Question 1197105
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Answer:  -0.12 dollars


The player expects to lose about 12 cents per game. 


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Explanation:


X = profit in dollars
P(X) = probability of getting that profit<table border = "1" cellpadding = "5"><tr><td>Outcome</td><td>X</td><td>P(X)</td><td>X*P(X)</td></tr><tr><td>Straight Flush</td><td>200</td><td>0.00217</td><td>0.434</td></tr><tr><td>Three of a kind</td><td>150</td><td>0.00235</td><td>0.3525</td></tr><tr><td>Straight</td><td>30</td><td>0.03258</td><td>0.9774</td></tr><tr><td>Flush</td><td>20</td><td>0.04959</td><td>0.9918</td></tr><tr><td>Pair</td><td>5</td><td>0.16941</td><td>0.84705</td></tr><tr><td>Any other hand</td><td>-5</td><td>0.7439</td><td>-3.7195</td></tr></table>Note the last outcome "any other hand" has probability of 1 - (sum of the other probabilities)
All of the P(X) values must add to 1.


The expected value is the sum of the X*P(X) values
0.434 + 0.3525 + 0.9774 + 0.9918 + 0.84705 + (-3.7195) = -0.11675


This rounds to -0.12 when rounding to the nearest penny.


The player expects to profit about -0.12 dollars per game.
In other words, the player expects to lose about $0.12 (aka 12 cents) per game. 


This is not a mathematically fair game since the expected value isn't zero. 
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