Lotto or Keno?

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Mar 31, 2022, 1:32 pm

10-spot 20/70

0 ; 10 ; 1 * 10272278170 ; = ; 10272278170 ; of ; 396704524216
1 ; 9 ; 20 * 2505433700 ; = ; 50108674000 ; of ; 396704524216
2 ; 8 ; 190 * 536878650 ; = ; 102006943500 ; of ; 396704524216
3 ; 7 ; 1140 * 99884400 ; = ; 113868216000 ; of ; 396704524216
4 ; 6 ; 4845 * 15890700 ; = ; 76990441500 ; of ; 396704524216
5 ; 5 ; 15504 * 2118760 ; = ; 32849255040 ; of ; 396704524216
6 ; 4 ; 38760 * 230300 ; = ; 8926428000 ; of ; 396704524216
7 ; 3 ; 77520 * 19600 ; = ; 1519392000 ; of ; 396704524216
8 ; 2 ; 125970 * 1225 ; = ; 154313250 ; of ; 396704524216
9 ; 1 ; 167960 * 50 ; = ; 8398000 ; of ; 396704524216
10 ; 0 ; 184756 * 1 ; = ; 184756 ; of ; 396704524216

You now can order desc the column with the counts and continue.

Do the same with lotto 6+1 / 45 and add the payouts to both tables, order the tables, compare the tables.

Speler

Belgium
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Mar 31, 2022, 1:40 pm

Let's do 20 / 80 with 20 spot or chances for 20 picked numbers if you want to cmp to keno 20/80.

0 ; 20 ; 1 * 4191844505805495 ; = ; 4191844505805495 ; of ; 3535316142212174320
1 ; 19 ; 20 * 2044802197953900 ; = ; 40896043959078000 ; of ; 3535316142212174320
2 ; 18 ; 190 * 925029565741050 ; = ; 175755617490799500 ; of ; 3535316142212174320
3 ; 17 ; 1140 * 387221678682300 ; = ; 441432713697822000 ; of ; 3535316142212174320
4 ; 16 ; 4845 * 149608375854525 ; = ; 724852581015173625 ; of ; 3535316142212174320
5 ; 15 ; 15504 * 53194089192720 ; = ; 824721158843930880 ; of ; 3535316142212174320
6 ; 14 ; 38760 * 17345898649800 ; = ; 672327031666248000 ; of ; 3535316142212174320
7 ; 13 ; 77520 * 5166863427600 ; = ; 400535252907552000 ; of ; 3535316142212174320
8 ; 12 ; 125970 * 1399358844975 ; = ; 176277233701500750 ; of ; 3535316142212174320
9 ; 11 ; 167960 * 342700125300 ; = ; 57559913045388000 ; of ; 3535316142212174320
10 ; 10 ; 184756 * 75394027566 ; = ; 13929498956983896 ; of ; 3535316142212174320
11 ; 9 ; 167960 * 14783142660 ; = ; 2482976641173600 ; of ; 3535316142212174320
12 ; 8 ; 125970 * 2558620845 ; = ; 322309467844650 ; of ; 3535316142212174320
13 ; 7 ; 77520 * 386206920 ; = ; 29938760438400 ; of ; 3535316142212174320
14 ; 6 ; 38760 * 50063860 ; = ; 1940475213600 ; of ; 3535316142212174320
15 ; 5 ; 15504 * 5461512 ; = ; 84675282048 ; of ; 3535316142212174320
16 ; 4 ; 4845 * 487635 ; = ; 2362591575 ; of ; 3535316142212174320
17 ; 3 ; 1140 * 34220 ; = ; 39010800 ; of ; 3535316142212174320
18 ; 2 ; 190 * 1770 ; = ; 336300 ; of ; 3535316142212174320
19 ; 1 ; 20 * 60 ; = ; 1200 ; of ; 3535316142212174320
20 ; 0 ; 1 * 1 ; = ; 1 ; of ; 3535316142212174320

We now go to EN.wikipedia.org and read what we can find about keno 20/80:

... (1 in 3,535,316,142,212,180,000). ...

