Baseball fans do lots of dumb things. Wear a foam finger. Act like they’re smart because they correctly chose the attendance from the four choices on the big board. Throw trash at the lower levels. Streak the field. Root for the Yankees. (And while we’re at it, the 1980’s called. They want “The Wave” back.)
Yet few things are as dumb as the following game, which some friends and I play at Nationals Park – nationals.com.
- To start, everyone puts in a $1 ante.
- The first gambler then adds another $1 to the cup. If the player batting gets a hit, that gambler gets all the money in the cup. If the player batting does not get a hit, that gambler passes the cup to the second person.
- The second gambler then adds $2 to the cup. Again, that gambler gets the money if the player batting gets a hit, or passes the cup to the next gambler if the player batting does not get a hit.
- This continues, with the next gambler adding double what the previous gambler added, until there’s a hit.
Because of exponential growth, it doesn’t take long for this game to exceed most people’s comfort level. At a recent game, we had gone through five batters without a hit when the cup was passed to Dave. He gladly added $32, but then passed the cup to Joe when the batter struck out.
Now that the cup was requesting a three-digit donation, this was getting serious. Most of my friends don’t carry $128 to a baseball game, and even fewer of them are willing to put it in a betting cup. Dave looked at me. “You in?” he asked.
“Sure am,” I replied as I put $100 in the cup. “You’ll have to trust that I’m good for the other $28,” I said. “That’s the last of my cash.”
It occurred to me that 52.9% of the money now in the cup had come from my wallet. That made it extra hard to pass the cup to Adam when the batter struck out.
But Adam just looked at it. “Don’t even think about handing that to me,” he said. “I’m out.”
So the cup went back to Dave, begging for $256 more. “If you’re in, I’m in,” he said to me. “Trust me that I’m good for it?” he asked. I nodded my head to let him know that I did.
When Dave handed the cup to Joe after the next batter flew out, it was Dave’s money that now accounted for 56.3% of the pot. Joe just passed the cup directly to me. “I’m out, too,” he said.
Judgment is the better part of valor. But no one has ever accused me of being valiant. If I put in $512 and there’s a hit, I thought, I’ll win $377. But if not, I’ll be passing a cup to Dave that has $649 of my money.
“I’m in,” I said, surprising even myself. Dave looked at me with equal parts disbelief and dismay… amazed that I had pulled the trigger, unsure what he would do if the cup came to him, stunned that we had gotten to this point.
He’d need to deal with the question sooner than he thought. The batter hit a routine ground ball to the second baseman on the first pitch. As the ball popped in the first baseman’s mitt, my gulp was audible. Folks in our section eyed Dave suspiciously as he cheered an out for the home team. I passed the cup to him and asked, “To you for $1,024, sir. Are you willing to sacrifice your kids’ college fund for this?”
Dave looked at the cup. He looked at me. He looked back at the cup. After several long seconds, he looked at me again. “Split it?” he asked.
I paused. “What?”
“Yeah… what?” said Joe.
Dave explained. “You and I split it. Joe and Adam are out.”
“No!” protested Joe. “That’s not fair! You set us up!”
I ignored Joe, because I realized I now had an exit strategy. “Are you suggesting 50/50?” I asked Dave.
“That’s what I was thinking.”
“But I put two-thirds of the money in that cup.”
“Okay, sure,” Dave said. “We’ll split it 2:1.”
So in the end, I won $33, Dave won $51, and Adam and Joe were disconsolate over what had just transpired.
There had been a streak of 10 batters without a hit (one of the batters had walked, but that doesn’t count as a hit, so our silly game continued), and the pot had grown to $1,027. It would have climbed to $2,051 if Dave had continued. That might only be a drop in the bucket for the Koch brothers, but it’s a sizable amount for a math educator.
The hitless streak made us wonder what game in baseball history would have made us dig deepest into our pockets. The all-time winner would have been a game on May 2, 1917, between the Cincinnati Reds and the Chicago Cubs, when Fred Toney and Hippo Vaughn each threw no-hitters through nine innings. In the top of the 10th, Vaughn got one out before giving up the first hit of the game… so that’s at least 55 batters without a hit. It’s hard to find play-by-play data for games from 1917, but the box score shows that there were 2 walks in the game. If both of them happened before the first hit, that’d increase the pot to a staggering 257 + 3 = $144,115,188,075,855,874. That’s 144 quadrillion, for those of you who, like me, go cross-eyed trying to read such large numbers.
Why do you dislike the number 144?
