fair bet at craps. Almost all bets

fair bet at craps. Almost all bets made at
gambling casinos favor the house. In other words,
the difference between the amount bet and the
mean of the distribution of the payoff is a positive
number. An exception is “taking the odds” at the
game of craps, a bet that a player can make under
certain circumstances. The bet becomes available
when a shooter throws a 4, 5, 6, 8, 9, or 10 on
the initial roll. This number is called the “point”;
when a point is rolled, we say that a point has been
established. If a 4 is the point, an odds bet can be
made that wins if a 4 is rolled before a 7 is rolled.
The probability of winning this bet is 0.5 and the
payoff for a $10 bet is $20. The same probability
of winning and payoff apply for an odds bet on a
10. For an initial roll of 5 or 9, the odds bet has
a winning probability of 2/3 and the payoff for a
$10 bet is $15. Similarly, when the initial roll is 6
or 8, the odds bet has a winning probability of 5/6
and the payoff for a $10 bet is $12. Find the mean
of the payoff distribution for each of these bets.
Then confirm that the bets are fair by showing
that the difference between amount bet and the
mean of the distribution of the payoff is zero.

Kết quả (Anh) 1:

fair bet at craps. Almost all bets made atgambling casinos favor the house. In other words,the difference between the amount bet and thethe mean of the distribution of the payoff is a positivenumber. An exception is "taking the odds" at thethe game of craps, a bet that a player can make undercertain circumstances. The bet becomes availableWhen a shooter throws a 4, 5, 6, 8, 9, or 10 onthe initial roll. This number is called the "point";When a point is rolled, we say that a point has beenestablished. If a 4 is the point, an odds bet can bemade that wins if a 4 is rolled before a 7 is rolled.The probability of winning this bet is 0.5 and thepayoff for a $10 bet is $20. The same probabilityof winning and payoff apply for an odds bet on a10. For an initial roll of 5 or 9, the odds bet hasa winning probability of 2/3 and the payoff for a$10 bet is $15. Similarly, when the initial roll is 6or 8, the odds bet has a winning probability of 5/6and the payoff for a $10 bet is $12. Find the meanof the payoff distribution for each of these bets.Then confirm that the bets are fair by showingthat the difference between amount bet and thethe mean of the distribution of the payoff is zero.

Kết quả (Anh) 2:

fair bet at craps. Almost all bets made at
gambling casinos favor the house. In other words,
the difference the between the amount bet and the
mean of the distribution of the payoff is a positive
number. An exception is "taking the odds" at the
game of craps, a player can make a bet có under
Certain Circumstances. The bet Becomes available
khi shooter throws a 4, 5, 6, 8, 9, or 10 on
the initial roll. This number is gọi the "point";
khi point is rolled, chúng drunk đã có a point
established. If a 4 is the point, an odds bet can be
made if a 4 có wins all before a 7 is rolled is rolled.
The probability of winning this bet is 0.5 and the
payoff for a $ 10 bet is $ 20. The same probability
of winning and payoff apply for an odds bet on a
10. For an initial roll of 5 or 9, the odds bet has
a winning probability of 2/3 and the payoff for a
$ 10 bet is $ 15. Similarly, khi initial roll is 6
or 8, the odds bet has a winning probability of 5/6
and the payoff for a $ 10 bet is $ 12. Find the mean
of the distribution for each of những payoff bets.
Then confirm là bets are fair by showing
là difference the between amount bet and the
mean of the distribution of the payoff is zero.