMBIN(45,2) = 990 Combinations
3 Numbers = COMBIN(3,3)*COMBIN(46,3) = 15,180 Combinations
2 Numbers = COMBIN(2,2)*COMBIN(47,4) = 178,365 Combinations
1 Numbers = COMBIN(1,1)*COMBIN(48,5) = 1,712,304 Combinations
0 Numbers = COMBIN(0,0)*COMBIN(49,6) = 12,076,932 Combinations

Total Combinations = 13,983,816

The 12,076,932 ( Match NO Numbers ) Combinations are the 13,983,816 Combinations Minus ALL the others.
You say the Odds for the Match NO Numbers is 1 in 1.16, could you possibly give me the Formula to work this out please.

Thanks
Good Luck
PAB

#### johnph77

##### Member
PAB

You are spot on with your formulas for the calculation of every number save the 0 number formula. The formula you cite (0 Numbers = COMBIN(0,0)*COMBIN(49,6) = 12,076,932 Combinations) is the formula used for the overall game and, when calculated, yields a result of 13,983,816.

As I tried to state in my previous post (and obviously failed) these formulas and possibilities are NOT linked to any of the other formulas and possibilities in the set but rather the formulas and possibilities for a standalone game only. If you were ever to host a game in which you would pay the bettor in the event that NO number selected by the bettor would be included in the 6 numbers selected by the lottery comission the formula would be:

COMBIN(0,0)*COMBIN(43,6) = 6,096,454 possibilities.

And that's the same formula used for calculating the possibilites of drawing 0 numbers in the overall game.

#### PAB

##### Member
Hi John,

Thanks for the explanation, it is much clearer now, I can see the logic behind it.
Thanks for your time and input, most appreciated.

Good Luck
PAB

#### PAB

##### Member
Lotto Information

Hi John,

A new Lotto started on Friday the 13th of February 2004 called Euro Millions. It is at present, only for France, Spain and the UK.
The Draw takes place on Friday evenings.
There are 5 ( five ) Main Numbers Drawn from 1 to 50, and 2 ( two ) Lucky Star Numbers Drawn from 1 to 9.
In all there are 12 ( twelve ) Prizes.
I have come up with the Information below as near as to the Format that you use on your site.

Euro Millions Lotto - Total Possibilities = 76,275,360.

5/50 2/9 Possibilities Odds - 1: Payout Total Payout Payout Pct
5 2 1 76275360.00 Pari-mutuel Pari-mutuel Pari-mutuel
5 1 14 5448240.00 Pari-mutuel Pari-mutuel Pari-mutuel
5 0 21 3632160.00 Pari-mutuel Pari-mutuel Pari-mutuel
4 2 225 339001.60 Pari-mutuel Pari-mutuel Pari-mutuel
4 1 3,150 24214.40 Pari-mutuel Pari-mutuel Pari-mutuel
4 0 4,725 16142.93 Pari-mutuel Pari-mutuel Pari-mutuel
3 2 9,900 7704.58 Pari-mutuel Pari-mutuel Pari-mutuel
3 1 138,600 550.33 Pari-mutuel Pari-mutuel Pari-mutuel
3 0 207,900 366.88 Pari-mutuel Pari-mutuel Pari-mutuel
2 2 141,900 537.53 Pari-mutuel Pari-mutuel Pari-mutuel
2 1 1,986,600 38.39 Pari-mutuel Pari-mutuel Pari-mutuel
2 0 2,979,900 25.60 0 0 0.00%
1 2 744,975 102.38 Pari-mutuel Pari-mutuel Pari-mutuel
1 1 10,429,650 7.31 0 0 0.00%
1 0 15,644,475 4.88 0 0 0.00%
0 2 1,221,759 62.43 0 0 0.00%
0 1 17,104,626 4.46 0 0 0.00%
0 0 25,656,939 2.97 0 0 0.00%
Winners 3,238,011 23.56 Pari-mutuel Pari-mutuel

There is also an Irish 642 Lotto.
The Draw takes place on Wednesday and Saturday evenings.
There are 6 ( six ) Main Numbers Drawn from 1 to 42, and 1 ( one ) Bonus Numbers Drawn from 1 to 42.
In all there are 6 ( six ) Prizes.
I have come up with the Information below as near as to the Format that you use on your site.
This also might be a useful addition.
I hope that the Formulas are O.K.