Because it’s gross.
Why do you dislike the number 144 quadrillion?
Because it’s very gross!
Perhaps most interesting to me, though, was the percent of the cup contributed by the person currently holding the cup. A tabulation of the possibilities is shown below. This scenario assumes four gamblers with no one dropping out. The rows highlighted in yellow (rounds 4n – 3) indicate when the first gambler is holding the cup. Likewise, the second gambler’s turns occur in rows 4n – 2, the third gambler’s turns occur in rows 4n – 1, and the fourth gambler’s turns occur in rows 4n.
|Round||Contribution||Gambler Total||Cup Value||Percent|
Here’s how to read the table:
- The Contribution is the amount that a gambler adds to the cup in that round.
- The Gambler Total is the combined amount contributed by that gambler so far. For instance, the “Gambler Total” in Row 13 is $4,370, because the gambler has contributed 4,096 + 256 + 16 + 1 on his previous four turns, plus the $1 ante at the beginning of the game.
- The Cup Value is the amount in the cup, which includes the ante plus all previous contributions.
- The Percent then shows the percent of the money in the cup that was contributed by the gambler holding the cup.
In Round n, the Cup Value is given by the wonderfully simplistic formula
because the sum of the first n powers of 2 is 2n – 1, and the initial ante contributes $4 more.
More difficult is the formula for the combined contribution shown in the Gambler Total column. For Gambler 1, the formula is:
The Gambler Total formula for gamblers 2, 3, and 4 are similarly complex. (You can have fun figuring those out on your own.) But the purpose of determining those formulas was to investigate the percent of the Cup Value represented by the Gambler Total. And as you can see in the final column, the percent of the cup contributed by the gambler holding the cup tends toward 53.33%.
So here’s the way to think about this. If you pass the cup and the next gambler wins, 53.33% of the money in the cup is his; 26.66% of the money in the cup was yours; and, the remaining 20.00% came from the other two gamblers. Which is to say, you’ve contributed 26.66/46.66 = 57.14% of the winner’s profit.
Taking all this into account, and realizing that I could bankrupt my family if there were ever a streak of just 20 batters without a hit, some additional rules became necessary:
- A person can choose to leave the game at any time. Play continues with those remaining. Obviously, if only one gambler remains, he or she wins.
- Anyone can declare a “cap,” wherein the amount added to the cup continues at the current rate without increasing. For instance, if I added $32 to the cup on my turn and called a “cap,” then every person thereafter would simply need to add $32 on their turn, instead of doubling.
This latter rule seems like a good idea; it transfers the game from exponential growth to linear growth. Still, the pot grows quite rapidly, as shown below:
After 10 consecutive batters without a hit, the pot would still grow to $160, even if a “cap” had been implemented at the $32 mark.
We’ve also switched to the Fibonacci sequence, because that grows less quickly over time.
At a recent Nationals-Cubs game, four of us played this game with the amended rules. Everyone anted $1 to start, and then the amounts added to the cup were:
1, 2, 3, 5, 8, 13, 21 (cap), 21, 21, 21, 21
Dave was third, and the amounts he added to the cup are bold in the sequence above. Both Tanner Roark and Tsuyoshi Wada started strong, and the first 10 batters were retired without a hit or a walk. But the 11th batter of the game got a hit in the bottom of the second inning. Dave had contributed $46 of the $141 in the cup, so he won $95 on that beautiful swing by Wilson Ramos of the Nationals. (It wouldn’t have been “beautiful” if it had been made by a Cub or if it had cost me more than $27.)
The adjustment of using the Fibonacci sequence was a good one. The seventh donation to the cup was a reasonable $21, compared to a $64 contribution using the doubling scheme. In addition, instituting the “cap” permitted folks to continue playing long after they otherwise would have dropped out.
We continued playing through the end of the game. Which brings me to one final rule:
- At the end of the game, the gambler holding the cup does not win. Instead, the money in the cup goes to the next gambler.
This only makes sense. You wouldn’t want a gambler winning if he was holding the cup when an out was recorded.
Last Friday’s game ended with an astonishing 18 hits. There were no other streaks of 10+ batters without a hit, so none of the wins were as large as Dave’s first. On the other hand, I won more than I lost the rest of the game, and I was only down about $10 by game’s end.
Still, I’m concerned that I’ll go broke by the end of the season. One solution, of course, would be to stop playing, but that would require willpower and a higher intellect. Instead, I’m thinking that perhaps I should try to earn some extra money. If you’d like to contribute to this worthy cause, I’m available for tutoring, stand-up comedy, and blog post writing.
