# Alice And Bob Fall In Love

Welcome back to The Riddler — I hope you had a wonderful Thanksgiving. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-size and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,1 and you may get a shoutout in next week’s column. If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter.

## Riddler Express

From Graydon Snider, road race intimidation tactics:

Two runners, Alice and Bob, are participating in a footrace. The route is a straight line out some distance and the same straight line back — the starting point and the finish line are the same. As the starting gun is about to go off, Alice hatches a race plan: Her legs feel good and she wants to run fast enough compared to Bob that after the U-turn, they are staring face-to-face for as long as possible. How much faster than Bob should Alice run to spend the maximum amount of time facing Bob before they pass each other going in opposite directions? Assume that, on the advice of their coaches, they’ve each committed to running at a constant speed the whole time, and that the turn-around time at the halfway point is negligible.

## Riddler Classic

From Dan Johnston, in which Alice and Bob then fall in love:

After their Riddler Express footrace, Alice and Bob fell in love and got married. Now they want lots of kids. However, as you may know, having one child, let alone many, is a lot of work. But Alice and Bob realized children require less of their parents’ time as they grow older. Alice and Bob, romantics that they are, decided to calculate how this relationship worked. They figured out that the work involved in having a child equals one divided by the age of the child in years. (Yes, that means the work is infinite for a child right after they are born. That may be true.)

Anyhow, since having a new child is a lot of work, Alice and Bob don’t want to have another child until the total work required by all their other children is 1 or less. Suppose they have their first child at time T=0. When T=1, their only child is turns 1, so the work involved is 1, and so they have their second child. After roughly another 1.61 years, their children are roughly 1.61 and 2.61, the work required has dropped back down to 1, and so they have their third child. And so on.

(Feel free to ignore twins, deaths, the real-world inability to decide exactly when you have a child, and so on.)

Five questions: Does it make sense for Alice and Bob to have an infinite number of children? Does the time between kids increase as they have more and more kids? What can we say about when they have their Nth child — can we predict it with a formula? Does the size of their brood over time show asymptotic behavior? If so, what are its bounds?

## Solution to the previous Riddler Express

Congratulations to 👏 Chris Sears 👏 of Maysville, Kentucky, winner of the previous Riddler Express!

The World Chess Championship ended this week after 12 straight draws followed by a series of speedier tie-breaking games. That’s fitting, because two weeks ago we posed this question: What are the chances that the better player wins a 12-game match? Specifically, suppose one of the players is better than his opponent to the degree that he wins 20 percent of all games and loses 15 percent of games; the other 65 percent end in draws.2 What are the chances the better player wins a 12-game match? How many games would a match have to be in order to give the better player a 75 percent chance of winning the match outright? A 90 percent chance? A 99 percent chance?

That better player wins a 12-game match about 52 percent of the time. The number of games required for those larger thresholds are, in order, 82, 248 and 773. (Call me crazy, but I’m totally game for a two-year-long World Chess Championship.)

So how do we get there? Solver Dan Swenson suggested this tidy approach. Consider the following expression:

\begin{equation*}\left(0.2x + 0.65 + 0.15x^{-1}\right)^{12}\end{equation*}

The coefficients 0.2, 0.65 and 0.15 are the probabilities of the three outcomes of an individual chess game, and the whole thing is raised to the 12th power because of the 12 games of the match. Expand that expression, multiplying it all out and grouping its like terms. Then, the coefficient on $$x^r$$, where the exponent $$r$$ is some integer, is the probability that the better player wins the match by $$r$$ games. Finally, add the coefficients on all the positive powers of $$x$$, which gives the probability that the better player wins the match. The result is about 0.5198, or about 52 percent.

For the second part of the problem, we can use that same approach, and just change the “12” in the exponent of the expression, and then, the same as before, expand it and sum the coefficients on the positive powers of $$x$$. The smallest exponent that gives a 75 percent chance or better is 82, the smallest that gives a 90 percent chance or better is 248, and the smallest that gives a 99 percent chance or better is 773.

Solver Chris Sears illustrated how the probability that the better player wins the match increases as the number of games increases.

Somebody get FIDE on the phone!

## Solution to the previous Riddler Classic

Congratulations to 👏 Scott Wu 👏 of Baton Rouge, Louisiana, winner of the previous Riddler Classic!

Two weeks ago, we presented you with a sort of Riddlerified version of beer pong. You had an infinite supply of ping-pong balls, each labeled with some number 1 through N. There was also a group of N cups, labeled 1 through N, each of which could hold an unlimited number of ping-pong balls. The game was played in rounds that had two phases: throwing and pruning. During the throwing phase, you draw balls randomly, one at a time, from the supply and toss them at the cups. The phase ends when every cup contains at least one ball. Next comes the pruning phase, in which you go through all the cups and remove any ball whose number does not match the number on its cup. Every ball drawn had a uniformly random number, every ball landed in a uniformly random cup, and every throw landed in some cup. The game was over when, after a round was completed, there were no empty cups.

