Super Way Keno

Introduction

Super Way Keno is a way of playing keno with seven cards, ranging from 2 to 9 picks each, at the same. The player picks four numbers for card A, three for card B, and two for card C. The player will also play four more cards, those combining the numbers chosen on A+B, A+C, B+C, and A+B+C.

Rules

1. The player shall choose four numbers from 1 to 80, each to be marked with an A.
2. The player shall choose three more numbers from 1 to 80, not including those already marked with an A, which shall be marked with a B.
3. The player shall choose two more numbers from 1 to 80, not including those already marked with an A or B, which shall be marked with a C.
4. The player will make a bet evenly divisible by seven credits, for seven equal bets as follows:
• One pick-2 bet on numbers marked with a C
• One pick-3 bet on numbers marked with a B
• One pick-4 bet on numbers marked with an A
• One pick-5 bet on numbers marked with a B or C
• One pick-6 bet on numbers marked with an A or C
• One pick-7 bet on numbers marked with an A or B
• One pick-9 bet on numbers marked with an A, B, or C
5. The game shall draw 20 numbers, from 1 to 80, without replacement.
6. If a number drawn by the game matches a number marked with an A, B, or C, then it shall be known as a "catch."
7. Each of the seven bets shall be paid according to the number of picks and catches and the pay table below.

Super Way Keno Pay Table

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 9
0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0
2 10 2 2 0 0 0 0
3   50 5 3 3 1 0
4     100 12 4 2 1
5       825 68 20 6
6         1600 400 44
7           7000 326
8             4700
9             10000

Example

In the image above I picked the following numbers:

• Pick 2 (C numbers) — 21, 22
• Pick 3 (B numbers) — 11, 12
• Pick 4 (A numbers) — 1, 2, 3, 4

Of these numbers, the ball draw of the game matched 1, 4, 11, 12, and 13.

The win is as follows:

• Pick 2 (C numbers) — 0 out of 2 catches for win of 0
• Pick 3 (B numbers) — 3 out of 3 catches for win of 50
• Pick 4 (A numbers) — 2 out of 4 catches for win of 2
• Pick 5 (B and C numbers) — 3 out of 5 catches for win of 3
• Pick 6 (A and C numbers) — 2 out of 6 catches for win of 0
• Pick 7 (A and B numbers) — 5 out of 7 catches for win of 20
• Pick 9 (A, B, and C numbers) — 5 out of 9 catches for win of 6

The total win is 81.

Analysis

The following table shows the number of combinations for all possible combinations of picks and catches relevant to Super Way Keno.

Super Way Keno Combinations Table

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 9
0 1,770 34,220 487,635 5,461,512 50,063,860 386,206,920 14,783,142,660
1 1,200 35,400 684,400 9,752,700 109,230,240 1,001,277,200 51,172,416,900
2 190 11,400 336,300 6,501,800 92,650,650 1,037,687,280 73,379,314,800
3   1,140 68,400 2,017,800 39,010,800 555,903,900 57,072,800,400
4     4,845 290,700 8,575,650 165,795,900 26,461,025,640
5       15,504 930,240 27,442,080 7,560,293,040
6         38,760 2,325,600 1,326,367,200
7           77,520 137,210,400
8             7,558,200
9             167,960
Total 3,160 82,160 1,581,580 24,040,016 300,500,200 3,176,716,400 231,900,297,200

The next table shows the probability of all combinations of picks and catches.

Super Way Keno Probability Table

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 9
0 0.560127 0.416504 0.308321 0.227184 0.166602 0.121574 0.063748
1 0.379747 0.430867 0.432732 0.405686 0.363495 0.315193 0.220666
2 0.060127 0.138754 0.212635 0.270457 0.308321 0.326654 0.316426
3   0.013875 0.043248 0.083935 0.129820 0.174993 0.246109
4     0.003063 0.012092 0.028538 0.052191 0.114105
5       0.000645 0.003096 0.008639 0.032601
6         0.000129 0.000732 0.005720
7           0.000024 0.000592
8             0.000033
9             0.000001
Total 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

The next table shows the contribution to the return for all combinations of picks and catches.

Super Way Keno Probability Table

Catch Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 9
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.379747 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.601266 0.277507 0.425271 0.000000 0.000000 0.000000 0.000000
3   0.693768 0.216239 0.251805 0.389459 0.174993 0.000000
4     0.306339 0.145108 0.114152 0.104382 0.114105
5       0.532063 0.210503 0.172770 0.195609
6         0.206376 0.292831 0.251661
7           0.170818 0.192887
8             0.153185
9             0.007243
Total 0.981013 0.971276 0.947850 0.928976 0.920490 0.915794 0.914689

The overall return of the game is the average of the returns from the bottom line of the table above, which equals 94.0012%.

