SNF $100,000 Scratcher
Check in at the players club and get a scratch card. Only the first 200 players receive cards.
Each card has two columns with a single digit for each team by quarter.
If the numbers on your scratch card match the last digit of each team's score in the corresponding quarter, you win.
If you match all 8 scores in all four quarters, you win $100,000.
Prizes must be claimed by midnight.
Is it worth hanging around to see if you have a match? What are the odds of winning the big moolah?
Cincy would have to have either 3 or 13, then how do they get to 8? 3-18/28 or 13-18/28. Once they get the 8 it would be easier to get to the other numbers but still tough. Say they actually do get to 18/28, then they would have to get to 30/40 by the 3rd. If they happen to get there then they need to score 41/51 by the end. Those point totals are all very weird numbers.
Even NE's 2 would be very very rare. 2 or 12 in the 1st.
If you can scratch the numbers as soon as you get the card and you have some standard numbers then I would stick around. If you end up with a card like above then I would leave.
The probability of getting any particular quarter is 1/100.
Probability of getting all four quarters: (1 / 100)4 = 1 / 100,000,000; note that any slot machine that had those odds of hitting the jackpot would have to display that fact
Probability of getting exactly three: 4 x (1 / 100)3 x 99 / 100 = 396 / 100,000,000 = 1 / 252,525
Probability of getting exactly two: 6 x (1 / 100)2 x (99 / 100)2 = 58,806 / 100,000,000 = 1 / 1700
Probability of getting exactly one: 4 x (1 / 100) x (99 / 100)3 = 3,881,196 / 100,000,000 = 1 / 26
Assuming $10 in free play is worth $5, the EV of the card is:
(1 x 100,000 + 396 x 5000 + 58,806 x 250 + 3,881,196 x 5) / 100,000,000 = $0.3619
Check the rules to see how the "fourth quarter" score is handled if the game goes into overtime.
Quote: ThatDonGuyIf the numbers are completely random (which I doubt, since there are only 200 cards), then you "shoot the arrows and then draw the target" - that is, you don't think of trying to match the score to the numbers, but trying to match the numbers to the score.
The probability of getting any particular quarter is 1/100.
Probability of getting all four quarters: (1 / 100)4 = 1 / 100,000,000; note that any slot machine that had those odds of hitting the jackpot would have to display that fact
Probability of getting exactly three: 4 x (1 / 100)3 x 99 / 100 = 396 / 100,000,000 = 1 / 252,525
Probability of getting exactly two: 6 x (1 / 100)2 x (99 / 100)2 = 58,806 / 100,000,000 = 1 / 1700
Probability of getting exactly one: 4 x (1 / 100) x (99 / 100)3 = 3,881,196 / 100,000,000 = 1 / 26
Assuming $10 in free play is worth $5, the EV of the card is:
(1 x 100,000 + 396 x 5000 + 58,806 x 250 + 3,881,196 x 5) / 100,000,000 = $0.3619
Check the rules to see how the "fourth quarter" score is handled if the game goes into overtime.
Thanks for the analysis folks. Overtime is ignored. The score at the end of the fourth quarter is used for this contest.
When I saw the number 2, my immediate thought was that this was how they controlled their exposure, but based on my limited sample size, I suppose the numbers could still be randomly seeded.
With only 200 cards in play max (they were still pushing the promotion two hours prior to kick-off), it seems their only real risk might be $80 in free play.
Quote: Ayecarumba
With only 200 cards in play max (they were still pushing the promotion two hours prior to kick-off), it seems their only real risk might be $80 in free play.
but after you figure in their extra income from people sticking around to gamble and buy drinks. Plus the people who win $10 free play are most likely going to use the $10 and not cash out anything from it.
Then again, I doubt there are 100,000,000 cards, even if there is a single source for them used in different locations for different games, so who knows what the true distribution of numbers is.