How many balls would you expect to need to draw and throw to finish this game? How many rounds would you expect to need before finishing this game?

The first question — how many throws would you expect to need — is like a “coupon collector’s problem,” and versions of it have appeared in this column before, for example in a problem about collecting Riddler League football cards. In this case, we’re filling cups instead of collecting coupons.The solution to this problem is well-known and stems from the fact that as we collect coupons — or fill cups — it becomes more and more difficult to collect or fill the ones that remain. The specific solution is quite mathy and involves something called the Euler-Mascheroni constant, but the main takeaway is that the more coupons or cups there are, the more and more time we can expect to spend collecting coupons or throwing balls.

Solver Laurent Lessard illustrated how the expected number of throws increases roughly quadratically as the number of cups (and numbers on the balls) increases:

The second question — how many rounds would you expect to play — turns out to be much trickier. Lessard also illustrated his mathematical approach when playing with three cups. The cups in his diagram are either empty (white), filled with a correct ball (green), or filled with an incorrect ball (red). The arrows and the numbers next to them represent transition probabilities — the chances a cup goes from empty to correctly filled, for example, are 1/N. Our goal, of course, appears in the bottom right of the diagram, where all three cups are correctly filled and the game is over.

From there, Laurent describes how to turn this diagrammatic approach into an answer. He uses a Markov chain, which describes probabilistic sequences of events that depend on the current state of events — such as the balls currently in our cups. And from there he invokes a holy Riddler trinity: absorbing states and limiting distributions and nilpotent matrices.

The result of all this is that while the number of throws required grows roughly quadratically, the number of rounds required grows roughly linearly.

Of course, this is also a problem that admits programmatic, simulation-based approaches. Solver Robin Chin shared Python code for a Monte Carlo simulation, and Michael Branicky shared his code as well. Finally, solver Tim Book shared the results of his computer simulations, which illustrate how the expected number of rounds increases as the number of cups (and the number of numbers on the balls) increases — roughly linearly:

Happy tossing!

## Want more riddles?

Well, aren’t you lucky? There’s a whole book full of the best puzzles from this column and some never-before-seen head-scratchers. It’s called “The Riddler,” and it’s in stores now! Consider your holiday shopping done.

## Want to submit a riddle?

Email me at [email protected]

# Mike Espy Needs An Unprecedented Swing To Win The Mississippi Runoff

We don’t often see a runoff in a general election, but if Sen. Cindy Hyde-Smith were to lose Mississippi’s Senate runoff on Tuesday, after the two Republican candidates combined to win a sizable majority of the initial vote, that would be even more unusual.

In the first round, Republicans Hyde-Smith and Chris McDaniel combined for a bit less than 58 percent of the vote, while Democrat Mike Espy and one other candidate from his party together won a little more than 42 percent. For Espy to win, the runoff vote has to swing more than 15 points more Democratic than the initial vote margin. But if we look at the five Senate elections since 1990 where an initial round of voting was held on the national Election Day and two candidates advanced to a runoff,1 no challenger has ever come close to outperforming the previous round of voting by the kind of margin Espy would need to win. What’s more, no runoff has ever shifted that much in either party’s direction.

##### Democrats need a record-setting swing to win Mississippi

Shifts in vote share margin between first election and runoff, in Senate races since 1990 where the first election took place on the national November Election Day in a midterm or presidential cycle

vote share margin
Year State First Election Runoff Swing
1992 GA D+1.6 R+1.3 R+2.9
2002 LA R+2.9 D+3.4 D+6.3
2008 GA R+2.9 R+14.9 R+12.0
2014 LA R+12.3 R+11.9 D+0.4
2016 LA R+25.4 R+21.3 D+4.1
2018 MS R+15.3

In cases where the first election included multiple candidates from the same party (all Louisiana and Mississippi races in the table), the margin is based on the difference in the total vote share between all Democratic and Republican candidates. In some cases, parties had unequal numbers of candidates running, which may have exaggerated the differences in vote share. Some data may not add up due to rounding.

Sources: ABC News, Georgia Secretary of State, Louisiana Secretary of State, UVA Center for Politics, Federal Election Commission

In fact, the biggest swing recorded — 12 points in the 2008 Georgia Senate runoff — favored the incumbent and not the challenger. Of the five previous Senate elections that went to a runoff, four featured incumbents, and in those contests, the swing in party vote share moved in the challenger’s favor only once. In Georgia’s 1992 Senate election, Democratic Sen. Wyche Fowler missed a majority by 1 percentage point in the general election, and in the runoff, challenger Republican Paul Coverdell squeaked out a narrow victory as the margin shifted 3 points in the GOP’s direction.

