Keno Odds

    Wherever you choose to play the payout schedule overall is geared to provide around a 70% return for live Keno and around 85-90% for Online and Video Keno. This doesn't sem like a big difference but think of it in the inverse terms - the casino's profit. A game that gives you a 95% return means the casino is keeping 5% but a game that is giving you a 70% return then the casino is keeping 30% - 6 times as much! You can download my Keno Odds spreadsheet by right-clicking KenoOdds.xls and selecting "Save target as" to figure out what the casino edge is in your keno game.

    The equation for calculating the probability (p) of hitting (n) numbers out of the (x) numbers you picked when (y) numbers were drawn out of (z). (i.e. - "What is the probability of hitting 4 out of the 5 numbers I picked when 20 numbers were drawn out of 80").

    n = 4
    x = 5
    y = 20
    z = 80

    p(x,n) = (combin(x,n) * combin(z-x,y-x+n)) / combin(z,y)

    It is important not to look at the payout schedules but to actually see how much profit the casino is keep from the money you wager. That's what the following does. I took 2 payout schedules and calculated the casino edge on all the bets and showed it in red. At first glance the 2nd payout schedule looks better because the high-end payouts are much higher but payouts are smaller on the lower end. But the payouts on the small end occur much more frequently and that's where the value of the ticket is most of the time. The 1st payout schedule shows a casino edge of about 7% while the 2nd schedule shows an edge anywhere 21-66%! You will lose your money anywhere from 3-9 times as fast playing the 2nd schedule if you choose to play the game with the big payoffs.

    Odds based on the standard 80 ball game, 20 balls drawn.

    ODDS

    SCHEDULE 1

    SCHEDULE 2

    Numbers Caught

    Odds of Hitting

    Payout 1

    EV

    Payout 2

    EV
    1 Payout Odds

    		1 Payout EV

    		1 Payout EV
    1
    0    		 1 in 4.00
    1 in 3.33    		 $3.00
    -    		 $0.75
    -

    Total EV $0.75 Total EV
    Cost of Ticket $1.00 Cost of Ticket
    Casino Edge 25% Casino Edge
    2 Numbers Picked Odds

    		Payout EV

    		Payout EV
    2
    1
    0    		 1 in 16.63
    1 in 2.63
    1 in 1.78    		 $9.00
    $1.00
    -    		 $0.54
    $0.38
    -

    Total EV $0.92 Total EV
    Cost of Ticket $1.00 Cost of Ticket
    Casino Edge 8% Casino Edge
    3 Numbers Picked Odds

    		Payout EV

    		Payout EV
    3
    2
    1
    0    		 1 in 72.07
    1 in 7.20
    1 in 2.32
    1 in 2.40    		 $16.00
    $2.00
    $1.00
    -    		 $0.22
    $0.28
    $0.43
    -    		 $25.00
    $2.00
    -
    -    		 $0.35
    $0.28
    -
    -
    Total EV $0.93 Total EV $0.62
    Cost of Ticket $1.00 Cost of Ticket $1.00
    Casino Edge 7% Casino Edge 37.6%
    4 Numbers Picked Odds

    		Payout EV

    		Payout EV
    4
    3
    2
    1
    0    		 1 in 326.43
    1 in 23.12
    1 in 4.70
    1 in 2.31
    1 in 3.24    		 $12.00
    $6.00
    $2.00
    $0.50
    -    		 $0.04
    $0.26
    $0.43
    $0.22
    -    		 $50.00
    5.00
    $2.00
    -
    -    		 $0.15
    $0.22
    $0.43
    -
    -
    Total EV $0.94 Total EV $0.79
    Cost of Ticket $1.00 Cost of Ticket $1.00
    Casino Edge 6% Casino Edge 21%
    5 Numbers Picked Odds

    		Payout EV

    		Payout EV
    5
    4
    3
    2
    1
    0    		 1 in 1,550.57
    1 in 82.70
    1 in 11.91
    1 in 3.70
    1 in 2.46
    1 in 4.40    		 $30.00
    $15.00
    $3.00
    $1.00
    $0.50
    -    		 $0.02
    $0.18
    $0.25
    $0.27
    $0.20
    -    		 $250.00
    $10.00
    $2.00
    -
    -
    -    		 $0.16
    $0.12
    $0.17
    -
    -
    -
    Total EV $0.94 Total EV $0.45
    Cost of Ticket $1.00 Cost of Ticket $1.00
    Casino Edge 6% Casino Edge 55%
    6 Numbers Picked Odds

    		Payout EV

    		Payout EV
    6
    5
    4
    3
    2
    1
    0    		 1 in 7,752.84
    1 in 323.03
    1 in 35.04
    1 in 7.70
    1 in 3.24
    1 in 2.75
    1 in 6.00    		 $75.00
    $30.00
    $3.00
    $2.00
    $1.00
    $0.50
    -
    		 $0.01
    $0.09
    $0.09
    $0.26
    $0.31
    $0.18
    -    		 $1,000.00
    $50.00
    $5.00
    $2.00
    -
    -
    -    		 $0.13
    $0.15
    $0.14
    $0.26
    -
    -
    -
    Total EV $0.94 Total EV $0.69
    Cost of Ticket $1.00 Cost of Ticket $1.00
    Casino Edge 6% Casino Edge 31%
    7 Numbers Picked Odds

    		Payout EV

    		Payout EV
    7
    6
    5
    4
    3
    2
    1
    0    		 1 in 40,979.31
    1 in 1,365.98
    1 in 115.76
    1 in 19.16
    1 in 5.71
    1 in 3.06
    1 in 3.17
    1 in 8.22    		 $100.00
    $36.00
    $12.00
    $6.00
    $1.00
    $0.50
    $0.50
    -    		 $0.00
    $0.03
    $0.10
    $0.31
    $0.17
    $0.16
    $0.16
    -
    		 $2,000.00
    $250.00
    $15.00
    $2.00
    -
    -
    -
    -    		 $0.05
    $0.18
    $0.13
    $0.10
    -
    -
    -
    -
    Total EV $0.94 Total EV $0.47
    Cost of Ticket $1.00 Cost of Ticket $1.00
    Casino Edge 6% Casino Edge 53%
    8 Numbers Picked Odds

    		Payout EV

    		Payout EV
    8
    7
    6
    5
    4
    3
    2
    1
    0    		 1 in 230,114.60
    1 in 6,232.27
    1 in 422.53
    1 in 54.64
    1 in 12.27
    1 in 4.65
    1 in 3.05
    1 in 3.75
    1 in 11.33    		 $720.00
    $90.00
    $19.00
    $6.00
    $3.00
    $1.0
    $0.50
    $0.50
    -
    		 $0.00
    $0.01
    $0.04
    $0.11
    $0.24
    $0.21
    $0.16
    $0.13
    -    		 $4,000.00
    $400.00
    $40.00
    $8.00
    -
    -
    -
    -
    -    		 $0.02
    $0.06
    $0.09
    $0.15
    -
    -
    -
    -
    -
    Total EV $0.93 Total EV $0.32
    Cost of Ticket $1.00 Cost of Ticket $1.00
    Casino Edge 7% Casino Edge 64%
    9 Numbers Picked Odds

    		Payout EV

    		Payout EV
    9
    8
    7
    6
    5
    4
    3
    2
    1
    0    		 1 in 1,380,687.65
    1 in 30,681.95
    1 in 1,690.11
    1 in 174.84
    1 in 30.67
    1 in 8.76
    1 in 4.06
    1 in 3.16
    1 in 4.53
    1 in 15.67    		 $1,200.00
    $80.00
    $20.00
    $8.00
    $4.00
    $2.00
    $1.00
    $0.50
    $0.50
    $0.00
    		 $0.00
    $0.00
    $0.01
    $0.05
    $0.13
    $0.23
    $0.25
    $0.16
    $0.11
    $0.00    		 $5,000.00
    $500.00
    $80.00
    $20.00
    $5.00
    $0.00
    -
    -
    -
    -    		 $0.00
    $0.00
    $0.02
    $0.05
    $0.11
    $0.16
    -
    -
    -
    Total EV $0.93 Total EV $0.34
    Cost of Ticket $1.00 Cost of Ticket $1.00
    Casino Edge 7% Casino Edge 66%
    10 Numbers Picked Odds

    		Payout EV

    		Payout EV
    10
    9
    8
    7
    6
    5
    4
    3
    2
    1
    0    		 1 in 8,911,711.18
    1 in 163,381.37
    1 in 7,384.47
    1 in 620.68
    1 in 87.11
    1 in 19.44
    1 in 6.79
    1 in 3.74
    1 in 3.39
    1 in 5.57
    1 in 21.84    		 $1,800.00
    $600.00
    $30.00
    $10.00
    $5.00
    $3.00
    $2.00
    $1.00
    $0.50
    -
    -
    		 $0.00
    $0.00
    $0.00
    $0.02
    $0.06
    $0.15
    $0.29
    $0.27
    $0.15
    -
    -    		 $5,000.00
    $1,000.00
    $500.00
    $100.00
    $20.00
    $2.00
    -
    -
    -
    -
    -    		 $0.00
    $0.01
    $0.07
    $0.16
    $0.23
    $0.10
    -
    -
    -
    -
    -
    Total EV $0.95 Total EV $0.72
    Cost of Ticket $1.00 Cost of Ticket $1.00
    Casino Edge 5% Casino Edge 27%
    11 Numbers Picked Odds