Hits	Probability
0	1 in 843.380 (0.11857057%)
1	1 in 86.446 (1.15678605%)
2	1 in 20.115 (4.97142576%)
3	1 in 8.009 (12.48637168%)
4	1 in 4.877 (20.50318987%)
5	1 in 4.287 (23.32807380%)
6	1 in 5.258 (19.01745147%)
7	1 in 8.826 (11.32954556%)
8	1 in 20.055 (4.98618021%)
9	1 in 61.420 (1.62814048%)
10	1 in 253.801 (0.39401000%)
11	1 in 1,423.822 (0.07023351%)
12	1 in 10,968.701 (0.00911685%)
13	1 in 118,084.920 (0.00084685%)
14	1 in 1,821,881.628 (0.00005489%)
15	1 in 41,751,453.986 (0.00000240%)
16	1 in 1,496,372,110.872 (0.00000007%)
17	1 in 90,624,035,964.712
18	1 in 10,512,388,171,906.553
19	1 in 2,946,096,785,176,811.500
20	1 in 3,535,316,142,212,173,800.000

So I'll check the results above.

Speler

Belgium
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April 17, 2021
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Mar 31, 2022, 1:50 pm

Quote: Originally posted by Speler on Mar 31, 2022

Let's do 20 / 80 with 20 spot or chances for 20 picked numbers if you want to cmp to keno 20/80.

0 ; 20 ; 1 * 4191844505805495 ; = ; 4191844505805495 ; of ; 3535316142212174320
1 ; 19 ; 20 * 2044802197953900 ; = ; 40896043959078000 ; of ; 3535316142212174320
2 ; 18 ; 190 * 925029565741050 ; = ; 175755617490799500 ; of ; 3535316142212174320
3 ; 17 ; 1140 * 387221678682300 ; = ; 441432713697822000 ; of ; 3535316142212174320
4 ; 16 ; 4845 * 149608375854525 ; = ; 724852581015173625 ; of ; 3535316142212174320
5 ; 15 ; 15504 * 53194089192720 ; = ; 824721158843930880 ; of ; 3535316142212174320
6 ; 14 ; 38760 * 17345898649800 ; = ; 672327031666248000 ; of ; 3535316142212174320
7 ; 13 ; 77520 * 5166863427600 ; = ; 400535252907552000 ; of ; 3535316142212174320
8 ; 12 ; 125970 * 1399358844975 ; = ; 176277233701500750 ; of ; 3535316142212174320
9 ; 11 ; 167960 * 342700125300 ; = ; 57559913045388000 ; of ; 3535316142212174320
10 ; 10 ; 184756 * 75394027566 ; = ; 13929498956983896 ; of ; 3535316142212174320
11 ; 9 ; 167960 * 14783142660 ; = ; 2482976641173600 ; of ; 3535316142212174320
12 ; 8 ; 125970 * 2558620845 ; = ; 322309467844650 ; of ; 3535316142212174320
13 ; 7 ; 77520 * 386206920 ; = ; 29938760438400 ; of ; 3535316142212174320
14 ; 6 ; 38760 * 50063860 ; = ; 1940475213600 ; of ; 3535316142212174320
15 ; 5 ; 15504 * 5461512 ; = ; 84675282048 ; of ; 3535316142212174320
16 ; 4 ; 4845 * 487635 ; = ; 2362591575 ; of ; 3535316142212174320
17 ; 3 ; 1140 * 34220 ; = ; 39010800 ; of ; 3535316142212174320
18 ; 2 ; 190 * 1770 ; = ; 336300 ; of ; 3535316142212174320
19 ; 1 ; 20 * 60 ; = ; 1200 ; of ; 3535316142212174320
20 ; 0 ; 1 * 1 ; = ; 1 ; of ; 3535316142212174320

We now go to EN.wikipedia.org and read what we can find about keno 20/80:

... (1 in 3,535,316,142,212,180,000). ...

Hits	Probability
0	1 in 843.380 (0.11857057%)
1	1 in 86.446 (1.15678605%)
2	1 in 20.115 (4.97142576%)
3	1 in 8.009 (12.48637168%)
4	1 in 4.877 (20.50318987%)
5	1 in 4.287 (23.32807380%)
6	1 in 5.258 (19.01745147%)
7	1 in 8.826 (11.32954556%)
8	1 in 20.055 (4.98618021%)
9	1 in 61.420 (1.62814048%)
10	1 in 253.801 (0.39401000%)
11	1 in 1,423.822 (0.07023351%)
12	1 in 10,968.701 (0.00911685%)
13	1 in 118,084.920 (0.00084685%)
14	1 in 1,821,881.628 (0.00005489%)
15	1 in 41,751,453.986 (0.00000240%)
16	1 in 1,496,372,110.872 (0.00000007%)
17	1 in 90,624,035,964.712
18	1 in 10,512,388,171,906.553
19	1 in 2,946,096,785,176,811.500
20	1 in 3,535,316,142,212,173,800.000

So I'll check the results above.