As for that big swing in Georgia’s 2008 Senate election, it came about in part because of the unprecedented circumstances surrounding the general election. The initial vote took place during Barack Obama’s first presidential bid, which saw African-American voters turn out at much higher rates than usual, both nationally and in Georgia. That turnout did not repeat itself in the runoff, however, and Republican Sen. Saxby Chambliss won re-election by 15 points.

The next-largest shift (and the largest shift in a midterm election) also benefited an incumbent, although it was much smaller. In 2002, four GOP candidates combined for a narrow edge over two Democratic candidates in the initial vote, but Democratic Sen. Mary Landrieu narrowly won the Louisiana Senate runoff by shifting the margin 6 points in a Democratic direction. So a Democrat has moved the needle enough to win a runoff in the Deep South in the recent past, although the politics of Louisiana (and the rest of the region) have shifted further toward the GOP since the early 2000s. Moreover, Landrieu didn’t need nearly as large a swing as Espy does in 2018.

From this admittedly small sample of Senate runoffs, an Espy win looks like a long shot: These races rarely swing by nearly as much as he needs to win, and when they swing at all, it’s more often toward the incumbent than the challenger. Furthermore, the Nov. 6 result in Mississippi looks similar to the 2014 and 2016 contests in Louisiana, which also bodes poorly for Espy. In those races, the GOP candidates combined for a double-digit margin in the first election, and in the runoff, the Democrat only gained a little ground. In that 2014 race, Landrieu was voted out of office after nearly 20 years in the Senate (no incumbent ran in 2016). As Nathaniel Rakich wrote in our preview of the Mississippi runoff, Espy needs today’s electorate to be substantially different from the voters who turned out earlier this month; Espy likely needs a strong turnout from black voters, who lean very Democratic, combined with some apathy among white voters, who are strongly Republican in Mississippi.

# Caruana ‘Suffers Successfully’ In Game 11 Of The World Chess Championship

With his last chance to command the white pieces in a regulation game in the World Chess Championship, defending champion Magnus Carlsen was unable to drum up any attacking chances. Game 11 — like the 10 that preceded it — ended in a draw. Carlsen’s challenger, Fabiano Caruana, defended admirably and the two are tied 5.5-5.5 with one regulation game to go.

Saturday’s game began with the Petroff Defense, Caruana’s favorite opening with the black pieces. Not surprisingly, this was familiar mental territory for the No. 1 and No. 2 players in the world. Within 90 seconds, they’d blitzed out their first 10 moves, arriving at the position below.

r1bq1rk1/pp2bppp/3p1n2/2p5/8/2PBBN2/PPPQ1PPP/2KR3R w – – 0 0
You must activate JavaScript to enhance chess diagram visualization.

This specific choice of opening was interesting for two reasons. One, Sergey Karjakin, the 2016 championship challenger, won a game with the white pieces from this exact position in 2016, against the elite Indian grandmaster Pentala Harikrishna. Two, the infamous deleted video that appeared to show secret aspects of Caruana’s pre-match preparation once again reared its head. That video showed a laptop screen with a variation of the Petroff that included the move “9…Nf6.” And indeed, on his ninth move, Caruana moved his knight to the f6 square.

But little else was interesting on Saturday. That “leaked” variation led to nothing sharp from either player and the secretive preparation unleashed no interesting secrets.

Karjakin happened to be in attendance at the venue in London on Saturday, and he provided some early commentary for the viewers that has also become the mantric chant of this match: “It looks very drawish,” he said. He was right. The queens came off the board by the 14th move. Only a pair of bishops and some pawns remained by the 26th. Thirty fruitless moves later, Carlsen and Caruana shook hands.

This is what an uneventful world championship draw looks like at high speeds. Come for the Petroff, stay for the bishop dance.

“Not much really happened today,” Caruana said after the game, to a bit of uncomfortable laughter from the crowd.

While Caruana may have very briefly felt some unpleasantness in the middlegame, “he may suffer successfully,” said Sam Shankland, the U.S. national champion, on a Chess.com broadcast. (To suffer successfully — what a lovely idea.) And indeed Caruana did. Indeed we all have over these past two weeks. Here’s exactly how, according to the computer’s unblinking eye:

“Chess in its present form will die the death of the draw,” wrote Emanuel Lasker, a former world champion, nearly 100 years ago. Yet here we are! Draws “are ingrained in the fabric of the game, a part of chess theory and culture,” another former national champ, Joel Benjamin, wrote in 2006. “Grandmasters play the opening better and make fewer mistakes. Willpower alone cannot ensure a decisive result.”

There is an austere beauty in the equilibrium of draws that this match has reached: Two goliaths, pushing each other with all their might, yet moving nowhere. At any moment, though, the ground can shift.