6/42 Bonus? Formula
6 N/A ((6!/0!)/(6!))x((36!/36!)/(0!))
5 Y ((6!/1!)/(5!))x((36!/35!)/(1!))x(1/36)
5 N ((6!/1!)/(5!))x((36!/35!)/(1!))x(35/36)
4 Y ((6!/2!)/(4!))x((36!/34!)/(2!))x(2/36)
4 N ((6!/2!)/(4!))x((36!/34!)/(2!))x(34/36)
3 Y ((6!/3!)/(3!))x((36!/33!)/(3!))x(3/36)
3 N ((6!/3!)/(3!))x((36!/33!)/(3!))x(33/36)
2 N/A ((6!/4!)/(2!))x((36!/32!)/(4!))x(32/36)
1 N/A ((6!/5!)/(1!))x((36!/31!)/(5!))x(31/36)
0 N/A ((6!/6!)/(0!))x((36!/30!)/(6!))x(30/36)

Irish 642 Lotto - Formula for Total Possibilities - ((42!/36!)/(6!)) = 5,245,786.

6/42 Bonus? Possibilities Odds - 1: Payout Total Payout Payout Pct
6 N/A 1 5245786.00 Pari-mutuel Pari-mutuel Pari-mutuel
5 Y 6 874297.67 Pari-mutuel Pari-mutuel Pari-mutuel
5 N 210 24979.93 Pari-mutuel Pari-mutuel Pari-mutuel
4 Y 525 9991.97 Pari-mutuel Pari-mutuel Pari-mutuel
4 N 8,925 587.76 Pari-mutuel Pari-mutuel Pari-mutuel
3 Y 11,900 440.82 Pari-mutuel Pari-mutuel Pari-mutuel
3 N 130,900 40.07 0 0 0.00%
2 N/A 883,575 5.94 0 0 0.00%
1 N/A 2,261,952 2.32 0 0 0.00%
0 N/A 1,947,792 2.69 0 0 0.00%
Winners 21,567 243.23 Pari-mutuel Pari-mutuel

The Very Best of Luck
PAB

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#### johnph77

##### Member
Response - Irish Lottery

Rather lengthy responses to the last post upcoming - will treat them separately. Hope no one minds.

On the Irish Lottery information the formulas for hitting 2, 1 and 0 of 6 would be:

2 - ((6!/4!)/(2!))x((36!/32!)/(4!))
1 - ((6!/5!)/(1!))x((36!/31!)/(5!))
0 - ((6!/6!)/(0!))x((36!/30!)/(6!))

Note that if the bonus ball doesn't come into play the bonus ball calculation qualifiers ( x(32/36), x(31/36), and x(30/36), respectively ) are not included in the formula or the calculation process of the possibilities. The possibilities you do cite for the game, however, are right on the money.

TY for the info - I'll get it on site ASAP.

#### johnph77

##### Member
Response - Euro Millions

PAB -

I had known about the Euro Millions game since its inception but was mystified as to how to approach the calculation process and the formulas that would be used in doing so. Thanks to your post I think I now have a handle on how it should be accomplished.

I believe the formulas you posted are incorrect, but not the possibilities. I came to the conclusion that formulas have to be determined and calculations have to be performed for each draw - the 5/50 and the 2/9 - separately, then combined. Pardon any errors, both math and grammar - I'm doing this on the fly. The data will be rechecked before posting.

Given this:

5/50 - (50!/45!)/(5!) - 2,118,760 possibilities.

Hit 5 - ((5!/0!)/(5!))x((45!/45!)/(0!)) - 1 possibility.
Hit 4 - ((5!/1!)/(4!))x((45!/44!)/(1!)) - 225 possibilities.
Hit 3 - ((5!/2!)/(3!))x((45!/43!)/(2!)) - 9.900 possibilities.
Hit 2 - ((5!/3!)/(2!))x((45!/42!)/(3!)) - 141,900 possibilities.
Hit 1 - ((5!/4!)/(1!))x((45!/41!)/(4!)) - 744,975 possibilities.
Hit 0 - ((5!/5!)/(0!))x((45!/40!)/(5!)) - 1,221,759 possibilities.

2/9 - (9!/7!)/(2!) - 36 possibilities.

Hit 2 - ((2!/0!)/(2)!)x((7!/7!)/(0!)) - 1 possibility.
Hit 1 - ((2!/1!)/(1!))x((7!/6!)/(1!)) - 14 possibilities.
Hit 0 - ((2!/2!)/(0!))x((7!/5!)/(2!)) - 21 possibilities.

Therefore:

Euro Millions - ((50!/45!)/(5!))x((9!/7!)/(2!)) - 76,275,360 possibilities.