A table with 1 IN ...

0 ; 20 ; 1 IN 843.3795999150 ;
1 ; 19 ; 1 IN 86.4464089913 ;
2 ; 18 ; 1 IN 20.1149538927 ;
3 ; 17 ; 1 IN 8.0087316425 ;
4 ; 16 ; 1 IN 4.8772898584 ;
5 ; 15 ; 1 IN 4.2866805396 ;
6 ; 14 ; 1 IN 5.2583281286 ;
7 ; 13 ; 1 IN 8.8264793587 ;
8 ; 12 ; 1 IN 20.0554323890 ;
9 ; 11 ; 1 IN 61.4197616912 ;
10 ; 10 ; 1 IN 253.8006681453 ;
11 ; 9 ; 1 IN 1423.8217482953 ;
12 ; 8 ; 1 IN 10968.7008757563 ;
13 ; 7 ; 1 IN 118084.9203655644 ;
14 ; 6 ; 1 IN 1821881.6284972795 ;
15 ; 5 ; 1 IN 41751453.9863959890 ;
16 ; 4 ; 1 IN 1496372110.8724322442 ;
17 ; 3 ; 1 IN 90624035964.7116777918 ;
18 ; 2 ; 1 IN 10512388171906.5546238478 ;
19 ; 1 ; 1 IN 2946096785176811.9333333333 ;
20 ; 0 ; 1 IN 3535316142212174320.0000000000 ;

Speler

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April 17, 2021
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Mar 31, 2022, 1:58 pm

Quote: Originally posted by cottoneyedjoe on Mar 31, 2022

If one of the prize tiers is a rolling jackpot that could potentially be split among several people, you could take the average of past payouts. Some people omit jackpots from these kinds of calculations as the odds are too astronomical to ever be realized. It's your money, only you can decide the best way to gamble it. Best of luck to you.

I'll redo the table above.

It is better to use classes for that calculation.

Cashing a jackpot that is rolling is a wild fantasy.

Speler

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Mar 31, 2022, 2:01 pm

To do p and 1/p.

0 ; 20 ; 1 IN 843.3795999150 ; p = ; 0.00118570570132449521 ;
1 ; 19 ; 1 IN 86.4464089913 ; p = ; 0.01156786050072678255 ;
2 ; 18 ; 1 IN 20.1149538927 ; p = ; 0.04971425762812343451 ;
3 ; 17 ; 1 IN 8.0087316425 ; p = ; 0.12486371683342630063 ;
4 ; 16 ; 1 IN 4.8772898584 ; p = ; 0.20503189866397841410 ;
5 ; 15 ; 1 IN 4.2866805396 ; p = ; 0.23328073803545988449 ;
6 ; 14 ; 1 IN 5.2583281286 ; p = ; 0.19017451470282055801 ;
7 ; 13 ; 1 IN 8.8264793587 ; p = ; 0.11329545556763777924 ;
8 ; 12 ; 1 IN 20.0554323890 ; p = ; 0.04986180205971558513 ;
9 ; 11 ; 1 IN 61.4197616912 ; p = ; 0.01628140475419284413 ;
10 ; 10 ; 1 IN 253.8006681453 ; p = ; 0.00394009995051466828 ;
11 ; 9 ; 1 IN 1423.8217482953 ; p = ; 0.00070233510704361288 ;
12 ; 8 ; 1 IN 10968.7008757563 ; p = ; 0.00009116849947200744 ;
13 ; 7 ; 1 IN 118084.9203655644 ; p = ; 0.00000846848180872058 ;
14 ; 6 ; 1 IN 1821881.6284972795 ; p = ; 0.00000054888308019485 ;
15 ; 5 ; 1 IN 41751453.9863959890 ; p = ; 0.00000002395126168123 ;
16 ; 4 ; 1 IN 1496372110.8724322442 ; p = ; 0.00000000066828297102 ;
17 ; 3 ; 1 IN 90624035964.7116777918 ; p = ; 0.00000000001103460014 ;
18 ; 2 ; 1 IN 10512388171906.5546238478 ; p = ; 0.00000000000009512586 ;
19 ; 1 ; 1 IN 2946096785176811.9333333333 ; p = ; 0.00000000000000033943 ;
20 ; 0 ; 1 IN 3535316142212174320.0000000000 ; p = ; 0.00000000000000000028 ;

For people not knowing p: p is a value between 0 and 1.

