Odds and Total Combinations for a 649 Lotto
- Thread starter PAB
- Start date
New Additions
Hi John,
I can see you have been busy with the Additions of the Euro Millions and Irish Lottos to your site.
http://www.johnph77.com/math/stlot.html
I have checked my figures of Possibilities and Odds with yours for the following Lottos :-
Euro Millions
Irish 642
UK 649 Main
UK 649 Extra
UK HotPicks
UK ThunderBall
UK Daily Play
Everything agrees except for the following three :-
(1) On the Euro Millions, you show the Match 0 Main Numbers & 2 Lucky Star Numbers as Odds of 1 in 62.83, I actually make it Odds of 1 in 62.43.
(2) On the UK 649 Extra, you show the Total Winners as 1 with Odds of 1 in 13,986,816.00, the Odds should be 1 in 13,983,816.00.
(3) On the UK Daily Play, you show the Total Winners as 121,551 with Odds of 1 in 7.51, I actually make it Odds of 1 in 7.31.
I hope that this does not cause too many problems for you.
All the Very Best
PAB
Hi John,
I can see you have been busy with the Additions of the Euro Millions and Irish Lottos to your site.
http://www.johnph77.com/math/stlot.html
I have checked my figures of Possibilities and Odds with yours for the following Lottos :-
Euro Millions
Irish 642
UK 649 Main
UK 649 Extra
UK HotPicks
UK ThunderBall
UK Daily Play
Everything agrees except for the following three :-
(1) On the Euro Millions, you show the Match 0 Main Numbers & 2 Lucky Star Numbers as Odds of 1 in 62.83, I actually make it Odds of 1 in 62.43.
(2) On the UK 649 Extra, you show the Total Winners as 1 with Odds of 1 in 13,986,816.00, the Odds should be 1 in 13,983,816.00.
(3) On the UK Daily Play, you show the Total Winners as 121,551 with Odds of 1 in 7.51, I actually make it Odds of 1 in 7.31.
I hope that this does not cause too many problems for you.
All the Very Best
PAB
johnph77
Member
PAB -
Not any problem whatsoever - I'll rerun through the software and make corrections as necessary. I'm not the world's greatest typist, there are a lot of numbers with which to deal and I've always welcomed corrections and comments.
Page has been edited and uploaded.
Thanks and gl.
john
Not any problem whatsoever - I'll rerun through the software and make corrections as necessary. I'm not the world's greatest typist, there are a lot of numbers with which to deal and I've always welcomed corrections and comments.
Page has been edited and uploaded.
Thanks and gl.
john
HotPicks
Hi John,
I am glad I was able to help.
Out of Interest are you going to do any more work on the HotPicks?. I have listed the figures I have come up with below if that is of any use to you.
UK HotPicks Lotto
Description Possibilities Odds - 1: Payout Total Payout Payout Pct
Pick 6 of 6 1 13,983,816.00
Pick 5 of 6 44 317,814.00
Pick 4 of 6 990 14,125.07 7,000 6,930,000 49.56%
Pick 3 of 6 15,180 921.20 450 6,831,000 48.86%
Pick 2 of 6 178,365 78.40 40 7,134,600 51.03%
Pick 1 of 6 1,712,304 8.17
Pick 0 of 6 12,076,932 1.00
Total Winners 194,535 71.88
Thank you very much for the kind mention on your site.
Good Luck and All the Best
PAB
Hi John,
I am glad I was able to help.
Out of Interest are you going to do any more work on the HotPicks?. I have listed the figures I have come up with below if that is of any use to you.
UK HotPicks Lotto
Description Possibilities Odds - 1: Payout Total Payout Payout Pct
Pick 6 of 6 1 13,983,816.00
Pick 5 of 6 44 317,814.00
Pick 4 of 6 990 14,125.07 7,000 6,930,000 49.56%
Pick 3 of 6 15,180 921.20 450 6,831,000 48.86%
Pick 2 of 6 178,365 78.40 40 7,134,600 51.03%
Pick 1 of 6 1,712,304 8.17
Pick 0 of 6 12,076,932 1.00
Total Winners 194,535 71.88
Thank you very much for the kind mention on your site.
Good Luck and All the Best
PAB
Last edited:
johnph77
Member
Text #1
PAB -
Re mention - yqw, and thanks again for the help.
I told myself I wasn't going to fool around with HotPicks any more, that I had posted the numbers and the payout percentages on site and that was going to be it. I lied. I was still apprehensive and/or paranoid about the posted numbers and I wanted to be certain they were correct, so I tried a new approach.