Hit 5/2 - ((5!/0!)/(5!))x((45!/45!)/(0!))x((2!/0!)/(2)!)x((7!/7!)/(0!)) - 1 possibility, odds - 1::76,275,360.00.
Hit 5/1 - ((5!/0!)/(5!))x((45!/45!)/(0!))x((2!/1!)/(1!))x((7!/6!)/(1!)) - 14 possibilities, odds - 1::5,448,240.00.
Hit 5/0 - ((5!/0!)/(5!))x((45!/45!)/(0!))x((2!/2!)/(0!))x((7!/5!)/(2!)) - 21 possibilities, odds - 1::3,632,160.00.
Hit 4/2 - ((5!/1!)/(4!))x((45!/44!)/(1!))x((2!/0!)/(2)!)x((7!/7!)/(0!)) - 225 possibilities, odds - 1::339,001.60.
Hit 4/1 - ((5!/1!)/(4!))x((45!/44!)/(1!))x((2!/1!)/(1!))x((7!/6!)/(1!)) - 3,150 possibilities, odds - 1::24,214.40.
Hit 4/0 - ((5!/1!)/(4!))x((45!/44!)/(1!))x((2!/2!)/(0!))x((7!/5!)/(2!)) - 4,725 possibilities, odds - 1::16,142.93.
Hit 3/2 - ((5!/2!)/(3!))x((45!/43!)/(2!))x((2!/0!)/(2)!)x((7!/7!)/(0!)) - 9,900 possibilities, odds - 1::7,704.58.
Hit 3/1 - ((5!/2!)/(3!))x((45!/43!)/(2!))x((2!/1!)/(1!))x((7!/6!)/(1!)) - 138,600 possibilities, odds - 1::550.33.
Hit 3/0 - ((5!/2!)/(3!))x((45!/43!)/(2!))x((2!/2!)/(0!))x((7!/5!)/(2!)) - 207,900 possibilities, odds - 1::366.88.
Hit 2/2 - ((5!/3!)/(2!))x((45!/42!)/(3!))x((2!/0!)/(2)!)x((7!/7!)/(0!)) - 141,900 possibilities, odds - 1::537.53.
Hit 2/1 - ((5!/3!)/(2!))x((45!/42!)/(3!))x((2!/1!)/(1!))x((7!/6!)/(1!)) - 1,986,600 possibilities, odds - 1::38.39.
Hit 2/0 - ((5!/3!)/(2!))x((45!/42!)/(3!))x((2!/2!)/(0!))x((7!/5!)/(2!)) - 2,979,900 possibilities, odds - 1::25.60.
Hit 1/2 - ((5!/4!)/(1!))x((45!/41!)/(4!))x((2!/0!)/(2)!)x((7!/7!)/(0!)) - 744,975 possibilities, odds - 1::102.39.
Hit 1/1 - ((5!/4!)/(1!))x((45!/41!)/(4!))x((2!/1!)/(1!))x((7!/6!)/(1!)) - 10,429,650 possibilities, odds - 1::7.31.
Hit 1/0 - ((5!/4!)/(1!))x((45!/41!)/(4!))x((2!/2!)/(0!))x((7!/5!)/(2!)) - 15,644,475 possibilities, odds - 1::4.88.
Hit 0/2 - ((5!/5!)/(0!))x((45!/40!)/(5!))x((2!/0!)/(2)!)x((7!/7!)/(0!)) - 1,221,759 possibilities, odds - 1::62.43.
Hit 0/1 - ((5!/5!)/(0!))x((45!/40!)/(5!))x((2!/1!)/(1!))x((7!/6!)/(1!)) - 17,104,626 possibilities, odds - 1::4.46.
Hit 0/0 - ((5!/5!)/(0!))x((45!/40!)/(5!))x((2!/2!)/(0!))x((7!/5!)/(2!)) - 25,656,939 possibilities, odds - 1::2.97.
Total winners (5/2 through 2/1 + 1/2) - 3,238,011, odds - 1::23.56.

gl

john

Last edited:

#### PAB

##### Member
Hi John,

I came up with the same answers as yourself using Formulas in Excel, my problem was not fully understanding how to interpret them into the Format that you use, my appologies.

If you would like the Excel Formulas please let me know and I will post them here.

Once again, thank you

Cheers
PAB

#### johnph77

##### Member
PAB -

No apologies necessary, and sorry about the errors, particularly with your name - I might get them all edited out eventually. It's a little comforting to know we can use different approaches and come up with the same answers.

I'm a little irked with myself with not being able to come up with this sooner, though - I had done a similar posting of a lottery with two different draws on the site last year. Senility sets in, I guess, and there is no recovery.....

Posting the Excel COMBIN functions won't be necessary, but thanks for the offer. One of these years I may convert my spreadsheet calculator over to that method (or do it just for the exercise) but I'll continue to post the formulas on the site in math format.

gl

john

#### PAB

##### Member
Hi John,

I think that the different approaches is worthwhile not only for the Statistics aspect, but also with help in understanding how the answer is achieved and the Logic behind it.
I have just completely checked the figures for the Euro Millions and have just got one query. On the Match 1 Main Number & 0 Lucky Star Numbers I have the same Combinations as yourself ( 15,644,475 ) but have the Odds as 1 in 4.88 as opposed to yours of 1 in 4.48.

All the Best
PAB