A Probability Quiz For Gamblers

Some of you may know that I recently wrote a fairly short, simplified book on probability with the help of Professor Justin Conrad from the University of Georgia called Probability and Statistics The Vegas Way.
The book was written mainly for those who are not that into math but need to know this stuff to get a good grade in a required course or to have a bigger edge in their gambling endeavors. We bent over backwards to make this the easiest to understand probability book you will ever see. 
The last chapter is titled 21 Questions and Detailed Answers. They are of all different types but are all answerable using the info in the book. This column will summarize several of those questions, give the correct answer plus a few tips on how we approach them. More extensive explanations (for those who haven’t obtained the book) will be given in my next column.
Question: What is the probability of throwing three coins and obtaining exactly two heads?
Answer: 3/8. 
Question: If an urn contains six white balls and four black balls, what’s the probability  that grabbing five results in three black ones and two white ones?
Answer: 5/21. We show two different ways to get this. 
Question: You have $100 to your name for the next few days and are contemplating betting it all on a 60% shot getting even money. But if you wait until tomorrow, you can bet that $100, but no more, on an 80% shot.  Should you wait? What if the second bet was 70%?
Answer: Wait for the 80% shot but not the 70% shot. It’s simple algebra related to “expected value.”
Question: If you are x standard deviations above the mean what are the chances you are x plus one standard deviations above it?
Answer: It depends what x is. We show you how to use a chart to get it. 
Question: If a baseball team is 40% to win each game of the World Series, what are the chances they win in exactly six games?
Answer:  1440/15625 You can reduce the fraction but it’s not necessary. The non reduced fraction arises naturally from multiplying a bunch of them.
Question: A draw poker machine allows you to draw twice. The second draw is to the results of the first draw. You always go for it regardless of what that first draw brings. What’s your chance of making the Royal?
Answer: 8/2162. Again, no need to reduce. Note that the one or two cards that are not used in the first draw are out of the deck for the second draw.
Question: If while ice skating on your home rink you average falling 1.5 times per hour, what are the chances that you will fall four times in the next hour?
Answer: It’s about 5%. This is another example of a “statistics” question, like question 10 that is expected to be answered with the use of a chart since the math technique is well beyond the scope of typical students and barely improves accuracy.
Question: You laid $200 to $100 on a football game. Your team is now threatening to score and if they do, they will be 60 percent to win. If they don’t you make them 20%. You think they are 70% to score.  What is the fair price to get out of your bet at this moment.
Answer: $56. There is an easy way to do this problem and a harder way, and we explain both. We also explain how to do the reverse problem where the settlement is known, and we need to calculate the winning chances that settlement implies. ♠

David Sklansky is the author of The Theory of Poker, as well as nearly two dozen other guides on gambling, poker, and other games. The three-time WSOP bracelet winner’s latest book, Small Stakes No-Limit Hold’em: Help Them Give You Their Money, is now available on Amazon. You can contact Sklansky at
[email protected].