What am I screwing up?
You have a bag with 6 red balls and 4 white balls. In the game you are playing, you are trying to consecutively pick out a red balls, with the bag being reset after each turn. Also, in this game, 10 times is the most times you can get red in a row before the game ends. Pretend this is an even money gambling game, $10 to play. If, for instance, you get three red balls in a row, then get a white one on the fourth try, this counts (and pays) as three in a row.
# red balls...odds..............pay-out.........percentage
in a row.......against...........assuming......unique
..................one................$10 buy-in....occurrence
0................1.5000 to 1....$0.00............40.00%
1................0.6667 to 1....$6.67............24.00%
2................1.7778 to 1....$17.78..........14.40%
3................3.6296 to 1....$36.30............8.64%
4................6.7160 to 1....$67.16............5.18%
5................11.860 to 1....$118.60..........3.11%
6................20.433 to 1....$204.33..........1.87%
7................34.722 to 1....$347.22..........1.12%
8................58.537 to 1....$585.37..........0.67%
9................98.229 to 1....$982.29..........0.40%
10..............164.38 to 1....$1643.82........0.60%
Judging by my numbers, lets pretend you did this 1000 times. You would get 1 red ball the first time and miss the second time 24% of the time. So, 240 times out of 1000 you would get paid $6.67. Additionally, 6 times out of 1000 you would get a red ball all ten times, and get paid $1643.82 each time, for a total of $9939.53. If you played 1000 times, it would cost $10,000 to play....so how in the world can the game pay out so much? What am I screwing up?
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