If you draw a card with a value of five or less from a standard deck of cards, I will pay you $37. If not, you pay me $12
Well.......5 or less down to the deuce is only 4 x 4(suits) = 16 cards out of 52 that will give me a winner.
16/52 = 30.7 % chance of winning
obviously YOU have a 69.3% chance of winning.......
SO let's set up a ratio to see if the 'house' has the advantage....
30.7/69.3 =? 12/37
.443 = ? .324 it looks like that is a good bet to me !
Another way to look at it...if I play 100 times I will win 30.7 times and COLLECT 30.7 x 37 = 1135.90
I will LOSE 69.3 times and have to PAY 69.3 x 12 = 831.60
So if I play 100 times...I collect 1135.9 and PAY 831.6 for a net POSITIVE CASH FLOW of 304.30 WINNER!!!!
Incidentally the Powerball Jackpot for this Saturday's (1/9/15) drawing is over 700 MILLION for those of you old enough to play ! Yikes!!!!
The way these games usually work is that we must put up $12 to play, and the other party returns our $12 to us along with another $25 if we win = $37 "payout"
If so, on any one draw, we stand to be a loser.....here's why :
The probability of us drawing a card 5 or less * [$37 payout for us - $12 we must put up] + The probability of us not drawing a card 5 or less * [-$12 loss for us] = the expected value for us
(16/52) * [ 37-12] + (36/52) * (-12) = about - 61.5 cents
On average, we will lose -61.5 cents every time we play.........
P.S. - We could do better at playing roulette.......the average loss there is only about 5.3 cents per play......!!!!!
The one rule in gambling is......the house always has the "edge"
Now you know why there are all those big buildings in Las Vegas.......!!!!
You might be right Chris....... I went with what he stated the parameters of the game were,,,,....like the two of us were playing and I didn't have to 'ante' anything....AGAIN.....a little unclearly worded problem. !
In Technicality, it wasn't a question...
In my opinion it was more of a statement.
I couldn't argue with Coldplay or the guest......however....I will point out that the "house" would not stay in business long if it had to pay out more than it took in.......!!!!!!