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Gambling and Probability Odds
 
Gambling and Probability:
The rules of probability are no more apparent than in the world of gambling. Even before the birth of roulette in the early 1800's mathematicians were using the rules of probability to define the outcome of seemingly random events. Popular online casino games such as blackjack, poker, video poker and slot machines all use the rules of probability to their advantage.

Poker:
With nothing wild, in order of probability, with 5 cards being dealt:

Royal Flush - A,K,Q,J, 10 of the same suit
(1 in 650,000)

Straight Flush - Five cards of same suit in order
(1 in 65,000)

Four of a Kind - Four of the same number or "face card"
(1 in 4000)

Full House - Three of one number or "face", two of another same pair
(1 in 700)

Flush - 5 cards of the same suit
(1 in 500)

Straight - Five cards numerically in a row
(1 in 250)

Three of a Kind - Three of the same numbered or "face" card
(1 in 50)

Two Pair - Two different sets of matched numbered or "face" cards
(1 in 20)

One Pair - One set of the same numbered or "face" cards
(1 in 2 1 balls picked out of 3)
Lottery:
US PowerBall - 5 balls picked out of 45...
THEN 1 Powerball picked out of 42 - odds: 1 in 80,089,128

US The Big Game - 5 balls picked out of 50...
THEN 1 Powerball picked out of 36 - odds: 1 in 76,275,360

Australian PowerBall - 5 balls picked out of 45...
THEN 1 Powerball picked out of 45 odds: 1 in 54,979,155

California SuperLotto - 6 balls picked out of 51 odds: 1 in 18,009,460

New York Lotto - 6 balls picked out of 51 odds: 1 in 18,009,460

Texas Lotto - 6 balls picked out of 50 odds: 1 in 15,890,700

Spanish Pimera - 6 balls picked out of 49 odds: 1 in 13,983,816

French Lotto - 6 balls picked out of 49 odds: 1 in 13,983,816

Liechtenstein Plus Lotto - 6 balls picked out of 49 odds: 1 in 13,983,816
British Lotto - 6 balls picked out of 49 odds: 1 in 13,983,816

Canadian Lotto - 6 balls picked out of 49 odds: 1 in 13,983,816

Washington Lotto - 6 balls picked out of 49 odds: 1 in 13,983,816

Scandinavian Lotto - 6 balls picked out of 48 odds: 1 in 12,271,512

Hong Kong Lotto - 6 balls picked out of 47 odds: 1 in 10,737,573

Australian Tatts Lotto - 6 balls picked out of 45 odds: 1 in 8,145,060

Australian Oz Lotto - 6 balls picked out of 45 odds: 1 in 8,145,060

Irish Lotto - 6 balls picked out of 42 odds: 1 in 5,245,786
Roulette:
Red: Payoff: 1:1 True Odds: 47.37%
Black: Payoff: 1:1 True Odds: 47.37%
Odd: Payoff: 1:1 True Odds: 47.37%
Even: Payoff: 1:1 True Odds: 47.37%
numbers 1 to 18: Payoff: 1:1 True Odds: 47.37%
numbers 19 to 36: Payoff: 1:1 True Odds: 47.37%
numbers 1 to 12: Payoff: 2:1 True Odds: 31.58%
numbers 13 to 24: Payoff: 2:1 True Odds: 31.58%
numbers 25 to 36: Payoff: 2:1 True Odds: 31.58%
Any one number: Payoff: 35:1 True Odds: 2.63%
Two number combination: Payoff: 17:1 True Odds: 5.26%
Three number combination: Payoff: 11:1 True Odds: 7.89%
Four number combination: Payoff: 8:1 True Odds: 10.53%
Six number combination: Payoff: 5:1 True Odds: 15.79%
0,00,1,2,3 combination: Payoff: 6:1 True Odds: 13.16%

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