The mounting draws bring both good and bad news for the American challenger. On one hand, Caruana has proved beyond a doubt his ability to hang with and even outplay Carlsen, perhaps the best player of all time, in lengthy games under the sport’s brightest lights. On the other, should the match remain tied after the final game, the two will move on to speedier tie-breaking games. I wrote about what those look like in 2016. Carlsen is rated No. 1 in the world in both speedy chess formats that will be used, and he is almost universally thought to be a heavy favorite in the tiebreaker.

The match rests tomorrow. Game 12 — the final game of regulation and in which Caruana will have the white pieces — begins Monday at 10 a.m. Eastern. The tie-breaking games, if necessary, will happen on Tuesday. I’ll be covering it all here and on Twitter.

# Chase Home Value

Chase customers can take advantage of home value comps reports offered online but as accurate as one from your local relatorbecause they’re done by a local agent.  Chase offers a home estimator on its website but even they call it an estimator.  When you’re talking about a purchase thats usually six figures you need a more accurate assessment of a home’s value as 5 – 10% off could cost you tens of thousands over the duration of your mortgage.

Chase’s estimator notes this on the pageTHE ACCURACY OF THE VALUATIONS ARE ESTIMATED BASED ON AVAILABLE DATA AND DO NOT CONSTITUTE AN APPRAISAL OF THE SUBJECT PROPERTY AND SHOULD NOT BE RELIED UPONIN LIEU OF UNDERWRITING OR AN APPRAISAL.”  So they’re basically saying here is a guess but don’t put money on it being accurate.

## Guessing Value

Zillow, Trulia all offer estimates on a home’s value with little context about the neighborhood or the home.  They rely on reports from open records but those aren’t even available in about half the states they cover.

## Most Accurate Home Value

You can have the accuracy of an agent created report with the ease of an online site today.  RealEstateCompsToday.comcan usually provide you with the information that Chase Home Estimator doesn’t have access too in a couple days.

