knitr::opts_chunk$set(echo = TRUE)

This work extends that of `curacao1962_threeplayers.R`

by including
a rest monster.

library("hyper2") a <- read.table("curacao1962_candidates.txt",header=FALSE) colnames(a) <- c("W", "B", "result", "round") head(a)

specify the players:

players <- c("Petrosian", "Keres", "Geller", "Fischer", "Korchnoi", "Benko", "Tal", "Filip") names(players) <- # accused of collusion or not c("coll", "coll", "coll", "USA", "USSR", "USA", "USSR", "TCH") collusive_players <- c("Petrosian", "Keres", "Geller") ``` ```r d <- as.matrix(cbind(as.character(a$V1),as.character(a$V2))) colnames(d) <- c("white","black") stopifnot(all(c(d) %in% players)) jj <- matrix(0,28,8) colnames(jj) <- players cumulative_games <- jj cumulative_collusive_games <- jj cumulative_noncollusive_games <- jj for(i in seq_len(28)){ # 'i' loops through rounds for(j in seq_along(players)){ previous_games <- subset(a,a$round < i) cg <- 0 # cumulative games cncg <- 0 # cumulative noncollusive games for(k in seq_len(nrow(previous_games))){ w <- previous_games$W[k] # white player b <- previous_games$B[k] # black player this_game <- c(w,b) if((players[j] %in% this_game)){ if(players[j] %in% collusive_players){ # this player is collusive if((w %in% collusive_players) & (b %in% collusive_players)){ # both players collusive cg <- cg+1 # increment cm == cumulative games } else { # non-collusive game cncg <- cncg+1 # increment ncm == cumulative noncollusive games } } else { # noncollusive player cncg <- cncg+1 # increment ncm == cumulative noncollusive games } } } # k loop closes cumulative_collusive_games[i,j] <- cg cumulative_noncollusive_games[i,j] <- cncg cumulative_games[i,j] <- cg + cncg } # j loop closes } # i loop closes

So we have three matrices `cumulative_games`

,
`cumulative_collusive_games`

and `cumulative_noncollusive_games`

:

cumulative_games cumulative_collusive_games cumulative_noncollusive_games

In the above three matrices, each row is a round, and the entries show
the number of games, collusive games, and noncollusive games played up
to and including that round for each of the 8 players. Each (named)
column corresponds to a player. Looking at the last row of
`cumulative_noncollusive_games`

we see that in round 28, players
Petrosian, Keres, and Geller had played a total of 18 noncollusive
games while the other players had played considerably more and would
be expected to be more fatigued at this point in the tournament. Note
that Tal retired after round 21 due to illness, which explains why he
had played fewer noncollusive games than Fischer, Korchnoi, Benko, or
Filip at this point.

## To justify the footnote "No game in the tournament is played ## between two players with cumulative game count (collusivitity ## ignored), differ by more than one" in jebo_chess_revision2.tex, ## replace `cumulative_noncollusive_games` with ## `cumulative_games` in this chunk. ## a <- cbind(a,cncmp_white=0,cncmp_black=0) for(i in seq_len(nrow(a))){ r <- a$round[i] jj_w <- which(colnames(cumulative_noncollusive_games)==a$W[i]) jj_b <- which(colnames(cumulative_noncollusive_games)==a$B[i]) ncmp_w <- cumulative_noncollusive_games[r, jj_w] ncmp_b <- cumulative_noncollusive_games[r, jj_b] a$cncmp_white[i] <- ncmp_w a$cncmp_black[i] <- ncmp_b } head(a) tail(a)

Thus the final match, between Petrosian and Filip was played in round 28, ended in a draw, and by that time Petrosian had played 18 noncollusive games and Filip had played 26.

We can see the differences between cumulative noncollusive games played between Black and White, summed over the whole tournament:

diff <- a$cncmp_white-a$cncmp_black # difference in each game table(diff) table(abs(diff)) cumsum(table(abs(diff)))

We can assess a null of no effect of fatigue:

table(a[,3],a[,5]-a[,6])

Then Fisher test:

b <- subset(a,a[,5] != a[,6]) b <- subset(b,abs(b[,5]-b[,6])>1) b <- subset(b,b[,3] != "1/2-1/2") b <- cbind(b,white_rested = b[,5] < b[,6]) b M <- table(b[,3],white_rested=b[,7]) M fisher.test(M,alternative="greater")

Highly signficant.

Now create a hyper2 object with appropriate reified monsters:

problem <- function(...){stop("must be a white win or a black win or a draw")} H <- hyper2(pnames=c(players,"white","draw","rest")) for(i in seq_len(nrow(a))){ white_player <- a[i,1] black_player <- a[i,2] collusive <- (white_player %in% collusive_players) & (black_player %in% collusive_players) if(collusive){ drawmonster <- "draw" } else { drawmonster <- "draw" } white_player_rested <- a[i,6] - a[i,5] > 1 black_player_rested <- a[i,5] - a[i,6] > 1 result <- a[i,3] if(white_player_rested){ if( result == "1-0"){ H[c(white_player, "white","rest" )] %<>% inc } else if(result == "0-1"){ H[c( black_player )] %<>% inc } else if(result == "1/2-1/2"){ H[c( drawmonster)] %<>% inc } else { problem() } H[c(white_player,black_player,"white","rest",drawmonster)] %<>% dec } else if(black_player_rested){ if( result == "1-0"){ H[c(white_player, "white" )] %<>% inc } else if(result == "0-1"){ H[c( black_player, "rest" )] %<>% inc } else if(result == "1/2-1/2"){ H[c( drawmonster)] %<>% inc } else { problem() } H[c(white_player,black_player,"white","rest",drawmonster)] %<>% dec } else { # neither player rested, rest monster inactive if( result == "1-0"){ H[c(white_player, "white" )] %<>% inc } else if(result == "0-1"){ H[c( black_player )] %<>% inc } else if(result == "1/2-1/2"){ H[c( drawmonster)] %<>% inc } else { problem() } H[c(white_player,black_player,"white", drawmonster)] %<>% dec } } H summary(H) mH <- maxp(H) mH pie(mH)

Now a hypothesis test

specificp.gt.test(H,"rest",0)

specificp.gt.test(H,"draw",0)

specificp.gt.test(H,"white",0)

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