P(exact 5 balls in specific pocket| at least one pocket is empty)
=P(at least one pocket is empty| exact 5 balls in specific pocket) * P(exact 5 balls in specific pocket) / P(at least one pocket is empty)
=P(No Jackpot 65 balls on 24 pocket) * P(70 choose 5 then 25^65) / 0.80326
= 0.82227* 70 choose 5 * 24^65/25^70 / 0.80326
= 0.08932
P(exact 6 balls in specific pocket| at least one pocket is empty)
=P(at least one pocket is empty| exact 6 balls in specific pocket) * P(exact 6 balls in specific pocket) / P(at least one pocket is empty)
=P(No Jackpot 64 balls on 24 pocket) * P(70 choose 6 then 25^64) / 0.80326
= 0.83668* 70 choose 6 * 24^64/25^70 / 0.80326
= 0.04103
P(exact 7 balls in specific pocket| at least one pocket is empty)
=P(at least one pocket is empty| exact 7 balls in specific pocket) * P(exact 7 balls in specific pocket) / P(at least one pocket is empty)
=P(No Jackpot 63 balls on 24 pocket) * P(70 choose 7 then 25^63) / 0.80326
= 0.85060* 70 choose 7 * 24^63/25^70 / 0.80326
= 0.01589
P(exact 8 balls in specific pocket| at least one pocket is empty)
=P(at least one pocket is empty| exact 8 balls in specific pocket) * P(exact 8 balls in specific pocket) / P(at least one pocket is empty)
=P(No Jackpot 62 balls on 24 pocket) * P(70 choose 8 then 25^62) / 0.80326
= 0.86399* 70 choose 8 * 24^62/25^70 / 0.80326
= 0.00530
P(exact 9 balls in specific pocket| at least one pocket is empty)
=P(at least one pocket is empty| exact 9 balls in specific pocket) * P(exact 9 balls in specific pocket) / P(at least one pocket is empty)
=P(No Jackpot 61 balls on 24 pocket) * P(70 choose 9 then 25^61) / 0.80326
= 0.87681* 70 choose 9 * 24^61/25^70 / 0.80326
= 0.00154
P(exact 10 balls in specific pocket| at least one pocket is empty)
=P(at least one pocket is empty| exact 10 balls in specific pocket) * P(exact 10 balls in specific pocket) / P(at least one pocket is empty)
=P(No Jackpot 60 balls on 24 pocket) * P(70 choose 10 then 25^60) / 0.80326
= 0.88904* 70 choose 10 * 24^60/25^70 / 0.80326
= 0.00040
11+ balls in one pockets. odds are too small to make any difference.
Now we have the payout table for this pocket:
Balls
Odds
Payout
EV
0
0.07147
0
0
1
0.1586
0
0
2
0.2327
40
9.308
3
0.2242
120
26.904
4
0.1595
260
41.47
5
0.0053
460
2.438
6
0.08932
660
58.9512
7
0.04103
860
35.2858
8
0.01589
1060
16.8434
9
0.00154
1260
1.9404
10
0.0004
1460
0.584
Total:
0.99995
193.7248
So, one pocket has a EV of $193.7248,
25 pockets will have a EV of 193.7248* 25 = $4843