The ordering process is fast and accurate comps start at around $5. So before you chase home value get an agent report to know how much you’re chasing. # It Was Finally Fabiano Caruana’s Turn To Survive At The World Chess Championship Magnus Carlsen got a black eye before Game 9 of the World Chess Championship. But it didn’t hinder his vision of the board as Wednesday’s play began. For the first time in nearly two weeks of play, Carlsen, the defending champion, was able to successfully command the white pieces to an attacking advantage. Throughout much of Game 9, Carlsen outdueled his challenger, Fabiano Caruana. Caruana, the world No. 2, appeared to reel at points, and his allocated time melted off his clock as he pondered his defense. But Carlsen’s advantage melted, too. The game was drawn after 56 moves over 3.5 hours of play. It was the ninth consecutive draw and the best-of-12 match sits level at 4.5-4.5. Before the game Wednesday, the list of colorful stories orbiting the match ballooned to two. First came the infamous deleted YouTube video appearing to show elements of Caruana’s pre-match strategic preparation. Now we had the black eye. NRK, the Norwegian broadcaster, reported that Carlsen collided — excuse me, “kolliderte” — with one of its own journalists while playing soccer on Tuesday, a rest day from the chess. Questions were raised about Carlsen’s mental soundness — a grandmaster should do nothing but grandmastering, apparently. Per Google’s translation of NRK, he was reportedly “dumbfounded” after the crash. “If he has to use pain relief, there may be a potential problem,” NRK wrote. But those neurological questions seemed quickly answered at the board and Carlsen said he felt no pain while playing. The first eight moves on Wednesday exactly matched the first eight from Game 4 — their name sounds like something out of Tolkien, an English opening that became a Reverse Dragon. But the game took a radical and aggressive turn on move 9, when Carlsen scrambled his bishop to the g5 square, into enemy territory and with its mitre directly pointed at Caruana’s queen. r1bqr1k1/ppp2ppp/2n5/2bnp1B1/8/2NP1NP1/PP2PPBP/R2Q1RK1 b – – 0 0 You must activate JavaScript to enhance chess diagram visualization. This specific position has only ever materialized on a tournament chessboard once before, according to the ChessBase database, in an otherwise uncelebrated game in 2008 between two Croatian non-grandmasters. (Though black won that one.) The attack was on, and Caruana contributed with a misstep on his 17th move, capturing a knight in Carlsen’s territory that he oughtn’t have. That capture sparked a series of moves that eventually allowed Carlsen’s bishop to escape, flying across the board to capture the black pawn on b7. As deep into the game as the 18th move, Carlsen hadn’t spent more than a minute on any one move and quickly opened up a 40-minute advantage on the clock. One knock against the champ in this match has been his apparently lackadaisical preparation. But he was solidly prepared for his aggressive line on Wednesday, sailing through his moves. Caruana, meanwhile, took 9 minutes to make his 12th move, 21 minutes on his 13th, 8 on his 14th and 13 on his 17th. The fruits of the Norwegian’s preparation appeared to be a comfortable position: Either he would win or he would draw. Before Carlsen’s 24th move, the position looked like this. 3rr2k/pBp1q1pp/1b3p2/8/8/1Q2P1P1/P4P1P/3R1RK1 w – – 0 0 You must activate JavaScript to enhance chess diagram visualization. “I think there are some long-term dangers here for black,” said Hikaru Nakamura, a top American grandmaster commentating for Chess.com. Carlsen’s white bishop, for example, was far more active than Caruana’s. “If Caruana doesn’t find the right moves, he will lose.” It appeared to all the world that the Norwegian chess superstar would finally make real progress in the match, and indeed that a victory in the moves to come would effectively decide the match — and the world title — itself. “There are certain types of positions where Magnus is stronger than a computer,” said Anish Giri, the world No. 5, on a chess24 broadcast. It’s an evocative claim, but it was not true on Wednesday. Carlsen may have rushed his attack on move 25, shortly after the position above. He pushed his pawn up the flank on the edge of the board, to h4 and toward Caruana’s king. He then pushed it again, to h5. It may have been a square too far, or at least too soon. (The computer engine Stockfish preferred involving that active white bishop instead.) “He’s just not playing his best chess,” added Peter Svidler, the world No. 19, on that very same broadcast. The position simplified dramatically and the two shook hands — which they must be getting very good at — after 56 moves. Ah, chess is cruel. Here’s a chart to quantify that cruelty — and we’ll keep it updated throughout the rest of the match. There are three regular games left, and speedier tiebreaker games will follow on Nov. 27, if necessary. This match has been different for Carlsen than his 2016 World Chess Championship encounter against Russian challenger Sergey Karjakin, which began with seven consecutive draws. Many of those found Karjakin on the backfoot, escaping like Houdini from the shackles of the world champion. Caruana, however, has rarely been in real trouble until Wednesday, and this year Carlsen has been forced to play the part of escape artist. Carlsen would, however, be an enormous favorite should the tiebreakers become necessary. “I’m really not thinking about the tiebreak now,” Caruana said after the game. “I really don’t agree with most people about my chances in the tiebreak.” Game 10 begins Thursday at 3 p.m. Greenwich Mean Time — that’s 10 a.m. Eastern. But that’s also Thanksgiving. As a result, our next dispatch will come on Friday. Chess waits for no turkey, but FiveThirtyEight does. I’ll be covering the rest of the match here and on Twitter. # Politics Podcast: Will Pelosi Be Replaced? The FiveThirtyEight Politics podcast crew discusses whether Rep. Nancy Pelosi will be re-elected as Speaker of the House, now that Democrats have won back the majority, and what the opposition to her says about the party. They also look at new election results out of Florida, Georgia and Arizona and reflect on the significance of the “year of the woman.” You can listen to the episode by clicking the “play” button in the audio player above or by downloading it in iTunes, the ESPN App or your favorite podcast platform. If you are new to podcasts, learn how to listen. The FiveThirtyEight Politics podcast publishes Monday evenings, with occasional special episodes throughout the week. Help new listeners discover the show by leaving us a rating and review on iTunes. Have a comment, question or suggestion for “good polling vs. bad polling”? Get in touch by email, on Twitter or in the comments. # Why is AWS beating Google, Microsoft, Oracle and IBM? I believe Google Cloud was launched after AWS so a head start helps for one. AWS also has a free tier, it’s like giving the first hit of ecstasy to someone free. Why not use this free server. Then that server needs to expand and you make plans and youre hooked and know the AWS cloud better than Google. Google Cloud offers a credit of$300 right now to try and get you involved but its not the same as a free tier of service. Once the \$300 is gone its always going to cost you whereas you can downgrade a server back to the free tier if ya decide to do that.

There are also some wonky decisions that Google made that leave me annoyed almost daily. The fact you cant utilize smtp ports of the servers leaves me having to go all around to get a WordPress site to send emails…or the inability to easily transfer a project between accounts. I’ve landed myself in a situation where I transferred ownership but I didn’t remember to transfer billing but was no longer a project owner so I couldnt transfer billing anymore, customer service just acted like it made sense that I couldn’t use or config the resource but that my credit card was still going to be used.

SSH and SFTP into AWS fairly standardized and it is relatively seamless. Google makes these difficult.

The way they only give out one static ip address per zone. They have a BETA project and decide if its to allow multiple IPs but…what took so long?  IP Aliases or multiple network ip addresses … on AWS I just added the IP addresses, why do I need more than one?  Because my name servers need to have different IP address, but again I cant do it right now.

So with all these limits here and there I personally pay for my servers with AWS (its just easier to use) but I use Google Cloud for short experiments where I may need more than 1 IP, and a site that doesn’t ever send an email. Configuring Alias IP Ranges is new and overdue.