Values were rounded.

Speler

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Mar 31, 2022, 2:06 pm

Generally best have half or more of the played numbers correct.

Playing 70 numbers would require to have 35 numbers correct but only 20 are drawn.

You depend more of the specific result.

Speler

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Mar 31, 2022, 2:19 pm

I'll add the last one to wiki, for 70 and 80 numbers. Those above check other things. Ends in ideas on how to.

Speler

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Mar 31, 2022, 2:28 pm

If we use 1 drawing of 20 numbers as seed, we for fulllottoquickpicks can spread the last drawn numbers over all combinations. That's close to the expected without counting or calculating. ... We could develop that. Who of you did? How many of all of you? ...

Speler

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Mar 31, 2022, 2:29 pm

We could take the line of numbers ordered by games out and fill the columns of a fulllottoquickpicktable. Who of all of you did? How many of you did?

Speler

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Mar 31, 2022, 2:33 pm

Next you will do probability and expectation with WinD quality!

Speler

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Mar 31, 2022, 3:21 pm

Quote: Originally posted by Speler on Mar 31, 2022

To do p and 1/p.

0 ; 20 ; 1 IN 843.3795999150 ; p = ; 0.00118570570132449521 ;
1 ; 19 ; 1 IN 86.4464089913 ; p = ; 0.01156786050072678255 ;
2 ; 18 ; 1 IN 20.1149538927 ; p = ; 0.04971425762812343451 ;
3 ; 17 ; 1 IN 8.0087316425 ; p = ; 0.12486371683342630063 ;
4 ; 16 ; 1 IN 4.8772898584 ; p = ; 0.20503189866397841410 ;
5 ; 15 ; 1 IN 4.2866805396 ; p = ; 0.23328073803545988449 ;
6 ; 14 ; 1 IN 5.2583281286 ; p = ; 0.19017451470282055801 ;
7 ; 13 ; 1 IN 8.8264793587 ; p = ; 0.11329545556763777924 ;
8 ; 12 ; 1 IN 20.0554323890 ; p = ; 0.04986180205971558513 ;
9 ; 11 ; 1 IN 61.4197616912 ; p = ; 0.01628140475419284413 ;
10 ; 10 ; 1 IN 253.8006681453 ; p = ; 0.00394009995051466828 ;
11 ; 9 ; 1 IN 1423.8217482953 ; p = ; 0.00070233510704361288 ;
12 ; 8 ; 1 IN 10968.7008757563 ; p = ; 0.00009116849947200744 ;
13 ; 7 ; 1 IN 118084.9203655644 ; p = ; 0.00000846848180872058 ;
14 ; 6 ; 1 IN 1821881.6284972795 ; p = ; 0.00000054888308019485 ;
15 ; 5 ; 1 IN 41751453.9863959890 ; p = ; 0.00000002395126168123 ;
16 ; 4 ; 1 IN 1496372110.8724322442 ; p = ; 0.00000000066828297102 ;
17 ; 3 ; 1 IN 90624035964.7116777918 ; p = ; 0.00000000001103460014 ;
18 ; 2 ; 1 IN 10512388171906.5546238478 ; p = ; 0.00000000000009512586 ;
19 ; 1 ; 1 IN 2946096785176811.9333333333 ; p = ; 0.00000000000000033943 ;
20 ; 0 ; 1 IN 3535316142212174320.0000000000 ; p = ; 0.00000000000000000028 ;

For people not knowing p: p is a value between 0 and 1.

Values were rounded.

If your Canadian keno starts payouts at 6/10 then you need 11/20 and better or ... for a payout, playing two ten spots or 20 numbers.

sum of 11 ; 9 ; 1 IN 1423.8217482953 ; p = ; 0.00070233510704361288 ; ... 0 ; 20 ; 1 IN 843.3795999150 ; p = ; 0.00118570570132449521 ; ...

Speler

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Mar 31, 2022, 3:22 pm

The specific of it would be: 0/10 (paying) + 5/10 (not paying) etc

Speler

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Apr 1, 2022, 6:10 pm

There:

Speler

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Apr 29, 2022, 6:03 pm

Impressed. And those wikians like to set back pages to errors. Passed one value with a vicious note.
They simply were to lazy to calculate or adapt to their format a fully written value? Who knows?
That twatter seems to be wobbly too. On, off, on, off and on for a politician. It's sold, it's sold. What's next?

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