40-Ball Keno
Introduction
Internet casinos using Gamesys software offer a game called "40-Number Instant Keno." It is like conventional keno, except it uses only 40 numbers and the game draws ten balls instead of twenty.
Rules
The player picks 3 to 10 numbers from 1 to 40 and then the game shall pick 10. The more numbers drawn by the casino that match the player's picks, the more he wins.
The following table shows what each number of catches pays by the number of picks.
Pay TableExpand
Catch |
Pick 3 |
Pick 4 |
Pick 5 |
Pick 6 |
Pick 7 |
Pick 8 |
Pick 9 |
Pick 10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
5 |
2 |
1 |
1 |
0 |
0 |
0 |
0 |
3 |
24 |
10 |
5 |
2 |
2 |
1 |
1 |
0 |
4 |
|
62 |
25 |
10 |
8 |
4 |
2 |
2 |
5 |
|
|
125 |
50 |
25 |
8 |
12 |
8 |
6 |
|
|
|
1000 |
250 |
250 |
25 |
25 |
7 |
|
|
|
|
1000 |
1000 |
500 |
250 |
8 |
|
|
|
|
|
5000 |
2500 |
1250 |
9 |
|
|
|
|
|
|
10000 |
10000 |
10 |
|
|
|
|
|
|
|
20000 |
Analysis
The following table shows the number of combinations for each number of picks and catches.
Combination TableExpand
Catch |
Pick 3 |
Pick 4 |
Pick 5 |
Pick 6 |
Pick 7 |
Pick 8 |
Pick 9 |
Pick 10 |
0 |
4060 |
27405 |
142506 |
593775 |
2035800 |
5852925 |
14307150 |
30045015 |
1 |
4350 |
40600 |
274050 |
1425060 |
5937750 |
20358000 |
58529250 |
143071500 |
2 |
1350 |
19575 |
182700 |
1233225 |
6412770 |
26719875 |
91611000 |
263381625 |
3 |
120 |
3600 |
52200 |
487200 |
3288600 |
17100720 |
71253000 |
244296000 |
4 |
|
210 |
6300 |
91350 |
852600 |
5755050 |
29926260 |
124692750 |
5 |
|
|
252 |
7560 |
109620 |
1023120 |
6906060 |
35911512 |
6 |
|
|
|
210 |
6300 |
91350 |
852600 |
5755050 |
7 |
|
|
|
|
120 |
3600 |
52200 |
487200 |
8 |
|
|
|
|
|
45 |
1350 |
19575 |
9 |
|
|
|
|
|
|
10 |
300 |
10 |
|
|
|
|
|
|
|
1 |
Total |
9880 |
91390 |
658008 |
3838380 |
18643560 |
76904685 |
273438880 |
847660528 |
The next table shows the probability, to six decimal points, for each number of picks and catches.
Probability TableExpand
Catch |
Pick 3 |
Pick 4 |
Pick 5 |
Pick 6 |
Pick 7 |
Pick 8 |
Pick 9 |
Pick 10 |
0 |
0.410931 |
0.299869 |
0.216572 |
0.154694 |
0.109196 |
0.076106 |
0.052323 |
0.035445 |
1 |
0.440283 |
0.44425 |
0.416484 |
0.371266 |
0.318488 |
0.264717 |
0.214049 |
0.168784 |
2 |
0.13664 |
0.214192 |
0.277656 |
0.321288 |
0.343967 |
0.347441 |
0.335033 |
0.310716 |
3 |
0.012146 |
0.039392 |
0.07933 |
0.126929 |
0.176393 |
0.222363 |
0.260581 |
0.288200 |
4 |
|
0.002298 |
0.009574 |
0.023799 |
0.045732 |
0.074834 |
0.109444 |
0.147102 |
5 |
|
|
0.000383 |
0.00197 |
0.00588 |
0.013304 |
0.025256 |
0.042365 |
6 |
|
|
|
0.000055 |
0.000338 |
0.001188 |
0.003118 |
0.006789 |
7 |
|
|
|
|
0.000006 |
0.000047 |
0.000191 |
0.000575 |
8 |
|
|
|
|
|
0.000001 |
0.000005 |
0.000023 |
9 |
|
|
|
|
|
|
0.000000 |
0.000000 |
10 |
|
|
|
|
|
|
|
0.000000 |
Total |
1.000000 |
1.000000 |
1.000000 |
1.000000 |
1.000000 |
1.000000 |
1.000000 |
1.000000 |
The next table shows the contribution to the return, to six decimal points, for each number of picks and catches. The bottom row shows the total return for each number of picks.
Return TableExpand
Catch |
Pick 3 |
Pick 4 |
Pick 5 |
Pick 6 |
Pick 7 |
Pick 8 |
Pick 9 |
Pick 10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
0.683198 |
0.428384 |
0.277656 |
0.321288 |
0 |
0 |
0 |
0 |
3 |
0.291498 |
0.393916 |
0.396652 |
0.253857 |
0.352787 |
0.222363 |
0.260581 |
0 |
4 |
|
0.142466 |
0.239359 |
0.237991 |
0.365853 |
0.299334 |
0.218888 |
0.294204 |
5 |
|
|
0.047872 |
0.098479 |
0.146994 |
0.10643 |
0.303076 |
0.338924 |
6 |
|
|
|
0.054711 |
0.08448 |
0.296959 |
0.077952 |
0.169733 |
7 |
|
|
|
|
0.006437 |
0.046811 |
0.095451 |
0.14369 |
8 |
|
|
|
|
|
0.002926 |
0.012343 |
0.028866 |
9 |
|
|
|
|
|
|
0.000366 |
0.003539 |
10 |
|
|
|
|
|
|
|
0.000024 |
Total |
0.974696 |
0.964766 |
0.961538 |
0.966326 |
0.95655 |
0.974822 |
0.968656 |
0.978980 |
Strategy
As you can see in the table above, the greatest return is for the pick-10 at 97.90%.
Written by:
Michael Shackleford