## Sunday, January 5, 2014

### Playing Cards: Odds That The Next Card is Higher or Lower

In the classic game "Card Sharks", contestants had to guess and wager whether the proceeding card is higher or lower. The card game is popular to watch on TV and to play on yourself. All it takes a deck of cards to play.

This blog entry deals with the odds of whether the next card is higher or lower. Several assumptions: the odds are calculated with a standard 52 card deck without Jokers. The tables deal with the first cards drawn from the top of the deck.

Table 1: One card is drawn from the top of the deck.

Table 2: One card is drawn. A second drawn which is lower than the first card. Examples: Ace then King, Ten then Six.

The second card is the current card.

Table 3: One card is drawn. A second drawn which is higher than the first card. Examples: King then Ace, Six then Ten.

The second card is the current card.

Table 4: A pair of cards are drawn. Example: A pair of Eights.

General strategies of Card Sharks consisting of:
* Betting a lot on lower when you have an Ace or King
* Betting a lot on higher when you have a 2 or 3
* Betting minimum on a 7, 8, or 9 (middle ranks)

Analyzing a Hand

In general, the odds of whether cards are higher or lower as the number of cards decrease. Let's see how the odds change during a 8 card hand.

** Odds are rounded to 3 digits in this analysis.

Here is an Example Hand:

1st Card: King
Odds the next card is higher: 0.078
Odds the next card is another King: 0.059
Odds the next card is lower: 0.863

2nd Card: 10
Odds the next card is higher: 0.300
Odds the next card is another 10: 0.060
Odds the next card is lower: 0.640

3rd Card: 2
Odds the next card is higher: 0.939
Odds the next card is another 2: 0.061
Odds the next card is lower: 0.000

4th Card: 6
Odds the next card is higher: 0.624
Odds the next card is another 6: 0.063
Odds the next card is lower: 0.313

5th Card: 4
Odds the next card is higher: 0.787
Odds the next card is another 4: 0.064
Odds the next card is lower: 0.149

6th Card: 4
Odds the next card is higher: 0.805
Odds the next card is another 4: 0.043
Odds the next card is lower: 0.152

7th Card: King
Odds the next card is higher: 0.089
Odds the next card is another King: 0.044
Odds the next card is lower: 0.867

8th Card: 5
(The game ends).

Shuffle up and deal!

Eddie

This blog is property of Edward Shore. 2014

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