There are 6 HotPick games possible, but not necessarily offered - Pick 1, 2, 3, 4, 5 and 6. If you were to play a 6 HotPicks game it would be the same game as playing the regular 6/49 lottery, with the same number of possibilities and odds inherent in any 6/49 game.
But if you were to play a 5 HotPick game you are basically playing a 5/49 lottery game with the number of hits in each category (5 of 5, 4 of 5, etc.) being determined by the number of permutations in the 6 numbers of the main draw.
If you were to play a 1 HotPick game you would be playing a 1/49 game. There would be 49 possibilities, of which 6 of those numbers would hit 1 in 6/49 and 43 would hit 0 in 6/49.
Therefore, each of the numbers in HotPicks has to be treated as a standalone game with its own number of possibilities and odds. And each would be calculated in its own way - the 5 HotPicks game would be calculated as a 5/49 lottery, the 4 HotPicks game would be calculated as a 4/49 lottery, and so on. As stated before, the number of possibilities would be determined by the particular number of permutations possible in the 6 numbers drawn in the 6/49 lottery. Then, if you wanted to know how many of each number of hits would fall in the entire 6/49 draw, you would establish the ratio between the possibilities of each HotPick game and the possibilities in the 6/49 draw (13,983,816) and multiply each of the number of hits by that ratio. Note that in doing so the odds would remain constant. The charts in the next post may make this clearer.
PAB -
Re mention - yqw, and thanks again for the help.
I told myself I wasn't going to fool around with HotPicks any more, that I had posted the numbers and the payout percentages on site and that was going to be it. I lied. I was still apprehensive and/or paranoid about the posted numbers and I wanted to be certain they were correct, so I tried a new approach.
There are 6 HotPick games possible, but not necessarily offered - Pick 1, 2, 3, 4, 5 and 6. If you were to play a 6 HotPicks game it would be the same game as playing the regular 6/49 lottery, with the same number of possibilities and odds inherent in any 6/49 game.
But if you were to play a 5 HotPick game you are basically playing a 5/49 lottery game with the number of hits in each category (5 of 5, 4 of 5, etc.) being determined by the number of permutations in the 6 numbers of the main draw.
If you were to play a 1 HotPick game you would be playing a 1/49 game. There would be 49 possibilities, of which 6 of those numbers would hit 1 in 6/49 and 43 would hit 0 in 6/49.
Therefore, each of the numbers in HotPicks has to be treated as a standalone game with its own number of possibilities and odds. And each would be calculated in its own way - the 5 HotPicks game would be calculated as a 5/49 lottery, the 4 HotPicks game would be calculated as a 4/49 lottery, and so on. As stated before, the number of possibilities would be determined by the particular number of permutations possible in the 6 numbers drawn in the 6/49 lottery. Then, if you wanted to know how many of each number of hits would fall in the entire 6/49 draw, you would establish the ratio between the possibilities of each HotPick game and the possibilities in the 6/49 draw (13,983,816) and multiply each of the number of hits by that ratio. Note that in doing so the odds would remain constant. The charts in the next post may make this clearer.
johnph77
Member
Charts
6 HotPicks
Formula - ((49!/43!)/(6!)) - 13,983,816 possibilities.
6 in 6 - 1 possibility, odds - 1::13,983,816.00, 1 possibility in 6/49.
5 in 6 - 258 possibilities, odds - 1::54,200.84, 258 possibilities in 6/49.
4 in 6 - 13,545 possibilities, odds - 1::1,032.40, 13,545 possibilities in 6/49.
3 in 6 - 246,820 possibilities, odds - 1::56.66, 246,820 possibilities in 6/49.
2 in 6 - 1,851,150 possibilities, odds - 1::7.55, 1,851,150 possibilities in 6/49.
1 in 6 - 5,775,588 possibilities, odds - 1::2.42, 5,775,588 possibilities in 6/49.
0 in 6 - 6,096,454 possibilities, odds - 1::2.29, 6,096,454 possibilities in 6/49.
***************
5 HotPicks
Formula - ((49!/44!)/(5!)) - 1,906,884 possibilities.
5 in 6 - 6 possibilities, odds - 1::317,814.00, 44 possibilities in 6/49.
4 in 6 - 645 possibilities, odds - 1::2,956.41, 4,730 possibilities in 6/49.
3 in 6 - 18,060 possibilities, odds - 105.59, 132,440 possibilities in 6/49.