And if you have a need for analyzing the dumb games that boys play while watching a baseball game, well, there’s data to suggest that I’m pretty good at that, too.
I’d like to thank Marjan Hong for her help in analyzing this game. I’d also like to thank Dave Barnes for teaching me this game, for wasting countless hours discussing the rules and amendments, and for taking my money.
You have the right to your opinion. And I have the right to think you’re an idiot.
Too often we enjoy the comfort of opinion without the discomfort of thought. (John F. Kennedy)
Honestly, I don’t remember asking for your opinion, but since we’re sharing, then please go screw yourself.
Remember when I asked for your opinion? Neither do I.
It’s okay if we have different opinions. I can’t force you to be right.
Of all of your opinions, the one I value most is the one you keep to yourself.
Oh, I offended you with my opinion? I’m sorry, dear. You should hear the ones I keep to myself.
In order to be offended by your insult, I first have to respect your opinion. Nice try, though.
When I want your opinion, I’ll remove the duct tape.
Some doctors are saying which patients they like best. The first says, “I prefer librarians. Their organs are alphabetized.”
The second says, “I prefer mathematicians. Their organs are numbered.”
The third says, “I prefer lawyers. They are gutless, heartless, brainless, and spineless, and their heads and asses are interchangeable.”
And finally, a joke about opinions that’s math-related…
A professor asks a grad student, “What’s your opinion on the current state of mathematical research?”
“Absolute rubbish,” the grad student says.
“Well, probably,” says the professor, “but let’s hear it anyway.”
Allow me to alienate 99% of my readership by starting this post about strings with a computer science joke.
An int, a char, and a string walk into a bar and order some drinks. A short while later, the int and char start hitting on the bartendress, who gets very uncomfortable and walks away.
The string approaches the bartendress and says, “Sorry about my friends. Please forgive them. They’re primitive types.”
I thought it was cool that his last name was my first name. That may have even been the reason that he was my best friend. This caused me to create a mental game in which I’d string together a series of people where the first name of person n was the last name of person n – 1.
With our two names, I’d get the string Benjamin Patrick Vennebush. Sadly, there’s no one whose first name is Vennebush (at least, not according to a Google search).
How long is a string?
Seven characters. Eight, if you count the space.
I could add to the front of the string, though.
Arthur Benjamin is a mathemagician at Harvey Mudd College.
Beatrice Arthur starred in the TV shows Maude and The Golden Girls.
Those four names get us to the string…
Beatrice Arthur Benjamin Patrick Vennebush
Frank Beatrice is a realtor in Boston, an operations manager in Indianapolis, and a guitar shop owner in New York.
To that, we could add Anne Frank to get…
Anne Frank Beatrice Arthur Benjamin Patrick Vennebush
However, Beatrice Frank is a professor in Newfoundland, an HR Exec in Philadelphia, and a student in Australia — to be sure, this game was more fun and challenging before social media — and using her name with Frank Beatrice leads to…
Beatrice Frank Beatrice Frank Beatrice Frank Beatrice Frank Beatrice…
That’s a two-name infinite loop.
So, here’s your challenge:
- Without using search engines or social media, what’s the length of the longest string of names that you can create?
- Bonus points if you create a string where the first name of the first person is the last name of the last person, i.e., you create an infinite loop of names.
- Scoring: +1 for each name in your string; ×2 if you create an infinite loop.
- Use only names that other folks who read this blog would know. (Assume that some of them have actually been outside recently — which may or may not be a good assumption — and haven’t spent the last seven years in an attic trying to trisect an angle.)
Post your best effort in the comments.
There’s been a big deal made this week about the five people still alive who were born in the 1800’s, and rightfully so. As I wash down an A1 Peppercorn Burger from Red Robin and a bag of Cheetos with a Dr Pepper, I’m not even sure I’ll make it to 50, let alone 115.
I feel bad for these five women. The following internet math trick claims that it works “for everyone in the whole world,” but it doesn’t work for supercentenarians:
- Take the last two digits of the year in which you were born.
- Now add the age you will be this year.
- The result will be 115 for everyone in the whole world.
For instance, the oldest living person, Misao Okawa, was born on March 5, 1898. For her, this trick yields 98 + 117 = 215, not 115 as promised.
As it turns out, this trick doesn’t work for anyone born after 2000, either. For instance, my sons were born May 2, 2007, and for them, 07 + 8 = 15, not 115.
