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4. Free Power Keno Games
5. Free Triple Power Keno

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Introduction

Introduction

Triple Power Keno is a keno variation I noticed on a multi-game machine at the Red Rock casino on January 26, 2012. It plays like conventional keno, except if the last ball is one of the player's picks, then the player gets three extra balls and any win is tripled.

Return Tables

Following are various pay tables and their associated returns for various sets of pay tables I have seen.

Pay Table 1 has a maximum return of 88.75% for a pick 2.

Pay Table 1Expand

Catch	Pick 2	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	0
1	1	0	0	0	0	0	0	0	0
2	6	2	1	1	0	0	0	0	0
3	27	6	2	2	1	1	0	0
4	48	10	6	4	2	2	1
5	85	31	11	6	5	4
6	125	54	12	10	6
7	200	90	32	16
8	500	150	50
9	1000	400
10	1000
Return	86.49%	88.75%	88.62%	88.34%	88.50%	88.62%	88.55%	88.62%	88.40%

Pay Table 2 has a maximum return of 90.77% for a pick 2.

Pay Table 2Expand

Catch	Pick 2	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	0
1	1	0	0	0	0	0	0	0	0
2	6	2	1	1	0	0	0	0	0
3	28	6	2	2	1	1	0	0
4	51	10	6	4	2	2	1
5	100	33	12	5	3	3
6	150	55	20	13	7
7	200	100	80	25
8	500	200	120
9	1000	500
10	1000
Return	86.49%	90.77%	90.24%	90.44%	90.68%	90.56%	90.31%	90.41%	90.59%

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Pay Table 3 has a maximum return of 91.33% for a pick 7.

Pay Table 3Expand

Catch	Pick 2	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	0
1	1	0	0	0	0	0	0	0	0
2	6	2	1	1	0	0	0	0	0
3	28	7	2	2	1	1	0	0
4	40	12	8	4	2	2	1
5	75	19	12	6	5	4
6	150	59	16	10	7
7	200	95	42	14
8	500	200	72
9	1000	350
10	1000
Return	86.49%	90.77%	90.50%	91.07%	91.08%	91.33%	91.22%	91.27%	91.18%

Pay Table 4 has a maximum return of 92.50% for a pick 5.

Pay Table 4Expand

Catch	Pick 2	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	0
1	1	0	0	0	0	0	0	0	0
2	6	2	1	1	0	0	0	0	0
3	28	6	2	2	1	1	0	0
4	55	11	7	4	2	2	1
5	100	28	12	5	5	4
6	150	65	24	10	7
7	200	95	50	15
8	500	175	90
9	1000	250
10	1000
Return	86.49%	90.77%	92.38%	92.50%	92.18%	92.49%	92.44%	92.45%	92.35%

Pay Table 5 has a maximum return of 94.56% for a pick 5.

Pay Table 5Expand

Catch	Pick 2	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	0
1	1	0	0	0	0	0	0	0	0
2	6	3	1	1	0	0	0	0	0
3	21	6	2	2	1	1	0	0
4	58	12	8	5	2	2	1
5	100	24	8	5	5	3
6	150	65	27	12	9
7	250	92	45	27
8	500	180	80
9	1000	400
10	1000
Return	86.49%	93.68%	94.00%	94.56%	94.32%	94.35%	94.08%	94.35%	94.32%

Analysis

Following is an example pay table seen at the Red Rock.

Example Pay Table

Catch	Pick 2	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	0
1	1	0	0	0	0	0	0	0	0
2	6	2	1	1	0	0	0	0	0
3	27	6	2	2	1	1	0	0
4	48	10	6	4	2	2	1
5	85	31	11	6	5	4
6	125	54	12	10	6
7	200	90	32	16
8	500	150	50
9	1000	400
10	1000

The next table shows the probabilities for catching any given number of balls, assuming that the player did NOT catch the last ball.

20-Ball Probabilities if the 20th Ball Was Not CaughtExpand

Catch	Pick 2	Pick 3	Pick 4	Pick 5	Pick 6	Pick 7	Pick 8	Pick 9	Pick 10
0	0.560127	0.416504	0.308321	0.227184	0.166602	0.121574	0.088266	0.063748	0.045791
1	0.360759	0.409323	0.411095	0.385402	0.345320	0.299433	0.253141	0.209632	0.170593
2	0.054114	0.124878	0.191372	0.243412	0.277489	0.293989	0.295331	0.284784	0.265731
3	0.011794	0.036761	0.071345	0.110347	0.148744	0.182568	0.209193	0.227292
4	0.002451	0.009674	0.022830	0.041753	0.065203	0.091284	0.117855
5	0.000484	0.002322	0.006479	0.013727	0.024451	0.038571
6	0.000090	0.000512	0.001657	0.004004	0.008036
7	0.000016	0.000104	0.000385	0.001047
8	0.000003	0.000020	0.000081
9	0.000000	0.000003
10	0.000000
Total	0.975000	0.962500	0.950000	0.937500	0.925000	0.912500	0.900000	0.887500	0.875000

The next table shows the probability of each combination of picks and catches assuming the player DID catch the 20th ball.