2 in 6 - 185,115 possibilities, odds - 1::10.30, 1,357,510 possibilities in 6/49.
1 in 6 - 740,460 possibilities, odds - 1::2.58, 5,430,040 possibilities in 6/49.
0 in 6 - 962,598 possibilities, odds - 1::1.98, 7,059,052 possibilities in 6/49.
***************
4 HotPicks
Formula - ((49!/45!)/(4!)) - 211,876 possibilities.
4 in 6 - 15 possibilities, odds - 14,125.07, 990 possibilities in 6/49.
3 in 6 - 860 possibilities, odds - 1::246.37, 56,760 possiblities in 6/49.
2 in 6 - 13,545 possibilities, odds - 1::15.64, 893,970 possibilities in 6/49.
1 in 6 - 74,046 possibilities, odds - 1::2.86, 4,887,036 possibilities in 6/49.
0 in 6 - 123,410 possibilities, odds - 1::1.72, 8,145,060 possibilities in 6/49.
***************
3 HotPicks
Formula - ((49!/46!)/(3!)) - 18,424 possibilities.
3 in 6 - 20 possibilities, odds - 1::921.20, 15,180 possibilities in 6/49.
2 in 6 - 645 possibilities, odds - 1::28.56, 489,555 possibilities in 6/49.
1 in 6 - 5,418 possibilities, odds - 1::3.40, 4,112,262 possibilities in 6/49.
0 in 6 - 12,341 possibilities, odds - 1::1.49, 9,366,819 possibilities in 6/49.
***************
2 HotPicks
Formula - ((49!/47!)/(2!)) - 1,176 possibilities.
2 in 6 - 15 possibilities, odds - 1::78.40, 178,365 possibilities in 6/49.
1 in 6 - 258 possibilities, odds - 1::4.56, 3,067,878 possibilities in 6/49.
0 in 6 - 903 possibilities, odds - 1::1.30, 10,737,573 possibilities in 6/49.
***************
1 HotPick
Formula - ((49!/48)/(1!)) - 49 possibilities.
1 in 6 - 6 possibilities, odds - 1::8.17, 1,712,304 possibilities in 6/49.
0 in 6 - 43 possibilities, odds - 1::1.14, 12,271,512 possibilities in 6/49.
6 HotPicks
Formula - ((49!/43!)/(6!)) - 13,983,816 possibilities.
6 in 6 - 1 possibility, odds - 1::13,983,816.00, 1 possibility in 6/49.
5 in 6 - 258 possibilities, odds - 1::54,200.84, 258 possibilities in 6/49.
4 in 6 - 13,545 possibilities, odds - 1::1,032.40, 13,545 possibilities in 6/49.
3 in 6 - 246,820 possibilities, odds - 1::56.66, 246,820 possibilities in 6/49.
2 in 6 - 1,851,150 possibilities, odds - 1::7.55, 1,851,150 possibilities in 6/49.
1 in 6 - 5,775,588 possibilities, odds - 1::2.42, 5,775,588 possibilities in 6/49.
0 in 6 - 6,096,454 possibilities, odds - 1::2.29, 6,096,454 possibilities in 6/49.
***************
5 HotPicks
Formula - ((49!/44!)/(5!)) - 1,906,884 possibilities.
5 in 6 - 6 possibilities, odds - 1::317,814.00, 44 possibilities in 6/49.
4 in 6 - 645 possibilities, odds - 1::2,956.41, 4,730 possibilities in 6/49.
3 in 6 - 18,060 possibilities, odds - 105.59, 132,440 possibilities in 6/49.
2 in 6 - 185,115 possibilities, odds - 1::10.30, 1,357,510 possibilities in 6/49.
1 in 6 - 740,460 possibilities, odds - 1::2.58, 5,430,040 possibilities in 6/49.
0 in 6 - 962,598 possibilities, odds - 1::1.98, 7,059,052 possibilities in 6/49.
***************
4 HotPicks
Formula - ((49!/45!)/(4!)) - 211,876 possibilities.
4 in 6 - 15 possibilities, odds - 14,125.07, 990 possibilities in 6/49.
3 in 6 - 860 possibilities, odds - 1::246.37, 56,760 possiblities in 6/49.
2 in 6 - 13,545 possibilities, odds - 1::15.64, 893,970 possibilities in 6/49.
1 in 6 - 74,046 possibilities, odds - 1::2.86, 4,887,036 possibilities in 6/49.
0 in 6 - 123,410 possibilities, odds - 1::1.72, 8,145,060 possibilities in 6/49.
