The Probability of Black

20 July 2013

By Jerry Stickman

Dear Jerry Stickman,

Hi. My friends and I have been having long hours trying to work out the math logic behind a simple betting scenario, but alas to no avail. We hope you can shed some light.

Scenario:

• In a make-believe game where there are two equal options being RED or BLACK.
• A croupier, in an unimaginable scenario, has already drawn 9 REDs in a row.
• At this stage, Mr. X who observes this from the side, now decides to participate.
• He knows and is also told by others about the 9 in a row.
• The croupier is about to draw out for the 10th time.

Question: What is the math PROBABILITY that Mr. X will choose correctly (and win) if he now chooses BLACK.

Is it:
A) 50%
B) 1 - (1/2 to the power of 9) = 99.8%
C) 1 - (1/2 to the power of 10) = 99.9%
D) Less than 1%
E) None of the above, please tell us : ___________

The assumption of course is everything is reasonable & fair. For example, the same croupier, equal chance of pulling a red or black, no changes in any other parameters.

Any explanation of your answer will be mightily appreciated.

Thank you.

Tsang

Hi Tsang,

This is a very common issue with the general casino playing public. Many “can’t lose” betting schemes have been formulated on the assumption that after x number of like rolls the probability of a different roll increases.

Assuming we ignore green (0 and 00) – which in a real game is what gives the casino its edge of 5.26 percent – the answer is A). The scenario you cite is exactly the same as flipping a fair two-sided coin. The odds of a heads (red) or tails (black) are exactly 50 percent each flip (spin). It does not matter if one of the results has occurred once or 1,000 times previously. The probability is the same for each and every decision - 50 percent heads (red) and 50 percent tails (black). The probability of one decision (either heads or tails / red or black) happening 2, 3, 4, 5, or more times in a row does change with each additional like decision.

The same is true (the probability of a particular color or number, etc.) of any game where the same objects are used to determine the outcome. This could be roulette, dice, or even cards if all the cards are returned after each hand. In a regular show or pitch game of blackjack where cards are played for multiple hands, the odds of getting specific hands or cards does change, however, since the played cards are no longer available until the cards are reshuffled.

I hope this clears things up for you Tsang. If not, please write back and I will respond with additional details.

May all your wins be swift and large and all your losses slow and tiny.

Jerry “Stickman”

Jerry Stickman’s new book is “Everything Casino Poker: Get the Edge at Video Poker, Texas Hold’em, Omaha Hi-Lo and Pai Gow Poker.” In addition, Jerry “Stickman” gives private lessons in dice control with his partner Frank Scoblete. You can contact Jerry “Stickman” at stickmanjerry@aol.com