20-Ball Probabilities if the 20th Ball Was CaughtExpand

Catch	Pick 2	Pick 3	Pick 4	Pick 5	Pick 6	Pick 7	Pick 8	Pick 9	Pick 10
0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
1	0.018038	0.019426	0.018500	0.016431	0.013934	0.011423	0.009121	0.007126	0.005464
2	0.006962	0.015263	0.022201	0.026777	0.028919	0.028997	0.027541	0.025082	0.022079
3	0.002812	0.008325	0.015336	0.022493	0.028724	0.033367	0.036147	0.037093
4	0.000974	0.003651	0.008179	0.014185	0.020985	0.027806	0.033941
5	0.000304	0.001388	0.003675	0.007384	0.012460	0.018602
6	0.000088	0.000473	0.001450	0.003323	0.006318
7	0.000023	0.000147	0.000514	0.001326
8	0.000006	0.000042	0.000165
9	0.000001	0.000011
10	0.000000
Total	0.025000	0.037500	0.050000	0.062500	0.075000	0.087500	0.100000	0.112500	0.125000

The next table shows the contribution to the return for all combinations of picks and catches, assuming the 20th ball was not caught.

Free Power Keno Games

Return if the 20th Ball Was Not CaughtExpand

Catch	Pick 2	Pick 3	Pick 4	Pick 5	Pick 6	Pick 7	Pick 8	Pick 9	Pick 10
0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
1	0.360759	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
2	0.324684	0.374635	0.191372	0.243412	0.000000	0.000000	0.000000	0.000000	0.000000
3	0.247675	0.220564	0.142690	0.220693	0.148744	0.182568	0.000000	0.000000
4	0.142141	0.116086	0.182643	0.208764	0.130406	0.182568	0.117855
5	0.048369	0.055721	0.051831	0.068635	0.122256	0.115712
6	0.013543	0.033309	0.044731	0.048044	0.072320
7	0.003965	0.009595	0.017307	0.028276
8	0.001304	0.003520	0.006500
9	0.000398	0.001347
10	0.000056
Total	0.685443	0.622310	0.554078	0.550557	0.472601	0.446614	0.437239	0.374093	0.342066

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The next table shows the contribution to the return for all combinations of picks and catches, assuming the 20th ball was caught.

Return Table if 20th Ball Was CaughtExpand

Catch	Pick 2	Pick 3	Pick 4	Pick 5	Pick 6	Pick 7	Pick 8	Pick 9	Pick 10
0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
1	0.054114	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
2	0.125316	0.137366	0.066602	0.080331	0.000000	0.000000	0.000000	0.000000	0.000000
3	0.177130	0.149854	0.092016	0.134956	0.086171	0.100100	0.000000	0.000000
4	0.169426	0.131451	0.196300	0.212769	0.125912	0.166834	0.101824
5	0.091285	0.099903	0.088202	0.110756	0.186901	0.167421
6	0.039435	0.092140	0.117442	0.119617	0.170580
7	0.017616	0.040494	0.069323	0.107402
8	0.008825	0.022636	0.039675
9	0.004137	0.013284
10	0.000906
Total	0.179430	0.314496	0.385881	0.395083	0.470594	0.496898	0.503530	0.569449	0.601094

The final analysis table shows the combined return for all picks and catches, whether or not the 20th ball was caught.

Free Triple Power Keno

Combined ReturnExpand

Catch	Pick 2	Pick 3	Pick 4	Pick 5	Pick 6	Pick 7	Pick 8	Pick 9	Pick 10
0	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
1	0.414873	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
2	0.450000	0.512001	0.257974	0.323743	0.000000	0.000000	0.000000	0.000000	0.000000
3	0.424805	0.370418	0.234705	0.355649	0.234916	0.282669	0.000000	0.000000
4	0.311567	0.247537	0.378943	0.421533	0.256318	0.349402	0.219679
5	0.139655	0.155624	0.140033	0.179391	0.309157	0.283134
6	0.052979	0.125449	0.162173	0.167661	0.242901
7	0.021581	0.050089	0.086630	0.135678
8	0.010129	0.026156	0.046175
9	0.004535	0.014631
10	0.000962
Total	0.864873	0.936806	0.939959	0.945640	0.943195	0.943512	0.940769	0.943542	0.943160

Written by:Michael Shackleford