***************
3 HotPicks
Formula - ((49!/46!)/(3!)) - 18,424 possibilities.
3 in 6 - 20 possibilities, odds - 1::921.20, 15,180 possibilities in 6/49.
2 in 6 - 645 possibilities, odds - 1::28.56, 489,555 possibilities in 6/49.
1 in 6 - 5,418 possibilities, odds - 1::3.40, 4,112,262 possibilities in 6/49.
0 in 6 - 12,341 possibilities, odds - 1::1.49, 9,366,819 possibilities in 6/49.
***************
2 HotPicks
Formula - ((49!/47!)/(2!)) - 1,176 possibilities.
2 in 6 - 15 possibilities, odds - 1::78.40, 178,365 possibilities in 6/49.
1 in 6 - 258 possibilities, odds - 1::4.56, 3,067,878 possibilities in 6/49.
0 in 6 - 903 possibilities, odds - 1::1.30, 10,737,573 possibilities in 6/49.
***************
1 HotPick
Formula - ((49!/48)/(1!)) - 49 possibilities.
1 in 6 - 6 possibilities, odds - 1::8.17, 1,712,304 possibilities in 6/49.
0 in 6 - 43 possibilities, odds - 1::1.14, 12,271,512 possibilities in 6/49.
Last edited:
johnph77
Member
Text #2
PAB -
Note that there is no mention of the artificially generated number we both posted for 0 picks, 12,076,932. It's meaningless and irrelevant.
The sum of the 6/49 possibilities in each game is equal to the possibilities in the 6/49 game itself - 13,983,816.
The number of possibilities in each like game in each category, such as 2 in 6, 3 in 6 and so forth, is different due to the inherent number of permutations in each game.
Hope this does what you want.
gl
john
PAB -
Note that there is no mention of the artificially generated number we both posted for 0 picks, 12,076,932. It's meaningless and irrelevant.
The sum of the 6/49 possibilities in each game is equal to the possibilities in the 6/49 game itself - 13,983,816.
The number of possibilities in each like game in each category, such as 2 in 6, 3 in 6 and so forth, is different due to the inherent number of permutations in each game.
Hope this does what you want.
gl
john
HotPicks Statistics
Hi John,
Thanks very much for the HotPicks Information. I had already worked out the Statistics for the 6 ( Six ) different HotPicks that you quoted ( after your post making it clearer what should happen, thanks for that ) above in Excel, and you will be glad to know that we both have Exactly the same figures for the Possibilities and Odds.
Thanks for all your time and effort to get us to this stage.
All the Best, Cheers
PAB
Hi John,
Thanks very much for the HotPicks Information. I had already worked out the Statistics for the 6 ( Six ) different HotPicks that you quoted ( after your post making it clearer what should happen, thanks for that ) above in Excel, and you will be glad to know that we both have Exactly the same figures for the Possibilities and Odds.
Thanks for all your time and effort to get us to this stage.
All the Best, Cheers
PAB
johnph77
Member
PAB -
yqw.
What bothered me the most about all this, up until this morning when I sat down in front of the computer, is that I had no formulas for data backup - all the numbers were generated by programming. This isn't necessarily a bad thing - I created a spreadsheet to check the numbers (and still had to edit the chart post last night) but it's comforting to have irrevocable proof when dealing with math. Even in the posted data onsite the formulas read "TBD", as if I were going to post later. I had no idea what I was going to put in there.
Something (someone?) hit me over the head with a hammer this AM - if one were to treat it as a Keno game where 6 numbers are drawn from a field of 49 and all possibilities are developed, formulas could be created and numbers could be checked - and I already have the developmental information. I'll be working on this some time in the future - will let you know if there are any changes.
gl
john
yqw.
What bothered me the most about all this, up until this morning when I sat down in front of the computer, is that I had no formulas for data backup - all the numbers were generated by programming. This isn't necessarily a bad thing - I created a spreadsheet to check the numbers (and still had to edit the chart post last night) but it's comforting to have irrevocable proof when dealing with math. Even in the posted data onsite the formulas read "TBD", as if I were going to post later. I had no idea what I was going to put in there.
Something (someone?) hit me over the head with a hammer this AM - if one were to treat it as a Keno game where 6 numbers are drawn from a field of 49 and all possibilities are developed, formulas could be created and numbers could be checked - and I already have the developmental information. I'll be working on this some time in the future - will let you know if there are any changes.
gl
john
.
.Lotto$Master
Member
More Odds Info from the Past