Now, I know what you’re thinking. Surely, something must be wrong. There’s not really an error floating around the internet, right? But it does appear to be the case.
Luckily, I have a solution for this problem. My modification of the trick is as follows, and then it really will work for everyone in the whole world:
- Take the year in which you were born.
- Now add the age you will be this year.
- The result will be 2015 for everyone in the whole world.
Unsatisfying, sure, but at least it’s correct.
There are lots of reasons to which the very old attribute their longevity. Chief among them is having never taken a statistics course at a community college. But not far behind are eating healthy, exercising regularly, remaining active, having friends, and staying happy. Some simply attribute it to “living right.”
A reporter asked a centenarian, “To what do you attribute your longevity?”
“Simple,” said the man. “I never argue.”
“Oh, surely there must be more to it than that,” said the reporter.
“Well,” said the elderly man. “I guess you’re right.”
It’s not uncommon for reporters to interview centenarians and ask them about their longevity.
A 100-year old man was asked, “To what do you attribute your long life?”
“I’m not quite sure yet,” he replied. “I’m still negotiating with two cereal companies.”
And finally, to celebrate her 100th birthday, Dorothy Carchman was invited on-stage with the cast of Old Jews Telling Jokes. She delivered the following punch line with aplomb:
Becky, who was 90 years old, and her best friend, Dorothy, are driving down the road. Becky said, “Dorothy, that’s the third car you almost hit in five minutes.”
And Dorothy replied, “Wait… I’m driving?”
I recently had a meeting at the National Basketball Association (NBA) offices in New York City. I had gotten very excited about this meeting, thinking maybe I’d bump into Lebron or Kobe or Shaq or Dr. J or Jerry West or David Stern. (It could happen, ya know. Not so long ago, I bumped into Brooke Shields while attending a meeting for MoMath. All things are possible in NYC.)
But irony of ironies… when I arrived, I met no one famous; rather, one of the NBA staffers wanted to meet me because Math Jokes 4 Mathy Folks is his mom’s coffee table book. She’s a retired chemical-cum-mechanical engineer, so geeky jokes are her ilk.
Three engineers are arguing about God’s profession.
The first says, “God has to be a mechanical engineer. Look at the design of the joints and muscles.”
“No, no,” said the second. “Look at the central nervous system. All that wiring? Surely, God is an electrical engineer.”
“I think you’re both wrong,” said the third. “He’s got to be a civil engineer. Who else would put a waste management facility in the middle of a recreation area?”
Now, I know that this story likely sounds like an elaborate set-up.
Yo momma is so dorky, she reads Math Jokes 4 Mathy Folks.
Well, it’s not. All of this is true.
The wonderful young man who wanted to meet me was Daniel Feinberg. I asked about his mother’s favorite joke from Math Jokes 4 Mathy Folks, and he told me it was this one (which is sometimes known as the Pizza Theorem):
Via email, Daniel told me:
It’s funny, because she [Daniel’s mom] hadn’t taken a look at the book in some time, and when I asked her for her favorite joke, she got sucked into reading the entire thing — again.
Now that’s a nice compliment.
Daniel isn’t an engineer or even a math guy. He loves golf, though, and his favorite joke from Math Jokes 4 Mathy Folks is:
A pastor, a doctor, and a mathematician were stuck behind a slow foursome while playing golf. The greenskeeper noticed their frustration and explained to them, “The slow group ahead of you is a bunch of blind firemen. They lost their sight saving our clubhouse from a fire last year, so we always let them play for free.”
The pastor responded, “That’s terrible! I’ll say a prayer for them.”
The doctor said, “I’ll contact my ophthalmologist friends and see if there isn’t something that can be done.”
And the mathematician asked, “Why can’t these guys play at night?”
I’d like to thank Daniel and his mom for their continued support. Hearing that MJ4MF made even one person smile is enough to think that it was worth writing.
Before you go, here are some basketball-related math jokes. Or maybe they’re math-related basketball jokes. Whatever. Enjoy.
What do basketball players call the last occurrence of the function that gives the greatest integer less than or equal to x?
The Final Floor.
What do athletes playing basketball and students taking a math test have in common?
They both dribble.
What’s the difference between the Knicks and a dollar bill?
You can get four quarters from a dollar bill.
Okay, maybe that last one isn’t very mathy, so here’s a mathy quote from basketball commentator and former coach Doug Collins:
Any time Detroit scores more than 100 points and holds the other team below 100 points, they almost always win.