The next table shows the contribution to the return for all combinations of picks and catches. The bottom row shows the overall return for each number of picks.

Super Way Keno Combined Return Table

Card C
Catches
Card B
Catches
Card A
Catches
Total
Win
Combinations Probability Return
0 0 0 0 18,626,759,751,600 0.063748 0.000000
0 0 1 0 28,656,553,464,000 0.098074 0.000000
0 0 2 2 15,409,656,108,000 0.052738 0.105475
0 0 3 9 3,424,368,024,000 0.011719 0.105475
0 0 4 107 264,610,256,400 0.000906 0.096899
0 1 0 0 21,492,415,098,000 0.073555 0.000000
0 1 1 0 30,819,312,216,000 0.105475 0.000000
0 1 2 3 15,409,656,108,000 0.052738 0.158213
0 1 3 11 3,175,323,076,800 0.010867 0.119539
0 1 4 130 226,808,791,200 0.000776 0.100909
0 2 0 2 7,704,828,054,000 0.026369 0.052738
0 2 1 3 10,273,104,072,000 0.035158 0.105475
0 2 2 7 4,762,984,615,200 0.016301 0.114105
0 2 3 36 907,235,164,800 0.003105 0.111777
0 2 4 550 59,686,524,000 0.000204 0.112348
0 3 0 54 856,092,006,000 0.002930 0.158213
0 3 1 56 1,058,441,025,600 0.003622 0.202854
0 3 2 81 453,617,582,400 0.001552 0.125749
0 3 3 505 79,582,032,000 0.000272 0.137542
0 3 4 7483 4,802,364,000 0.000016 0.122987
1 0 0 1 14,328,276,732,000 0.049037 0.049037
1 0 1 1 20,546,208,144,000 0.070317 0.070317
1 0 2 6 10,273,104,072,000 0.035158 0.210951
1 0 3 12 2,116,882,051,200 0.007245 0.086937
1 0 4 177 151,205,860,800 0.000517 0.091595
1 1 0 1 15,409,656,108,000 0.052738 0.052738
1 1 1 1 20,546,208,144,000 0.070317 0.070317
1 1 2 8 9,525,969,230,400 0.032601 0.260812
1 1 3 18 1,814,470,329,600 0.006210 0.111777
1 1 4 233 119,373,048,000 0.000409 0.095190
1 2 0 6 5,136,552,036,000 0.017579 0.105475
1 2 1 8 6,350,646,153,600 0.021734 0.173875
1 2 2 19 2,721,705,494,400 0.009315 0.176979
1 2 3 79 477,492,192,000 0.001634 0.129099
1 2 4 900 28,814,184,000 0.000099 0.088752
1 3 0 65 529,220,512,800 0.001811 0.117728
1 3 1 71 604,823,443,200 0.002070 0.146965
1 3 2 132 238,746,096,000 0.000817 0.107855
1 3 3 798 38,418,912,000 0.000131 0.104924
1 3 4 11931 2,116,296,000 0.000007 0.086413
2 0 0 10 2,568,276,018,000 0.008790 0.087896
2 0 1 13 3,424,368,024,000 0.011719 0.152353
2 0 2 17 1,587,661,538,400 0.005434 0.092371
2 0 3 90 302,411,721,600 0.001035 0.093147
2 0 4 1756 19,895,508,000 0.000068 0.119566
2 1 0 13 2,568,276,018,000 0.008790 0.114265
2 1 1 17 3,175,323,076,800 0.010867 0.184742
2 1 2 26 1,360,852,747,200 0.004657 0.121091
2 1 3 132 238,746,096,000 0.000817 0.107855
2 1 4 2059 14,407,092,000 0.000049 0.101522
2 2 0 25 793,830,769,200 0.002717 0.067920
2 2 1 34 907,235,164,800 0.003105 0.105567
2 2 2 76 358,119,144,000 0.001226 0.093147
2 2 3 443 57,628,368,000 0.000197 0.087371
2 2 4 6824 3,174,444,000 0.000011 0.074137
2 3 0 892 75,602,930,400 0.000259 0.230798
2 3 1 934 79,582,032,000 0.000272 0.254384
2 3 2 1237 28,814,184,000 0.000099 0.121984
2 3 3 6058 4,232,592,000 0.000014 0.087753
2 3 4 19585 211,629,600 0.000001 0.014185
Total 292,194,374,472,000 1.000000 6.580086

The standard deviation relative to one bet is 69.0809 and relative to all seven units bet is 9.8687.

Other Pay Tables

I am not aware of any other pay tables, but I didn't look very hard. The one seen above is used at both VideoPoker.com and the Wynn Las Vegas.