# Game odds

Posted by umerblackeagle on September 27th, 2010

Now here are some game odds regarding different card games.

Remember:
minuses sign decrease them.

Blackjack Rule: Double Exposure

Description: the cards are dealt face up, including the dealer's cards.

Effect on Odds          + 8.80 %

Blackjack Rule: Blackjack Pays 2:1

Description: Normally blackjack pays 3:2, which means you win \$15 for a \$10 bet. When blackjack pays 2:1, you win \$20 for a \$10 bet. Good rule.

Effect on Odds          + 2.27 %

Blackjack Rule: Five Card Charlie

Description: player having 5 cards totaling 21 or less automatically beats anything except a dealer blackjack, even if the dealer has a higher total.

Effect on Odds          + 1.46 %

Blackjack Rule: Suited Blackjack Pays 2:1

Description: Normally blackjack pays 3:2, which means you win \$15 for a \$10 bet. When blackjack pays 2:1, you win \$20 for a \$10 bet. Suited blackjack means of the same suit.

Effect on Odds          + .57 %

Blackjack Rule: 21 Wins

Description: A player's hand totaling 21 automatically wins.

Effect on Odds          + .54 %

Blackjack Rule: ESR - Early Surrender (Dealer Up card = Ace)

Description: the option to give up without playing your hand before the dealer checks for blackjack. You lose half of your bet.

Effect on Odds          + .39%

Blackjack Rule: Player Wins Blackjack Ties

Description: When the dealer and player both have blackjack, the player wins.

Effect on Odds          + .30 %

Factors That Influence Bingo Odds of Winning

The Bingo odds of winning depend in someone the number of cards that are played at any given time. No two players will get the same score, if the cards are very versatile; it is because of pure chance if they do win together. In Bingo, numbers are drawn until someone wins, and this is why having different cards is a must.

The number of players is another factor that influences Bingo odds. Unlike games such as poker, the more players there are, the less the chance is for winning. If there are 100 players, then the Bingo odds to win are 1 in a 100. If, on the other hand, there are 1,000 players, the odds are 1 in a 1,000. However, the prize for less crowded games is smaller too, so you need to make the decision between prize size and Bingo odds. Another factor that that influence is the number of Bingo cards also influences the winning odds. The more Bingo cards you play the better you?re winning Bingo odds are.

## Frequency of 7-card poker hands.

In some popular variations of poker, a player uses the best five-card poker hand out of seven cards. The frequencies are calculated in a manner similar to that shown for 5-card hands, except additional complications arise due to the extra two cards in the 7-card poker hand. The total number of distinct 7-card hands is 133,784,560. It is notable that the probability of a probability of a one-pair or two-pair hand is greater than the probability of no-pair hand.

The royal flush is not included in the cumulative probability calculation because it is a type of straight flush. The Ace-high straight flush or royal flush is slightly more frequent (4324) than the lower straight flushes (4140 each) because the remaining two cards can have any value; a King-high straight flush, for example, cannot have the Ace of its suit in the hand.

Note that the entire tables given below have frequencies exact, the probabilities and odds are approximate.

 Hand Frequency Probability Cumulative Odds 41,584 0.0311% 0.0311% 3,216 : 1 4,324 0.0032% --- 30,939 : 1 224,848 0.168% 0.199% 594 : 1 3,473,184 2.60% 2.80% 37.5 : 1 4,047,644 3.03% 5.82% 32.1 : 1 6,180,020 4.62% 10.4% 20.6 : 1 6,461,620 4.83% 15.3% 19.7 : 1 31,433,400 23.5% 38.8% 3.26 : 1 58,627,800 43.8% 82.6% 1.28 : 1 23,294,460 17.4% 100% 4.74 : 1 Total 133,784,560 100% 100% 0 : 1

Since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. Eliminating identical hands that ignore relative suit values leaves 6,009,159 distinct 7-card hands.

## Frequency of 5-card lowball poker hands.

Some variants of poker, called lowball, use a low hand to determine the winning hand. In most variants of lowball, the ace is counted as the lowest card and straights and flushes don't count against a low hand, so the lowest hand is the five-high hand A-2-3-4-5, also called a wheel. The probability is calculated to be equal to 2,598,960, the total number of 5-card combinations.

 Hand Distinct hands Frequency Probability Cumulative Odds 5-high 1 1,024 0.0394% 0.0394% 2,537.05 : 1 6-high 5 5,120 0.197% 0.236% 506.61 : 1 7-high 15 15,360 0.591% 0.827% 168.20 : 1 8-high 35 35,840 1.38% 2.21% 71.52 : 1 9-high 70 71,680 2.76% 4.96% 35.26 : 1 10-high 126 129,024 4.96% 9.93% 19.14 : 1 Jack-high 210 215,040 8.27% 18.2% 11.09 : 1 Queen-high 330 337,920 13.0% 31.2% 6.69 : 1 King-high 495 506,880 19.5% 50.7% 4.13 : 1 Total 1,287 1,317,888 50.7% 50.7% 0.97 : 1

## Frequency of 7-card lowball poker hands.

The probability is calculated to be 133,784,560 , the total number of 7-card combinations.

Hand

Frequency

Probability

Cumulative

Odds

5-high

781,824

0.584%

0.584%

170.12 : 1

6-high

3,151,360

2.36%

2.94%

41.45 : 1

7-high

7,426,560

5.55%

8.49%

17.01 : 1

8-high

13,171,200

9.85%

18.3%

9.16 : 1

9-high

19,174,400

14.3%

32.7%

5.98 : 1

10-high

23,675,904

17.7%

50.4%

4.65 : 1

Jack-high

24,837,120

18.6%