- Roulette (single number bet).
The player predicts which of 38 roulette numbers will be randomly chosen by the
roulette wheel. If the player is correct, the player keeps the amount bet and wins
35 times the bet amount (which has the effect of giving back the player an amount 36
times the amount bet).
Calculate the expected payout when the bet amount is $1:
-
Roulette (color bet).
The player predicts which color (red or black) will be randomly chosen by the roulette
wheel. If the player is correct, the player keeps the amount bet and also wins an amount
equal to the bet (which has the effect of giving double the amount bet back to the player).
On a roulette wheel, 18 of the 38 spaces are red and 18 of the 38 spaces are black.
The other two spaces are green, the zero and the double zero.
Calculate the expected payout when the bet amount is $1:
- Pick 3 Lottery – Straight.
The player picks a three digit sequence (numbers from zero to nine).
If the player’s numbers match the numbers randomly drawn, in the correct order,
the player wins 500 times the amount bet.
(The player does not also receive the initial bet back)
Calculate the expected payout when the bet amount is $1:
- Pick 3 Lottery – Boxed.
The player picks a three different digits (numbers from zero to nine).
If the player’s numbers match the numbers randomly drawn, in any order,
the player wins 80 times the amount bet.
(As before, the player does not also receive the initial bet back)
Calculate the expected payout when the bet amount is $1:
- Blackjack Insurance
The player sees the blackjack dealer is showing an ace.
By taking “insurance”, the player makes a separate bet not connected to
the original blackjack bet. If the dealer’s hidden card has a value of ten
(giving the dealer a total of 21), the player wins the “insurance” bet
amount back, plus another 1.5 times the amount bet (which has the effect of giving
the player 2.5 times the amount bet). Cards with the value of ten are the king, queen,
jack, and, of course, ten. Assume that the cards already seen have no effect on the
probabilities, so drawing each value (ace through king) is equally likely.
Calculate the expected payout when the bet amount is $1:
- Simplified Slot Machine
Imagine a slot machine that simulates rolling three six-sided dice after a $1
token is inserted.
Calculate the expected payout when the bet amount is $1: