Chess collusion with hyper3 objects: work in progress

To cite the hyper2 package in publications, please use Hankin (2017). Here I analyse results from Curacao 1962 using hyper3 formalism using the weighted Draw monster approach outlined in kka.Rmd:

\[ \left(\frac{\lambda p_1, D(p_1+p_2),p_2}{\lambda p_1+D(p_1+p_2)+p_2}\right)^{(a,b,c)} \left(\frac{p_1, D(p_1+p_2),\lambda p_2}{p_1+D(p_1+p_2)+\lambda p_2}\right)^{(d,e,f)} \]

Above, \(p_1\) plays \(p_2\) a total of \(a+b+c+d+e+f\) times; we have \(a+b+c\) matches with \(p_1\) playing white and \(p_2\) black, with \(a\) wins, \(b\) draws and \(c\) losses [write \(\mathord{+}a\,\mathord{=}b\,\mathord{-}c\)], and \(d+e+f\) matches with \(p_1\) playing black and \(p_2\) playing white with \(\mathord{+}d\,\mathord{=}e\,\mathord{-}f\).

1 Short story

With this model [discussed in a broader context at kka.Rmd], whatever the value of \(D\) and \(\lambda\), there is a pathology which BT cannot deal with. Still not quite 100% sure but it seems that the maximum likelihood estimate of the players’ strengths is zero except for Fisher and Petrosian; and indeed we see Fisher at 57% and Petrosian at 42% [with \(\lambda = 1.1, D=1.888\)]. This on the grounds that these players never lost playing black (there are some \(2\times 3\) tables at the end). This might be considered a defect of the probability model.

2 Longer story

cur_matches <- read.table("stockholm1962_matches.txt", header=FALSE)
colnames(cur_matches) <- c("white", "black", "result")
head(cur_matches)

##       white    black  result
## 1     Aaron   Barcza     0-1
## 2     Benko Bisguier     1-0
## 3    Bertok Gligoric 1/2-1/2
## 4 Bolbochan Schweber 1/2-1/2
## 5     Filip Yanofsky     1-0
## 6    Geller  Cuellar     0-1

nrow(cur_matches)

## [1] 256

Above, we see on the first line that Aaron (white) lost to Barcza (black). We will set up hyper2 and hyper3 objects corresponding to likelihood functions for these observations.

jj <- read.table("stockholm1962.txt",header=FALSE)[,1:2]
(players <- jj$V1)

##  [1] "Fischer"   "Geller"    "Petrosian" "Korchnoi"  "Filip"     "Gligoric" 
##  [7] "Benko"     "Stein"     "Uhlmann"   "Portisch"  "Pomar"     "Olafsson" 
## [13] "Bolbochan" "Barcza"    "Bilek"     "Bisguier"  "Yanofsky"  "Bertok"   
## [19] "German"    "Schweber"  "Teschner"  "Cuellar"   "Aaron"

(nationalities <- jj$V2)

##  [1] "USA"  "USSR" "USSR" "USSR" "TCH"  "YUG"  "USA"  "USSR" "GDR"  "HUN" 
## [11] "ESP"  "ISL"  "ARG"  "HUN"  "HUN"  "USA"  "CAN"  "YUG"  "BRA"  "ARG" 
## [21] "FRG"  "COL"  "IND"

f <- function(lambda,D){
  H3 <- hyper3()
  for(i in seq_len(nrow(cur_matches))){
    white_player <- cur_matches[i,1]
    black_player <- cur_matches[i,2]
    result <- cur_matches[i,3]
    if(result == "1-0"){ # white player wins
       num <- lambda 
       names(num) <- white_player
    } else if(result == "0-1"){  # black player wins
       num <- 1
       names(num) <- black_player
    } else if (result == "1/2-1/2"){ # draw, duh
      num <- c(D,D)
      names(num) <- c(white_player,black_player)
    } else {
      stop("this cannot happen")
    }

    H3[num] %<>% inc()       
    den <- c(lambda+D,1+D)
    names(den) <- c(white_player,black_player)
    H3[den] %<>% dec()
  }
  return(H3)
}

Now use it

H3 <- f(1.1, 1.888)

H3

## log( (Aaron=1)^1 * (Aaron=1.1)^1 * (Aaron=1.888, Bertok=1.888)^1 *
## (Aaron=1.888, Cuellar=1.888)^1 * (Aaron=1.888, Schweber=1.888)^1 *
## (Aaron=1.888, Yanofsky=1.888)^1 * (Aaron=2.888, Benko=2.988)^-1 *
## (Aaron=2.888, Bilek=2.988)^-1 * (Aaron=2.888, Bisguier=2.988)^-1 *
## (Aaron=2.888, Bolbochan=2.988)^-1 * (Aaron=2.888, German=2.988)^-1 *
## (Aaron=2.888, Korchnoi=2.988)^-1 * (Aaron=2.888, Olafsson=2.988)^-1 *
## (Aaron=2.888, Petrosian=2.988)^-1 * (Aaron=2.888, Pomar=2.988)^-1 *
## (Aaron=2.888, Schweber=2.988)^-1 * (Aaron=2.888, Uhlmann=2.988)^-1 *
## (Aaron=2.988, Barcza=2.888)^-1 * (Aaron=2.988, Bertok=2.888)^-1 *
## (Aaron=2.988, Cuellar=2.888)^-1 * (Aaron=2.988, Filip=2.888)^-1 *
## (Aaron=2.988, Fischer=2.888)^-1 * (Aaron=2.988, Geller=2.888)^-1 *
## (Aaron=2.988, Gligoric=2.888)^-1 * (Aaron=2.988, Portisch=2.888)^-1 *
## (Aaron=2.988, Stein=2.888)^-1 * (Aaron=2.988, Teschner=2.888)^-1 *
## (Aaron=2.988, Yanofsky=2.888)^-1 * (Barcza=1)^2 * (Barcza=1.1)^3 *
## (Barcza=1.888, Benko=1.888)^1 * (Barcza=1.888, Bertok=1.888)^1 *
## (Barcza=1.888, Bilek=1.888)^1 * (Barcza=1.888, Bisguier=1.888)^1 *
## (Barcza=1.888, Bolbochan=1.888)^1 * (Barcza=1.888, Geller=1.888)^1 *
## (Barcza=1.888, German=1.888)^1 * (Barcza=1.888, Petrosian=1.888)^1 *
## (Barcza=1.888, Portisch=1.888)^1 * (Barcza=1.888, Schweber=1.888)^1 *
## (Barcza=1.888, Stein=1.888)^1 * (Barcza=1.888, Yanofsky=1.888)^1 *
## (Barcza=2.888, Bertok=2.988)^-1 * (Barcza=2.888, Bilek=2.988)^-1 *
## (Barcza=2.888, Cuellar=2.988)^-1 * (Barcza=2.888, Filip=2.988)^-1 *
## (Barcza=2.888, Fischer=2.988)^-1 * (Barcza=2.888, Geller=2.988)^-1 *
## (Barcza=2.888, Gligoric=2.988)^-1 * (Barcza=2.888, Stein=2.988)^-1 *
## (Barcza=2.888, Teschner=2.988)^-1 * (Barcza=2.888, Yanofsky=2.988)^-1 *
## (Barcza=2.988, Benko=2.888)^-1 * (Barcza=2.988, Bisguier=2.888)^-1 *
## (Barcza=2.988, Bolbochan=2.888)^-1 * (Barcza=2.988, German=2.888)^-1 *
## (Barcza=2.988, Korchnoi=2.888)^-1 * (Barcza=2.988, Olafsson=2.888)^-1 *
## (Barcza=2.988, Petrosian=2.888)^-1 * (Barcza=2.988, Pomar=2.888)^-1 *
## (Barcza=2.988, Portisch=2.888)^-1 * (Barcza=2.988, Schweber=2.888)^-1 *
## (Barcza=2.988, Uhlmann=2.888)^-1 * (Benko=1)^2 * (Benko=1.1)^6 *
## (Benko=1.888, Bolbochan=1.888)^1 * (Benko=1.888, Filip=1.888)^1 *
## (Benko=1.888, Fischer=1.888)^1 * (Benko=1.888, Gligoric=1.888)^1 *
## (Benko=1.888, Korchnoi=1.888)^1 * (Benko=1.888, Petrosian=1.888)^1 *
## (Benko=1.888, Pomar=1.888)^1 * (Benko=1.888, Portisch=1.888)^1 *
## (Benko=1.888, Stein=1.888)^2 * (Benko=1.888, Teschner=1.888)^1 *
## (Benko=2.888, Bertok=2.988)^-1 * (Benko=2.888, Cuellar=2.988)^-1 *
## (Benko=2.888, Filip=2.988)^-1 * (Benko=2.888, Fischer=2.988)^-1 *
## (Benko=2.888, Geller=2.988)^-1 * (Benko=2.888, Gligoric=2.988)^-1 *
## (Benko=2.888, Portisch=2.988)^-1 * (Benko=2.888, Stein=2.988)^-2 *
## (Benko=2.888, Teschner=2.988)^-1 * (Benko=2.888, Yanofsky=2.988)^-1 *
## (Benko=2.988, Bilek=2.888)^-1 * (Benko=2.988, Bisguier=2.888)^-1 *
## (Benko=2.988, Bolbochan=2.888)^-1 * (Benko=2.988, German=2.888)^-1 *
## (Benko=2.988, Korchnoi=2.888)^-1 * (Benko=2.988, Olafsson=2.888)^-1 *
## (Benko=2.988, Petrosian=2.888)^-1 * (Benko=2.988, Pomar=2.888)^-1 *
## (Benko=2.988, Schweber=2.888)^-1 * (Benko=2.988, Uhlmann=2.888)^-1 *
## (Bertok=1.1)^1 * (Bertok=1.888, Bilek=1.888)^1 * (Bertok=1.888,
## Bisguier=1.888)^1 * (Bertok=1.888, Bolbochan=1.888)^1 * (Bertok=1.888,
## Filip=1.888)^1 * (Bertok=1.888, Geller=1.888)^1 * (Bertok=1.888,
## German=1.888)^1 * (Bertok=1.888, Gligoric=1.888)^1 * (Bertok=1.888,
## Pomar=1.888)^1 * (Bertok=1.888, Stein=1.888)^1 * (Bertok=1.888,
## Teschner=1.888)^1 * (Bertok=1.888, Yanofsky=1.888)^1 * (Bertok=2.888,
## Bilek=2.988)^-1 * (Bertok=2.888, Bisguier=2.988)^-1 * (Bertok=2.888,
## Bolbochan=2.988)^-1 * (Bertok=2.888, German=2.988)^-1 * (Bertok=2.888,
## Korchnoi=2.988)^-1 * (Bertok=2.888, Olafsson=2.988)^-1 * (Bertok=2.888,
## Petrosian=2.988)^-1 * (Bertok=2.888, Pomar=2.988)^-1 * (Bertok=2.888,
## Schweber=2.988)^-1 * (Bertok=2.888, Teschner=2.988)^-1 * (Bertok=2.988,
## Cuellar=2.888)^-1 * (Bertok=2.988, Filip=2.888)^-1 * (Bertok=2.988,
## Fischer=2.888)^-1 * (Bertok=2.988, Geller=2.888)^-1 * (Bertok=2.988,
## Gligoric=2.888)^-1 * (Bertok=2.988, Portisch=2.888)^-1 * (Bertok=2.988,
## Stein=2.888)^-1 * (Bertok=2.988, Uhlmann=2.888)^-1 * (Bertok=2.988,
## Yanofsky=2.888)^-1 * (Bilek=1)^2 * (Bilek=1.1)^5 * (Bilek=1.888,
## Bisguier=1.888)^1 * (Bilek=1.888, Bolbochan=1.888)^1 * (Bilek=1.888,
## Filip=1.888)^1 * (Bilek=1.888, Olafsson=1.888)^1 * (Bilek=1.888,
## Portisch=1.888)^1 * (Bilek=1.888, Stein=1.888)^1 * (Bilek=2.888,
## Bisguier=2.988)^-1 * (Bilek=2.888, Bolbochan=2.988)^-1 * (Bilek=2.888,
## German=2.988)^-1 * (Bilek=2.888, Korchnoi=2.988)^-1 * (Bilek=2.888,
## Olafsson=2.988)^-1 * (Bilek=2.888, Petrosian=2.988)^-1 * (Bilek=2.888,
## Pomar=2.988)^-1 * (Bilek=2.888, Portisch=2.988)^-1 * (Bilek=2.888,
## Schweber=2.988)^-1 * (Bilek=2.888, Uhlmann=2.988)^-1 * (Bilek=2.988,
## Cuellar=2.888)^-1 * (Bilek=2.988, Filip=2.888)^-1 * (Bilek=2.988,
## Fischer=2.888)^-1 * (Bilek=2.988, Geller=2.888)^-1 * (Bilek=2.988,
## Gligoric=2.888)^-1 * (Bilek=2.988, Stein=2.888)^-1 * (Bilek=2.988,
## Teschner=2.888)^-1 * (Bilek=2.988, Yanofsky=2.888)^-1 * (Bisguier=1)^1
## * (Bisguier=1.1)^3 * (Bisguier=1.888, Bolbochan=1.888)^1 *
## (Bisguier=1.888, Filip=1.888)^1 * (Bisguier=1.888, Korchnoi=1.888)^1 *
## (Bisguier=1.888, Olafsson=1.888)^1 * (Bisguier=1.888,
## Petrosian=1.888)^1 * (Bisguier=1.888, Pomar=1.888)^1 * (Bisguier=1.888,
## Schweber=1.888)^1 * (Bisguier=1.888, Yanofsky=1.888)^1 *
## (Bisguier=2.888, Bolbochan=2.988)^-1 * (Bisguier=2.888,
## German=2.988)^-1 * (Bisguier=2.888, Korchnoi=2.988)^-1 *
## (Bisguier=2.888, Olafsson=2.988)^-1 * (Bisguier=2.888,
## Petrosian=2.988)^-1 * (Bisguier=2.888, Pomar=2.988)^-1 *
## (Bisguier=2.888, Portisch=2.988)^-1 * (Bisguier=2.888,
## Schweber=2.988)^-1 * (Bisguier=2.888, Uhlmann=2.988)^-1 *
## (Bisguier=2.988, Cuellar=2.888)^-1 * (Bisguier=2.988, Filip=2.888)^-1 *
## (Bisguier=2.988, Fischer=2.888)^-1 * (Bisguier=2.988, Geller=2.888)^-1
## * (Bisguier=2.988, Gligoric=2.888)^-1 * (Bisguier=2.988,
## Stein=2.888)^-1 * (Bisguier=2.988, Teschner=2.888)^-1 *
## (Bisguier=2.988, Yanofsky=2.888)^-1 * (Bolbochan=1)^2 *
## (Bolbochan=1.1)^3 * (Bolbochan=1.888, Gligoric=1.888)^1 *
## (Bolbochan=1.888, Korchnoi=1.888)^1 * (Bolbochan=1.888,
## Olafsson=1.888)^1 * (Bolbochan=1.888, Petrosian=1.888)^1 *
## (Bolbochan=1.888, Portisch=1.888)^1 * (Bolbochan=1.888,
## Schweber=1.888)^1 * (Bolbochan=1.888, Teschner=1.888)^1 *
## (Bolbochan=1.888, Uhlmann=1.888)^1 * (Bolbochan=2.888,
## Cuellar=2.988)^-1 * (Bolbochan=2.888, Filip=2.988)^-1 *
## (Bolbochan=2.888, Fischer=2.988)^-1 * (Bolbochan=2.888,
## Geller=2.988)^-1 * (Bolbochan=2.888, Gligoric=2.988)^-1 *
## (Bolbochan=2.888, Portisch=2.988)^-1 * (Bolbochan=2.888,
## Stein=2.988)^-1 * (Bolbochan=2.888, Uhlmann=2.988)^-1 *
## (Bolbochan=2.888, Yanofsky=2.988)^-1 * (Bolbochan=2.988,
## German=2.888)^-1 * (Bolbochan=2.988, Korchnoi=2.888)^-1 *
## (Bolbochan=2.988, Olafsson=2.888)^-1 * (Bolbochan=2.988,
## Petrosian=2.888)^-1 * (Bolbochan=2.988, Pomar=2.888)^-1 *
## (Bolbochan=2.988, Schweber=2.888)^-1 * (Bolbochan=2.988,
## Teschner=2.888)^-1 * (Cuellar=1)^1 * (Cuellar=1.1)^3 * (Cuellar=1.888,
## Petrosian=1.888)^1 * (Cuellar=1.888, Schweber=1.888)^1 *
## (Cuellar=2.888, Filip=2.988)^-1 * (Cuellar=2.888, Geller=2.988)^-1 *
## (Cuellar=2.888, German=2.988)^-1 * (Cuellar=2.888, Pomar=2.988)^-1 *
## (Cuellar=2.888, Schweber=2.988)^-1 * (Cuellar=2.888, Stein=2.988)^-1 *
## (Cuellar=2.888, Teschner=2.988)^-1 * (Cuellar=2.988, Fischer=2.888)^-1
## * (Cuellar=2.988, Gligoric=2.888)^-1 * (Cuellar=2.988,
## Korchnoi=2.888)^-1 * (Cuellar=2.988, Olafsson=2.888)^-1 *
## (Cuellar=2.988, Petrosian=2.888)^-1 * (Cuellar=2.988,
## Portisch=2.888)^-1 * (Cuellar=2.988, Uhlmann=2.888)^-1 *
## (Cuellar=2.988, Yanofsky=2.888)^-1 * (Filip=1)^3 * (Filip=1.1)^5 *
## (Filip=1.888, Fischer=1.888)^1 * (Filip=1.888, Geller=1.888)^1 *
## (Filip=1.888, Gligoric=1.888)^1 * (Filip=1.888, Olafsson=1.888)^1 *
## (Filip=1.888, Petrosian=1.888)^1 * (Filip=1.888, Pomar=1.888)^1 *
## (Filip=1.888, Portisch=1.888)^1 * (Filip=1.888, Schweber=1.888)^1 *
## (Filip=2.888, German=2.988)^-1 * (Filip=2.888, Korchnoi=2.988)^-1 *
## (Filip=2.888, Olafsson=2.988)^-1 * (Filip=2.888, Petrosian=2.988)^-1 *
## (Filip=2.888, Pomar=2.988)^-1 * (Filip=2.888, Schweber=2.988)^-1 *
## (Filip=2.888, Teschner=2.988)^-1 * (Filip=2.988, Fischer=2.888)^-1 *
## (Filip=2.988, Geller=2.888)^-1 * (Filip=2.988, Gligoric=2.888)^-1 *
## (Filip=2.988, Portisch=2.888)^-1 * (Filip=2.988, Stein=2.888)^-1 *
## (Filip=2.988, Uhlmann=2.888)^-1 * (Filip=2.988, Yanofsky=2.888)^-1 *
## (Fischer=1)^6 * (Fischer=1.1)^7 * (Fischer=1.888, Geller=1.888)^1 *
## (Fischer=1.888, Gligoric=1.888)^1 * (Fischer=1.888, Petrosian=1.888)^1
## * (Fischer=1.888, Pomar=1.888)^1 * (Fischer=1.888, Stein=1.888)^1 *
## (Fischer=1.888, Teschner=1.888)^1 * (Fischer=1.888, Uhlmann=1.888)^1 *
## (Fischer=2.888, Geller=2.988)^-1 * (Fischer=2.888, Gligoric=2.988)^-1 *
## (Fischer=2.888, Stein=2.988)^-1 * (Fischer=2.888, Teschner=2.988)^-1 *
## (Fischer=2.888, Yanofsky=2.988)^-1 * (Fischer=2.988, German=2.888)^-1 *
## (Fischer=2.988, Korchnoi=2.888)^-1 * (Fischer=2.988, Olafsson=2.888)^-1
## * (Fischer=2.988, Petrosian=2.888)^-1 * (Fischer=2.988, Pomar=2.888)^-1
## * (Fischer=2.988, Portisch=2.888)^-1 * (Fischer=2.988,
## Schweber=2.888)^-1 * (Fischer=2.988, Uhlmann=2.888)^-1 * (Geller=1)^4 *
## (Geller=1.1)^6 * (Geller=1.888, German=1.888)^1 * (Geller=1.888,
## Gligoric=1.888)^1 * (Geller=1.888, Korchnoi=1.888)^1 * (Geller=1.888,
## Olafsson=1.888)^1 * (Geller=1.888, Petrosian=1.888)^1 * (Geller=1.888,
## Schweber=1.888)^1 * (Geller=2.888, German=2.988)^-1 * (Geller=2.888,
## Olafsson=2.988)^-1 * (Geller=2.888, Petrosian=2.988)^-1 *
## (Geller=2.888, Pomar=2.988)^-1 * (Geller=2.888, Schweber=2.988)^-1 *
## (Geller=2.888, Teschner=2.988)^-1 * (Geller=2.988, Gligoric=2.888)^-1 *
## (Geller=2.988, Korchnoi=2.888)^-1 * (Geller=2.988, Portisch=2.888)^-1 *
## (Geller=2.988, Stein=2.888)^-1 * (Geller=2.988, Uhlmann=2.888)^-1 *
## (Geller=2.988, Yanofsky=2.888)^-1 * (German=1)^1 * (German=1.1)^2 *
## (German=1.888, Gligoric=1.888)^1 * (German=1.888, Korchnoi=1.888)^1 *
## (German=1.888, Schweber=1.888)^1 * (German=1.888, Stein=1.888)^1 *
## (German=1.888, Teschner=1.888)^1 * (German=2.888, Gligoric=2.988)^-1 *
## (German=2.888, Korchnoi=2.988)^-1 * (German=2.888, Olafsson=2.988)^-1 *
## (German=2.888, Petrosian=2.988)^-1 * (German=2.888, Portisch=2.988)^-1
## * (German=2.888, Uhlmann=2.988)^-1 * (German=2.888, Yanofsky=2.988)^-1
## * (German=2.988, Pomar=2.888)^-1 * (German=2.988, Schweber=2.888)^-1 *
## (German=2.988, Stein=2.888)^-1 * (German=2.988, Teschner=2.888)^-1 *
## (Gligoric=1)^4 * (Gligoric=1.1)^3 * (Gligoric=1.888, Korchnoi=1.888)^1
## * (Gligoric=1.888, Petrosian=1.888)^1 * (Gligoric=1.888, Pomar=1.888)^1
## * (Gligoric=1.888, Portisch=1.888)^1 * (Gligoric=1.888,
## Teschner=1.888)^1 * (Gligoric=1.888, Uhlmann=1.888)^1 *
## (Gligoric=2.888, Pomar=2.988)^-1 * (Gligoric=2.888, Stein=2.988)^-2 *
## (Gligoric=2.888, Teschner=2.988)^-1 * (Gligoric=2.888,
## Yanofsky=2.988)^-1 * (Gligoric=2.988, Korchnoi=2.888)^-1 *
## (Gligoric=2.988, Olafsson=2.888)^-1 * (Gligoric=2.988,
## Petrosian=2.888)^-1 * (Gligoric=2.988, Portisch=2.888)^-1 *
## (Gligoric=2.988, Schweber=2.888)^-1 * (Gligoric=2.988, Stein=2.888)^-1
## * (Gligoric=2.988, Uhlmann=2.888)^-1 * (Korchnoi=1)^1 *
## (Korchnoi=1.1)^8 * (Korchnoi=1.888, Petrosian=1.888)^1 *
## (Korchnoi=1.888, Stein=1.888)^1 * (Korchnoi=1.888, Uhlmann=1.888)^1 *
## (Korchnoi=1.888, Yanofsky=1.888)^1 * (Korchnoi=2.888,
## Portisch=2.988)^-1 * (Korchnoi=2.888, Stein=2.988)^-1 *
## (Korchnoi=2.888, Uhlmann=2.988)^-1 * (Korchnoi=2.888,
## Yanofsky=2.988)^-1 * (Korchnoi=2.988, Olafsson=2.888)^-1 *
## (Korchnoi=2.988, Petrosian=2.888)^-1 * (Korchnoi=2.988, Pomar=2.888)^-1
## * (Korchnoi=2.988, Schweber=2.888)^-1 * (Korchnoi=2.988,
## Teschner=2.888)^-1 * (Olafsson=1)^2 * (Olafsson=1.1)^6 *
## (Olafsson=1.888, Pomar=1.888)^1 * (Olafsson=1.888, Portisch=1.888)^1 *
## (Olafsson=1.888, Yanofsky=1.888)^1 * (Olafsson=2.888,
## Petrosian=2.988)^-1 * (Olafsson=2.888, Portisch=2.988)^-1 *
## (Olafsson=2.888, Uhlmann=2.988)^-1 * (Olafsson=2.888,
## Yanofsky=2.988)^-1 * (Olafsson=2.988, Pomar=2.888)^-1 *
## (Olafsson=2.988, Schweber=2.888)^-1 * (Olafsson=2.988, Stein=2.888)^-1
## * (Olafsson=2.988, Teschner=2.888)^-1 * (Petrosian=1.1)^8 *
## (Petrosian=1.888, Portisch=1.888)^1 * (Petrosian=1.888, Stein=1.888)^1
## * (Petrosian=1.888, Uhlmann=1.888)^1 * (Petrosian=1.888,
## Yanofsky=1.888)^1 * (Petrosian=2.888, Portisch=2.988)^-1 *
## (Petrosian=2.888, Stein=2.988)^-1 * (Petrosian=2.888, Uhlmann=2.988)^-1
## * (Petrosian=2.888, Yanofsky=2.988)^-1 * (Petrosian=2.988,
## Pomar=2.888)^-1 * (Petrosian=2.988, Schweber=2.888)^-1 *
## (Petrosian=2.988, Teschner=2.888)^-1 * (Pomar=1)^1 * (Pomar=1.1)^6 *
## (Pomar=1.888, Portisch=1.888)^1 * (Pomar=1.888, Schweber=1.888)^1 *
## (Pomar=1.888, Stein=1.888)^1 * (Pomar=2.888, Portisch=2.988)^-1 *
## (Pomar=2.888, Schweber=2.988)^-1 * (Pomar=2.888, Uhlmann=2.988)^-1 *
## (Pomar=2.988, Stein=2.888)^-1 * (Pomar=2.988, Teschner=2.888)^-1 *
## (Pomar=2.988, Yanofsky=2.888)^-1 * (Portisch=1)^4 * (Portisch=1.1)^4 *
## (Portisch=2.888, Stein=2.988)^-1 * (Portisch=2.888, Teschner=2.988)^-1
## * (Portisch=2.888, Yanofsky=2.988)^-1 * (Portisch=2.988,
## Schweber=2.888)^-1 * (Portisch=2.988, Uhlmann=2.888)^-1 *
## (Schweber=1.1)^2 * (Schweber=1.888, Yanofsky=1.888)^1 *
## (Schweber=2.888, Uhlmann=2.988)^-1 * (Schweber=2.988, Stein=2.888)^-1 *
## (Schweber=2.988, Teschner=2.888)^-1 * (Schweber=2.988,
## Yanofsky=2.888)^-1 * (Stein=1)^5 * (Stein=1.1)^6 * (Stein=2.888,
## Teschner=2.988)^-1 * (Stein=2.988, Uhlmann=2.888)^-1 * (Stein=2.988,
## Yanofsky=2.888)^-1 * (Teschner=1)^2 * (Teschner=1.1)^1 *
## (Teschner=1.888, Yanofsky=1.888)^1 * (Teschner=2.888, Uhlmann=2.988)^-1
## * (Teschner=2.988, Yanofsky=2.888)^-1 * (Uhlmann=1)^4 * (Uhlmann=1.1)^6
## * (Uhlmann=2.888, Yanofsky=2.988)^-1 * (Yanofsky=1.1)^3)

summary(H3)

## A hyper3 object of size 23.
## pnames:  Aaron Barcza Benko Bertok Bilek Bisguier Bolbochan Cuellar Filip Fischer Geller German Gligoric Korchnoi Olafsson Petrosian Pomar Portisch Schweber Stein Teschner Uhlmann Yanofsky 
## Number of brackets: 405 
## Sum of powers: 0 
## 
## Table of bracket lengths:
##   1   2 
##  42 363 
## 
## Table of powers:
##  -2  -1   1   2   3   4   5   6   7   8 
##   2 252 117   9   7   5   3   7   1   2 
## 
## Table of weights:
##     1   1.1 1.888 2.888 2.988 
##    19    23   218   254   254

equalp.test(H3,n=1)

## 
##  Constrained support maximization
## 
## data:  H3
## null hypothesis: Aaron = Barcza = Benko = Bertok = Bilek = Bisguier = Bolbochan = Cuellar = Filip = Fischer = Geller = German = Gligoric = Korchnoi = Olafsson = Petrosian = Pomar = Portisch = Schweber = Stein = Teschner = Uhlmann = Yanofsky
## null estimate:
##     Aaron    Barcza     Benko    Bertok     Bilek  Bisguier Bolbochan   Cuellar 
##  0.043478  0.043478  0.043478  0.043478  0.043478  0.043478  0.043478  0.043478 
##     Filip   Fischer    Geller    German  Gligoric  Korchnoi  Olafsson Petrosian 
##  0.043478  0.043478  0.043478  0.043478  0.043478  0.043478  0.043478  0.043478 
##     Pomar  Portisch  Schweber     Stein  Teschner   Uhlmann  Yanofsky 
##  0.043478  0.043478  0.043478  0.043478  0.043478  0.043478  0.043478 
## (argmax, constrained optimization)
## Support for null:  -297.85 + K
## 
## alternative hypothesis:  sum p_i=1 
## alternative estimate:
##      Aaron     Barcza      Benko     Bertok      Bilek   Bisguier  Bolbochan 
## 3.9573e-05 3.5404e-04 4.3809e-04 3.0836e-05 2.9394e-04 1.2877e-04 4.9684e-04 
##    Cuellar      Filip    Fischer     Geller     German   Gligoric   Korchnoi 
## 6.6869e-05 1.0731e-03 5.7130e-01 1.3111e-03 6.7143e-05 4.4481e-04 1.0783e-03 
##   Olafsson  Petrosian      Pomar   Portisch   Schweber      Stein   Teschner 
## 4.1238e-04 4.2035e-01 4.2064e-04 3.4757e-04 5.3196e-05 8.2187e-04 5.9774e-05 
##    Uhlmann   Yanofsky 
## 3.1082e-04 1.0557e-04 
## (argmax, free optimization)
## Support for alternative:  -255.59 + K
## 
## degrees of freedom: 22
## support difference = 42.259
## p-value: 2.8839e-09

m1121 <- maxp(f(1.1,2.1), n=1, give=TRUE)
m1123 <- maxp(f(1.1,2.3), n=1, give=TRUE)

pie(m1121$par)

A break here.

profl <- function(v){
    lambda <- v[1]
    D <- v[2]
    H <- f(lambda,v)
    return(loglik(maxp(H,n=1),H))
}

Now apply profl():

At this point the Rmd file fails* (probably due to recent defensive programming). So I will comment out all the R code from here on in, and fix it when I get a minute.

# profl(c(1.1,2.1))

# np <- 4
# lambda <- seq(from=0.1, to=1.5, len=np)
# D <- seq(from=0.1, to=0.4, len=np)
# jj <- as.matrix(expand.grid(lambda, D))
# LL <- apply(jj, 1, profl)
# LL

# LL <- LL - max(LL)
# m <- matrix(LL,np,np)
# m
# filled.contour(lambda,D,m,xlab="lambda",ylab="D",nlevels=40)

# res <- cur_matches$V3
# res
# table(res)
# white_wins <- cur_matches[res=="1-0"    ,]
# black_wins <- cur_matches[res=="0-1"    ,]
# draws      <- cur_matches[res=="1/2-1/2",]
# (players <- unique(sort(c(cur_matches[,1],cur_matches[,2]))))
# jj <- rep(0,length(players))
# names(jj) <- players
# jj
# plays_white_wins <- jj
# plays_white_lose <- jj
# plays_white_draw <- jj
# plays_black_wins <- jj
# plays_black_lose <- jj
# plays_black_draw <- jj
# for(i in seq_len(nrow(cur_matches))){
#   white_player <- cur_matches[i,1]
#   black_player <- cur_matches[i,2]
#   result       <- cur_matches[i,3]  
# 
#   if(result == "1-0"){
#       plays_white_wins[white_player] %<>% inc
#       plays_black_lose[black_player] %<>% inc
#   } else if(result == "0-1"){
#       plays_white_lose[white_player] %<>% inc
#       plays_black_wins[black_player] %<>% inc
#   } else if(result == "1/2-1/2"){
#       plays_white_draw[white_player] %<>% inc
#       plays_black_draw[black_player] %<>% inc
#   }
# }
# 
# plays_white_wins
# plays_white_lose
# plays_black_wins
# plays_black_lose

Now we need some way to describe each player’s wins/losses playing white and black:

# f <- function(player){
# out <- matrix(c(
#   plays_white_wins[player], plays_white_lose[player], plays_white_draw[player],
#   plays_black_wins[player], plays_black_lose[player], plays_black_draw[player]
#   ),byrow=TRUE,2,3)
#   dimnames(out) <- list(colour=c("white","black"),match=c("win","lose","draw"))
#   return(out)
# }
# f("Fischer")
# f("Korchnoi")
# f("Petrosian")
# M <- f("Aaron")*0
# for(p in players){ M <- M + f(p) }
# M

Hankin, R. K. S. 2017. “Partial Rank Data with the hyper2 Package: Likelihood Functions for Generalized Bradley-Terry Models.” The R Journal 9 (2): 429–39.