At the Santa Fe Station, there is a side bet in pick-20 keno that pays 200 for 1 for zero catches. What are the odds?
Upon doing some research, I found this isn't a side bet, but what the pick-20 ticket pays for catching zero. The following is my complete analysis of the Station Casinos pick 20 ticket.
Station Casinos Pick 20 Keno
CatchPaysCombinationsProbabilityReturn 20 50000 1 0.000000 0.000000 19 50000 1,200 0.000000 0.000000 18 50000 336,300 0.000000 0.000000 17 50000 39,010,800 0.000000 0.000001 16 10000 2,362,591,575 0.000000 0.000007 15 8000 84,675,282,048 0.000000 0.000192 14 4000 1,940,475,213,600 0.000001 0.002196 13 1000 29,938,760,438,400 0.000008 0.008468 12 200 322,309,467,844,650 0.000091 0.018234 11 20 2,482,976,641,173,600 0.000702 0.014047 10 10 13,929,498,956,983,900 0.003940 0.039401 9 5 57,559,913,045,388,000 0.016281 0.081407 8 2 176,277,233,701,501,000 0.049862 0.099724 7 1 400,535,252,907,552,000 0.113295 0.113295 6 0 672,327,031,666,248,000 0.190175 0.000000 5 0 824,721,158,843,931,000 0.233281 0.000000 4 0 724,852,581,015,174,000 0.205032 0.000000 3 0 441,432,713,697,822,000 0.124864 0.000000 2 1 175,755,617,490,799,000 0.049714 0.049714 1 2 40,896,043,959,078,000 0.011568 0.023136 0 200 4,191,844,505,805,500 0.001186 0.237141 Total 3,535,316,142,212,170,000 1.000000 0.686961
The lower right cell shows the overall return of the ticket is 69.70%, which is typical for live keno.
To answer the question about catching 0, the probability column shows the probability of that is 0.001186 and at a win of 200 for 1, it returns 23.71% towards the return.