Why is AWS beating Google, Microsoft, Oracle and IBM?

# Chess World Rattled As Someone Nearly Wins Game

Magnus Carlsen of Norway, the world’s No. 1 chess player, fended off a vicious siege at the hands of U.S. grandmaster Fabiano Caruana, the world No. 2, in London Friday. It was the sixth frame of the World Chess Championship, and one that for hours appeared likely to give the American a critical lead. But Carlsen escaped, and the match remains level, 3-3. Each of the six games so far have been a draw.

“It’s a miracle save,” said Robert Hess, an American grandmaster commentating on the match for Chess.com.

To catch you up: Carlsen is seeking his fourth world title while his challenger Caruana is trying for the first American world championship since Bobby Fischer in 1972. Their horns are locked in the middle of a best-of-12-game match for the game’s most important title.

The two began Friday’s Game 6 in one of Caruana’s favorite openings: the Petroff. (Specific lines of this opening were featured in the deleted video that scandalized the match days ago.) Game 6’s first three moves appear in 12,289 other games in the ChessBase database. In 11,802 — or 96 percent — of those, white moves its knight to f3 on its fourth move. In 17 of those — or 0.1 percent — white moves its knight to d3.

Carlsen moved his knight to d3.

rnbqkb1r/ppp2ppp/3p1n2/8/4P3/3N4/PPPP1PPP/RNBQKB1R w KQkq – 0 1
You must activate JavaScript to enhance chess diagram visualization.

Chess players are second only to maybe biological taxonomists in their proclivity to elaborately name things, and sure enough even this rare position has its own proper name: the Karklins-Martinovsky Variation. But neither player was troubled by Karklins-Martinovsky, they said after the game. Its theory is well known to these elite players.

And so they played on. The powerful queens came off the board by move 8, but this loss took no edge off the fight. For a while, the game looked less like a battle and more like a dressage competition, as 66 percent or more of each player’s first 12 moves were knight moves.

Many moves later, as the game cantered through its middlegame, winning chances emerged and swelled for Caruana’s black pieces, according to both the computer engine and human grandmaster commentators. (Surprisingly, black, which is usually at a disadvantage, has often had an advantage over white in this match.) While there was no single blunder for Carlsen, there was an accumulation of … what to call them? “Mistakes” seems too serious. “Slip-ups” make them sound like pratfalls. Let’s go with “inaccuracies.” Carlen admitted after the game that he’d made a number of imperfect moves. By move 34, knights and bishops were the only firepower left on the board, and they threatened salvo after salvo in a crucial struggle over the pawns.

By the 47th move, Carlsen was down a knight but up three pawns, which gave him a few slim hopes. Two had open routes to the end of the board, where they could become queens. Much delicate, asymmetrical and impossibly complex maneuvering commenced, as Caruana tried to prevent the pawns’ promotion.

6k1/5pp1/B2b4/5P2/7P/1P4P1/P2n2K1/8 b – – 0 0
You must activate JavaScript to enhance chess diagram visualization.

A dozen moves later, Caruana had captured three of Carlsen’s pawns, including those aspiring to become queens, and still had one of his own. That left him in a victorious position — if only he could see it. On the 68th move, a supercomputer analyzing the game found a guaranteed checkmate a distant 30 moves down the road — down a lengthy bridle path, say.

5k2/8/5pK1/3B1PbP/3n4/8/8/8 w – – 0 0
You must activate JavaScript to enhance chess diagram visualization.

Caruana is an unbelievably strong player — though not that strong. As play continued, the silicon’s guarantee quickly went away. If only Carlsen could eliminate the pawns, he’d survive: a bishop and a knight versus a bishop is a theoretically guaranteed draw.

Finally, through many feats, Carlsen was able to spirit away his king to a fortress on black’s side of the board.

5k2/8/5pKn/5PbP/2B5/8/8/8 b – – 0 0
You must activate JavaScript to enhance chess diagram visualization.

Despite black’s apparent material advantage, there was no progress to be made. The players agreed to a draw on the 80th move.

Carlsen had walked a slippery bridge and survived. His escape act drew attention. As the tension built toward the end of the game, the match became the most-viewed stream on the popular game-streaming site Twitch. Books could be written about this endgame. (Though not by me.)

So, another draw, huh? Yawn, am I right? Not so fast. Today’s Game 6 was an instant classic. Journalist David Hill, who’s been in London reporting on the match, tweeted that there can be beauty in draws. Not all of them are created equal.

