Minnesota's Scratch Games

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Revised 6/10/09

One of the current Minnesota's Scratch Games is called Cash Fireworks. In this $1 game there are a number of different payoffs according to the following schedule, and they have the indicated approximate probability of occurring: Cash Fireworks Odds

Payoff - - - - - - - - Probability

..$1000 - - - - - - - - 1/240,000
....$500 - - - - - - - - 1/48,000
....$100 - - - - - - - - 1/12,000
......$50 - - - - - - - - 1/1,920
......$25 - - - - - - - - 1/600
......$20 - - - - - - - - 1/600
......$10 - - - - - - - - 1/300
........$8 - - - - - - - - 1/300
........$6 - - - - - - - - 1/300
........$5 - - - - - - - - 1/100
........$4 - - - - - - - - 1/60
........$3 - - - - - - - - 1/42.86
........$2 - - - - - - - - 1/15.79
........$1 - - - - - - - - 1/7.89

These probabilities (odds) are based on the assumption that 4,800,000 tickets will be sold. So, for example, assuming there are 304,000 $2 winners as indicated in their chart, the probability of winning $2 would be 304,000/4,800,000 = .06333... = 1/15.79 (to two decimal places). The total approximate number of winners, according to their chart is 1,219,220, so the approximate probability of winning something is 1,219,220/4,800,000 = .254 = 1/3.94. It also follows that the approximate probability of having a losing ticket is .746, or roughly 3 times out of 4. Note also that the probability of just getting one's $1 back is 608,000/4,800,000 = .127, so the probability of coming out ahead is 611,220/4,800,000 = .127 = 1/7.85.

As in almost all gambling games, however, the probability of winning is not the main concern. Rather one wants to know what one can on average 'expect' to win when playing the game. To compute the expected payoff one multiplies the amount of each payoff times the probability (odds) of getting that payoff and adds these together:

1000/240,000 + 500/48,000 + 100/12,000 + 50/1,920 + 25/600 + 20/600 + 10/300 + 8/300 + 6/300 + 5/100 + 4/60 + 3/42.86 + 2/15.79 + 1/7.89 = .644.

Thus, the expected payoff on this $1 ticket is 64.4 cents. Expected payoffs on other Instant Games can be computed similarly, and the above result is typical of these games--see below. (Note, however, that most games cost more than $1 to play, but, in general, the more they cost the higher the expected payoff!)

Some other games are (Note: There are inconsistencies in the information given in the sites marked by *):

$200,000 Mega Slots
a $10 game which has an expected payoff of $7.056, or 70.6 cents per $1,
Fishin' for Fortune
a $2 game which has an expected payoff of $1.336, or 66.8 cents per $1,
$100,000 Treasure Hunt
a $5 game which has an expected payoff of $3.410, or 68.2 cents per $1,
$500,000 Cash Blowout
a $20 game which has an expected payoff of $14.531, or 72.7 cents per $1,
*Blazing Sevens Crossword Tripler
a $3 game which has an expected payoff of $1.992, or 66.4 cents per $1,
Fast Cash
a $1 game which has an expected payoff of $0.646, or 64.6 cents per $1,
Casino Action
a $10 game which has an expected payoff of $7.040, or 70.4 cents per $1,
MINNESOTA TWINS
a $5 game which has an expected payoff of $3.135, or 62.7 cents per $1,
Note: Losing tickets can be entered for chances at prizes.
Double Triple Slingo
a $3 game which has an expected payoff of $1.998, or 66.6 cents per $1,
$500,000 Cash Craze
a $20 game which has an expected payoff of $14.531, or 72.7 cents per $1,
Funky 5's
a $5 game which has an expected payoff of $3.427, or 68.5 cents per $1,
*Luck for a Buck
a $1 game which has an expected payoff of $0.646, or 64.6 cents per $1,
$200,000 Money Match
a $10 game which has an expected payoff of $7.056, or 70.6 cents per $1,
Platinum Payout
a $5 game which has an expected payoff of $3.415, or 68.3 cents per $1,
*Double Dollars
a $2 game which has an expected payoff of $1.330, or 66.5 cents per $1,
Red Hot Cherry 7's
a $5 game which has an expected payoff of $3.421, or 68.4 cents per $1,
*$500,000 Fortune
a $20 game which has an expected payoff of $14.477, or 72.4 cents per $1,
Hershey's Kisses™ and Cash
a $2 game which has an expected payoff of $1.328, or 66.4 cents per $1,
*Lucky Lines
a $3 game which has an expected payoff of $2.000, or 66.7 cents per $1,
$200,000 Winning Streak
a $10 game which has an expected payoff of $7.058, or 70.6 cents per $1,
*Break the Bank
a $5 game which has an expected payoff of $3.419, or 68.4 cents per $1,
$200,000 Player's Club
a $10 game which has an expected payoff of $7.022, or 70.2 cents per $1,
Bonus Bar Bingo
a $3 game which has an expected payoff of $2.008, or 66.9 cents per $1,
Deal or No Deal
a $5 game which has an expected payoff of $3.338, or 66.8 cents per $1,
*Scrabble
a $3 game which has an expected payoff of $1.993, or 66.4 cents per $1,
Money Roll
a $5 game which has an expected payoff of $3.420, or 68.4 cents per $1.

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