I was reminded of my second-favorite joke, which is only mildly mathy, while watching the Cubs-Nationals game last night…
What do you do with an elephant who has three balls?
Walk him, and pitch to the rhino.
(If you’re wondering what my favorite joke is, read all about it in Make Your Own (Math) Joke.)
When it comes to pitching and hitting, Jon Lester is clearly better at one than the other. His ERA is an impressive 3.30, but his batting average is .000. That’s right, he’s never gotten a hit in 9 Major League seasons. With two more outs last night — the first, a deep fly ball that was caught by Denard Span, which you can watch on Yahoo sports; the latter, a strikeout — he “improved” to an incredible 0-for-59, a Major League record for futility with the longest hitless streak to start a career.
Lester’s hitless streak is the longest ever by a pitcher. But pitchers aren’t paid to hit. The dubious distinction of the longest hitless streak for a position (non-pitching) player in the Major Leagues is held by Eugenio Vélez, who didn’t get a hit in 46 consecutive at-bats during the 2010-2011 seasons.
A starting player averages 3.3 at‑bats per game, so Velez’s record is equivalent to 14 games without a hit. Assuming that a player is actually trying to hit the ball, a 14-game hitless streak is an impressive accomplishment; and probabilistically, it’s damn near impossible. Not withstanding the likelihood that very few sane general managers would let such a player continue to bat, it also defies the odds that the sun wouldn’t shine at least once on this slumping hitter’s behind.
A while back, I created an Excel file (XLS) to analyze hit streaks. But you could also use it to analyze hitless streaks by changing a couple formulas.
Using Eugenio Velez’s career batting average of .241 (which is deflated, because it includes his record-breaking streak), a hitless streak of 14 games didn’t occur even once in 500,000 games using the Excel sheet model. With 162 games per season, that’s more than 3,000 seasons. Only the very best pro baseball players have a career that spans 20 seasons; those players who hit only .241 have careers that are far shorter, so 46 consecutive at-bats without a hit is impressive, indeed.
Have fun playing with the spreadsheet. Now for a trivia question…
Who is the only Major League player to have 7 hits in one 9-inning game?
Rennie Stennett, Pittsburgh Pirates, September 16, 1975. The Pirates won the game 22‑0 against the Cubs. (Johnny Burnett had 9 hits in an 18-inning game in 1932; three other players have had 7 hits in a game, but all of them required extra innings.)
And a joke…
Why was the calculus teacher bad at baseball?
He was better at fitting curves than hitting them.
And a quote…
Slowest pitch in baseball to reach the catcher? 30 mph, thrown at a 45° angle. Any slower at any other angle hits ground.
— Neil deGrasse Tyson
Pencils are infintely useful yet ridiculously simple — just a cylindrical piece of graphite surrounded by a hexagonal wooden sheath.
Pencils come in all shapes and sizes, actually. They often have hexagonal cross sections, though some are octagonal, rectangular, circular, and oval.
Heck, there are even pentagonal pencils…
Which has to make you wonder, do we really need pencils in such a wide variety of shapes?
The answer may be no, but there is a practical reason for the multitude of cross sections. Can you think of any possible benefits that a rectangular pencil would have over a circular one, or vice versa?
The following problem about a pencil comes from Peter Winkler’s Mathematical Mind-Benders:
A pencil with pentagonal cross-section has a maker’s logo imprinted on one of its five faces. If the pencil is rolled on the table, what is the probability that it stops with the logo facing up?
And here’s a good Fermi question:
How many pencils are there in the world?
I have no idea what the answer is, but one respondent to this question on www.answers.com said, “42,462,013,000,000,000 pencils about.” The amazing part is that 17 people found this useful!
Slightly less ambiguous is this question:
How many pencils were used to make this sculpture by George Hart?
Or maybe you prefer selected-response items…
Which of the following is the best estimate for the length of a continuous line that could be drawn using a standard pencil?
- 0.35 mile
- 3.50 miles
- 35.0 miles
- 350 miles
Or maybe you’re tired of all these questions. You didn’t come here for a quiz. You came here for some jokes. Fine.
Did you hear about the constipated mathematician?
He worked it out with a pencil.
What kind of pencil?
A #2 pencil, of course!
What’s the largest pencil in the world?
If you’d like to learn more about pencils and their history — and, let’s be honest, who wouldn’t — you can download a free copy of Every Pencil is a Sandwich. In return, you’ll be asked to sign up for the pencils.com newsletter. If you love pencils and use them as much as I do, receiving the newsletter will be a treat, not a burden!