And while the six consecutive draws we’ve seen thus far is a lot, it’s certainly not a record. Carlsen and Sergey Karjakin began their 2016 world championship match with seven draws. Garry Kasparov and Viswanathan Anand fought to eight in a row to open their 1995 match. And at one point in Kasparov’s 1984 championship match against Anatoly Karpov, there were 17 straight draws. “There was a 20-second burst of applause” after a decisive game broke the grueling streak, the New York Times reported. That match, which began in September, was finally halted in February of the following year — 40 of its 48 games were draws.

The data scientist Randal Olson analyzed hundreds of thousands of chess games in an article a few years ago. The closer players are in rating, he found, the longer games tend to go. And as the players get better, draws become far more common. Carlsen and Caruana are as good — and about as close in rating — as you can get. Indeed, they are even beyond the scope of Olson’s chart below, with Elo ratings (which measure the strength of players given the opponents they’ve played) north of 2800.

We’ll keep the draw-filled chart below updated throughout the match. And perhaps we’ll be able to add a decisive result to it at some point. Or perhaps not. And that could be exciting, too.1

The match rests tomorrow. Game 7 — in which Caruana will once again have the black pieces — begins Sunday at 3 p.m. Greenwich Mean Time. That’s 10 a.m. Eastern. I’ll be covering it here and on Twitter.

# Global Point – IT Managed Services

## IT Managed Services

Happy to work with a business to business organization in Chicago Global Point LLC.  They currently offer IT Managed Services, AWS Cloud Computing, Disaster Recovery and more.

From their website, Global Point was launched by corporate IT consultants who wanted to bring their skills and experience to companies that need them, helping businesses grow and avoid growing IT headaches. They bring a comprehensive understanding of technology, from small offices up to multinational corporate infrastructure. We emphasize working with customers to identify their immediate needs, as well as to anticipate growth. As a business ourselves, we understand how critical it is to dependably meet the needs of your growing businesses we support. Global Point Works with you and for you as a business partner.

If you’re looking for a help desk, cloud computing, disaster recovery IT services company I encourage you to consider them.

## Help Desk Support

Global Point lists the benefits of their business to business Help Desk Support and they include:

With our engineers holding years of experience in their respective fields, our clients are given access to exceptionally high level engineers with qualifications in migrations, integration, support engineering, and much more. All our technicians take the time to understand your environment. This is solely for the reason of enhancing efficiency of the resolution of all your issues.

Fixed monthly rate
Our fixed monthly rates ensure that you are not incurring any unexpected costs along the way. That way we can provide your business with updates of when you are nearing your limit or if the support is unlimited and we have a contract that doesn’t require so much work, we will advise you on the better options.

Have agreements built on your terms
We know how important it is to transparently communicate expectations. After understanding your business needs, we’ll suggest best practice ideas for responding to issues. However, all our clients are given the autonomy to dictate exactly what they expect from their computer systems. The SLAs simply enforce them!

Reduced financial risk
When you upgrade your support from casual support to a fixed monthly rate, it becomes an operational expense. This allows for more cash flow to occur without the massive bumps in the budget. This also allows us to understand your environments better than providing your business with ad-hoc support.

All-year round support of your IT
We know the importance of having a range of support options. But what about ensuring consistency? Throughout the year; we make sure that your team is supported and your systems are managed accordingly.

Highly responsive turn-around time
We often have new clients approach us because they are frustrated with their current IT. Our personal aim is make sure that your business receives the highest level of service, especially during the critical time-periods.

Global Point – IT Managed Services

# Villanova Won A Title. Now It Must Start Over From Scratch.

The Villanova Wildcats produced one of the most dominant seasons in NCAA history last year, going 36-4, including a complete dissection of a strong Michigan team to win the championship game. The Wildcats scorched teams on offense, ranking No. 1 in the country in offensive efficiency and effective field goal percentage, according to college basketball stats guru Ken Pomeroy. This helped them beat the Wolverines by 17 points.

But the team that is defending that title — currently ranked eighth heading into Wednesday’s rematch with Michigan — is hardly recognizable eight months later, as four of coach Jay Wright’s stalwarts from a season ago are now in the NBA.

The departure of Jalen Brunson and Mikal Bridges — a pair of juniors left over from the 2015-16 national title-winning team — has left a crater in Wright’s lineup. Along with the exits of Donte DiVincenzo and Omari Spellman, the outgoing quartet combined for a whopping 26.1 win shares last season1.

It’s typical for reigning national champions to lose a large chunk of their talent the following season, especially in the one-and-done era. And while the Wildcats may not have lost the most win shares of past champions, the immediate exodus of talent will have huge consequences for their prospects to repeat as champions this season. This is perhaps a long way of saying winning back-to-back titles, or even coming close, has become very difficult in college basketball — and for good reason.

