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#### The Republican Party Has Changed Dramatically Since George H.W. Bush Ran It

George H.W. Bush, whose death at 94 was announced on Friday by his family, was a hugely influential figure in the Republican Party: chairman of the Republican National Committee, vice president, president and father of another GOP president. But the GOP has changed dramatically since it nominated Bush for the presidency in 1988 — a fact reflected in the ex-president’s strained relationship with the GOP’s new standard-bearer, President Trump.

So, I think Bush’s death is another moment to highlight what my colleague Clare Malone described in the summer of 2016 as “The End Of A Republican Party.” Let’s run through some of the big shifts that have occurred within the GOP:

## The GOP was once a more moderate party

Ideology is complicated to measure. By some standards, the Republican Party has moved to the left. In a poll conducted last year, 42 percent of Republicans backed same-sex unions; it’s safe to assume that number was far lower during George H.W. Bush’s presidency. In 1992, one of South Carolina’s senators was Republican Strom Thurmond, who ran a 1948 presidential campaign featuring his opposition to civil rights for blacks. Today, one of South Carolina’s senators is Republican Tim Scott, who is African-American.

But by most other measures, the GOP is far more conservative than it used to be. The General Social Survey, for example, shows self-identified Republicans moving far more toward the “extremely conservative” end of its scale (as opposed to “extremely liberal”) over the past several decades.1

Political scientists, using DW-Nominate scores,2 have concluded that the Republicans now in Congress are much further to the right of congressional Republicans in the 1970s and 1980s. And even anecdotally, figures like former House Speaker John Boehner, Ohio Gov. John Kasich and the late Arizona Sen. John McCain — considered solid conservatives in the George H.W. Bush era — found themselves cast as insufficiently right-wing by the party’s base in recent years.

In Bush’s era, Fox News did not exist. Deeply conservative billionaires Charles and David Koch and their allies had not created a huge network of right-wing groups that constitute basically an alternative political party. There was no tea party or House Freedom Caucus. Trump may be personally more conservative than Bush, but even if he weren’t, the forces that push a Republican president to the ideological right are stronger now than they were in the 1980s.

Bush himself famously signed a tax increase to help reduce the federal budget deficit, a move that angered the party’s conservative base. His two GOP successors (George W. Bush and Trump) never even really considered tax hikes, aware of the power of the party’s conservative coalition.

## The GOP used to be more in line with the nation demographically

Trump’s rallies include lots of older white people, as the stereotype goes. But that is the Republican Party of today. The country has become older, more diverse and more educated. The GOP, meanwhile, has grown even more disproportionately old. And while its voters grew more diverse along with the country through the 1980s (though at a bit of a lag), that shift stalled in the party in the 1990s. Same with education: The share of non-Hispanic white voters without a college degree fell throughout the 1950s, ’60s, ’70s and ’80s — in the electorate overall and the GOP. But beginning in the 1990s, it stopped falling among Republicans.

In 1992, according to the Pew Research Center, about 38 percent of registered voters who identified as Republicans were 50 years or older. By 2016, that number had grown to 58 percent. In 1992, 61 percent of Republicans were under 50, compared with 41 percent today.3

## Republicans were once competitive on the coasts but weak in the South

The ideological and demographic shifts described above have corresponded with big changes in the GOP’s geographic coalition. In 1988, Bush won California — the sixth straight election in which the Republican presidential candidate carried the Golden State. Bush also won Connecticut, Delaware, Illinois, New Jersey and Vermont. The Republican caucus in the U.S. Senate from that era included two members from New Hampshire, two from Oregon and one from both Delaware and New York. There were zero Senate Republicans from Alabama, Arkansas, Georgia, Louisiana and Tennessee.

All but one of the 16 Senate seats I just described are now held by the opposite party that controlled them in 1992, as the GOP gained ground in the South but lost power on the coasts. Trump, reflecting the growing weakness of Republicans in California, lost there in 2016 by 30 percentage points. Bush lost West Virginia in 1988 by 5 percentage points. Trump’s 42-point win in West Virginia in 2016 was his second-biggest margin in any state.4

In short, today’s Republican Party is centered in the South and almost completely out of power on the West Coast.

Let me not overstate the changes in the Grand Old Party. It still loves to cut taxes, like it did in the George H.W. Bush era. It’s still overwhelmingly white. The majority of its voters are still whites without college degrees. White evangelical Protestants are still about a third of the party. It still deploys negative racial stereotypes about non-white Americans to appeal to white voters. (Remember the Willie Horton ad of the 1988 Bush campaign?)

But the changes highlighted here have dramatically altered the power dynamics in Washington. Presidents Nixon, Reagan and George H.W. Bush always had to share power with Democrats, who controlled the House from 1949 to 1994.5 But since the GOP won the House in 1994, the party has held the chamber for all but four years.6 (They won’t be in control in 2019, of course.)

When George H.W. Bush won 53 percent of the national popular vote in 1988, it was not that remarkable. Richard Nixon had won more than 60 percent in 1972, and Ronald Reagan breached 50 percent in both 1980 and 1984. But 1988 was a watershed moment for the Republican Party — it was about to start a measurable decline in terms of its national standing. In the seven presidential elections since then (including Bush’s 1992 defeat), Republicans have won more votes nationally than Democrats just once (2004).

The tensions between Trump and the Bush family, and between Trump and McCain, speak to this broader narrative. Trump is a different kind of Republican — and he is changing the party in his image in ways they don’t like. But he is also the product of a different Republican Party than the one that the Bushes and McCain ascended in. Trump got the GOP nomination in some ways by embracing what the Republican Party had become, not what the Bushes wished it were.

CORRECTION (Dec. 1, 2018, 1:30 p.m.): An earlier version of this article said President Trump’s largest margin of victory in any state in the 2016 election was in West Virginia. It was in Wyoming.

#### 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.

#### 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.