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Game expected value
Every game has its expected value for the player with its stated payment.
This value is characterized by an average profit in one game (the balance of
profits and loses divided by the number of the played rounds), in case of
playing that game endlessly.
Here is a mathematical formula defining it:
E[X]=p[profit]+(1-p)x[loses]
p-states the probability of the success in the game (as well as a
profit); value(1-p)- the probability of the failure and betting loses
Let`s have a look at what it is like in the game in which we throw a dice.
the player bets a given result. If the player`s guess is correct, s/he gets a
payment, "K" times multiplied accordingly to what was the bet. If the player is
wrong, s/he loses the bet.
What should the "K" value be to make the game fair for both sides?
The probability of guessing the betted side of the dice is 1/6.
The other dice sides that are left , there are five of them, thus the
probability is 5/6.
The game expected value for the player equals:
E[X]=1/6x[K x(bet)]+5/6x[(-1)x(bet)]
To make the game fair, its expected value should be zero (nobody gets a
profit because someone else loses). In this situation the value of "K" payment
should be 5 (i.e. $5 for $1 betted).
If the casino sets the "K" payment on i.e. level 4, thus the game expected
value for the player would be minus 1/6. It would be such a sum of money which
the player would lose to to the casino per every single bet on average (That is
about 16%).
If the bets value is constant and equals i.e. $1, the player would lose about
$0.16 in each game. However, if the "K" payment equals i.e. 6, then the game
expected value would be positive for the player.
That would mean that the player gets about 16 cents net on average in each
game.
So the player would aim to play as many rounds as possible. esult \par
of the match.\cf1 \cf2\par
\cf1 \cf2 The net profit is certain and equals $2.20. If you invest a sum ten times \par
higher, then the net profit will raise ten times up to $22.\cf1 \cf2\par
\cf1 \cf2 Internet services mentioned above offer searching for the differences in \par
bets, there is a fee obviously, you have to pay for some good information, and \par
guarantee about 5% sometimes even more (up to14%). No bank will guarantee such a \par
profit
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