##### Villanova’s departures have left a sizable hole

Total win share of players who left NCAA championship teams the season after their championship, since the beginning of college basketball’s one-and-done era

Departing players
Season Champion Number Win Share
2017-18 Villanova 7 26.1
2016-17 North Carolina 7 21.8
2015-16 Villanova 5 11.4
2014-15 Duke 4 25.5
2013-14 Connecticut 7 19.8
2012-13 Louisville 4 12.3
2011-12 Kentucky 7 36.3
2010-11 Connecticut 5 13.4
2009-10 Duke 6 20.7
2008-09 North Carolina 9 26.6
2007-08 Kansas 9 35.3
2006-07 Florida 10 33.7
2005-06 Florida 2 1.5

Source: Sports-reference.com

The Florida Gators, in 2006 and 2007, and the Duke Blue Devils, in 1991 and 1992, are the only programs in the past 45 years to repeat as NCAA men’s basketball champions, after John Wooden’s UCLA Bruins capped off seven consecutive titles. Back then, Wooden had the luxury of coaching future NBA Hall of Famers Kareem Abdul-Jabbar2 and Bill Walton for three seasons, something that is largely unheard of in today’s game.3 Likewise, Mike Krzyzewski was able to develop chemistry with college stars like Christian Laettner, Grant Hill, and Bobby Hurley — all of whom stayed a full four years.

And when it comes to the one-and-done era, the Gators are an anomaly themselves, as Donovan managed to persuade the likes of Joakim Noah, Al Horford and Corey Brewer to remain in Gainesville for their junior years before winning another title and then moving to lengthy careers in the NBA.

For most champions, winning a national title usually means saying goodbye to their best talent — the nation’s top freshman are forced to use college as a stopgap for a year before jumping to the NBA, and upperclassmen often ride their team’s success to test the NBA’s waters. For his part, Wright did well to keep Brunson and Bridges in Philadelphia for another two years after winning their first title, which built a bridge to that second championship.

But the team that cut down the nets last year has been gutted, particularly on the offensive side. Among the top four players of each champion since 2006, when the one-and-done began, Villanova’s departed quartet leave the greatest offensive hole for a reigning champion, a hole that might be too great to overcome.

Villanova fans might choose to view things in a more optimistic way, instead thinking themselves as fortunate that they only lost four players, especially seeing the Wildcats of Kentucky lose an unimaginable six players after their championship in 2012 and then stumbling into the NIT a year later. Nova’s relatively tiny rotation last year — Villanova ranked 302nd in total bench usage, according to KenPom — could be a blessing in disguise as the likes of Eric Paschall and Phil Booth are still available to make the leap to the top of the college ranks and potentially beyond.

Still, Villanova fans thinking of a repeat might want to curb the enthusiasm.

Any team not named Duke, Kentucky or Kansas — whose recruiting prowess means a revolving door of NBA-bound super freshmen — has struggled to be relevant again immediately. If you look past these three blue bloods, Louisville is the only reigning champion to reach the Sweet 16 the year following championship in the last dozen years. It’s why the 2010 North Carolina Tar Heels couldn’t even make the NCAA Tournament after winning the whole thing a year earlier. It’s why last year’s Tar Heels were swept aside in the second round of the tournament by Texas A&M.

##### Back-to-back has become a pipe dream

How men’s NCAA champions have fared the following season in college basketball’s one-and-done era

Season after championship …
Season Champion Wins Losses Postseason
2017-18 Villanova 2 0 ?
2016-17 North Carolina 26 11 2nd Round
2015-16 Villanova 32 4 2nd Round
2014-15 Duke 25 11 Sweet 16
2013-14 Connecticut 20 15 NIT
2012-13 Louisville 31 6 Sweet 16
2011-12 Kentucky 21 12 NIT
2010-11 Connecticut 20 14 2nd Round
2009-10 Duke 32 5 Sweet 16
2008-09 North Carolina 20 17 NIT
2007-08 Kansas 27 8 Sweet 16
2006-07 Florida 24 12 NIT
2005-06 Florida 35 5 Champion

The NCAA Tournament’s First Four was known as the First Round until the 2015 tournament.

Source: Sports-Reference.com

Joining senior Paschall, who’s being touted as a first-round pick in the 2019 NBA Draft, and redshirt senior Booth, who netted 23 in his season debut last week, is the 12th best recruiting class, according to ESPN. Five-star recruit Jahvon Quinerly is considered one of the best freshman point guards in the nation, and four-star forwards Cole Swider and Brendan Slater both also have a place on the ESPN 100. Whenever this is enough for Wright’s team to make waves again in March is a question for the season ahead. However, with currently the fifth-best ranked recruiting class for next year, Wildcats fans may have another title-winning team in the not-too-distant future, maybe just not in the immediate one.

CORRECTION (Nov. 14, 2018, 3:30 p.m.): An earlier version of this article incorrectly said the Florida Gators were the only team in 45 years to repeat as national champions in men’s college basketball. Duke also did, winning back-to-back titles in 1991 and 1992.