    		Payout EV

    		Payout EV
    11
    10
    9
    8
    7
    6
    5
    4
    3
    2
    1
    0    		 1 in 62,381,978.23
    1 in 945,181.49
    1 in 35,244.05
    1 in 2,430.62
    1 in 277.18
    1 in 49.49
    1 in 13.50
    1 in 5.60
    1 in 3.59
    1 in 3.73
    1 in 6.95
    1 in 30.57    		 $3,000.00
    $1,000.00
    $180.00
    $25.00
    $15.00
    $6.00
    $2.00
    $1.00
    $1.00
    $0.50
    -
    -    		 $0.00
    $0.00
    $0.01
    $0.01
    $0.05
    $0.12
    $0.15
    $0.18
    $0.28
    $0.13
    -
    -

    Total EV $0.93 Total EV
    Cost of Ticket $1.00 Cost of Ticket
    Casino Edge 7% Casino Edge
    12 Numbers Picked Odds

    		Payout EV

    		Payout EV
    12
    11
    10
    9
    8
    7
    6
    5
    4
    3
    2
    1
    0    		 1 in 478,261,833.14
    1 in 5,978,272.91
    1 in 184,230.29
    1 in 10,482.07
    1 in 980.78
    1 in 142.30
    1 in 31.05
    1 in 10.06
    1 in 4.86
    1 in 3.57
    1 in 4.21
    1 in 8.79
    1 in 43.05    		 $4,000.00
    $2,000.00
    $500.00
    $250.00
    $72.00
    $24.00
    $4.00
    $2.00
    $1.00
    $0.50
    -
    -
    -    		 $0.00
    $0.00
    $0.00
    $0.02
    $0.07
    $0.17
    $0.13
    $0.20
    $0.21
    $0.14
    -
    -
    -

    Total EV $0.94 Total EV
    Cost of Ticket $1.00 Cost of Ticket
    Casino Edge 6% Casino Edge
    13 Numbers Picked Odds

    		Payout EV

    		Payout EV
    13
    12
    11
    10
    9
    8
    7
    6
    5
    4
    3
    2
    1
    0    		 1 in 4,065,225,581.67
    1 in 41,694,621.35
    1 in 1,060,032.75
    1 in 49,844.80
    1 in 3,847.67
    1 in 458.05
    1 in 81.20
    1 in 21.05
    1 in 7.94
    1 in 4.40
    1 in 3.67
    1 in 4.84
    1 in 11.26
    1 in 60.99    		 $6,000.00
    $3,000.00
    $500.00
    $240.00
    $80.00
    $20.00
    $5.00
    $4.00
    $3.00
    $0.50
    $0.50
    -
    -
    -    		 $0.00
    $0.00
    $0.00
    $0.00
    $0.02
    $0.04
    $0.06
    $0.19
    0.38
    $0.11
    $0.14
    -
    -
    -

    Total EV $0.95 Total EV
    Cost of Ticket $1.00 Cost of Ticket
    Casino Edge 5% Casino Edge
    14 Numbers Picked Odds

    		Payout EV

    		Payout EV
    14
    13
    12
    11
    10
    9
    8
    7
    6
    5
    4
    3
    2
    1
    0    		 1 in 38,910,016,281.65
    1 in 324,250,135.68
    1 in 6,764,018.47
    1 in 262,397.27
    1 in 16,739.86
    1 in 1,644.09
    1 in 239.14
    1 in 50.37
    1 in 15.21
    1 in 6.58
    1 in 4.13
    1 in 3.86
    1 in 5.67
    1 in 14.59
    1 in 86.95    		 $7,500.00
    $2,000.00
    $1,000.00
    $500.00
    $150.00
    $50.00
    $12.00
    $5.00
    $3.00
    $2.00
    $0.50
    $0.50
    -
    -
    -    		 $0.00
    $0.00
    $0.00
    $0.00
    $0.01
    $0.03
    $0.05
    $0.10
    $0.20
    $0.30
    $0.12
    $0.13
    -
    -
    -

    Total EV $0.94 Total EV
    Cost of Ticket $1.00 Cost of Ticket
    Casino Edge 6% Casino Edge
    15 Numbers Picked Odds

    		Payout EV

    		Payout EV
    15
    14
    13
    12
    11
    10
    9
    8
    7
    6
    5
    4
    3
    2
    1
    0    		 1 in 428,010,179,098.40
    1 in 2,853,401,193.99
    1 in 48,362,732.10
    1 in 1,539,397.31
    1 in 81,020.91
    1 in 6,576.37
    1 in 789.16
    1 in 136.40
    1 in 33.46
    1 in 11.58
    1 in 5.68
    1 in 4.00
    1 in 4.16
    1 in 6.76
    1 in 19.13
    1 in 124.75    		 $10,000.00
    $2,500.000
    $1,200.00
    $600.00
    $300.00
    $150.00
    $50.00
    $15.00
    $5.00
    $2.00
    $1.00
    $0.50
    $0.50
    -
    -
    -    		 $0.00
    $0.00
    $0.00
    $0.00
    $0.00
    $0.02
    $0.06
    $0.11
    $0.15
    $0.17
    $0.18
    $0.13
    $0.12
    -
    -
    -

    Total EV $0.94 Total EV
    Cost of Ticket $1.00 Cost of Ticket
    Casino Edge 6% Casino Edge

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