SOLUTION: When playing a game of cardwars with a friend, what are the odds that I play nine hands in a row without winning? If you're not sure what cardwars are, it is a very simple game

Question 356899: When playing a game of cardwars with a friend, what are the odds that I play nine hands in a row without winning?
If you're not sure what cardwars are, it is a very simple game that involves 2 players drawing cards from a deck. If I draw a higher card I win, if I draw a lower card I lose. For this scenario, let's also assume that if 2 equal cards are drawn (ex: 2 Kings are drawn by him and me both) I lose as well. The only way I win is if I draw a higher card than my opponent.
So, what are the odds that I lose 9 hands in a row (I draw a lower or equal card nine straight times).
Thanks in advance for your help as I can not solve this problem on my own.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Out of 169 hands you will win 78 and lose 91
probability of losing one hand 91/169 = 7/13
Probability that you will lose nine hands in a row (7/13)^9=.0038...
1-.0038=.9962
Odds against losing 9 in a row: 9962 to 38 or 262 to 1
.
Ed
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