O8 nut low question
07-27-2014
, 04:59 AM
07-27-2014
, 01:54 PM
07-27-2014
, 05:35 PM
07-28-2014
, 01:10 PM
I have written a little code to evaluate the probability of any hand to make the nut low. The approach I took is the following:
- generate every possible board;
- for each board evaluate which are the couple of card that make the nut low (getNutLow function in the code);
- check if the given hand has that couple of cards (checkLow function).
The code I wrote is very slow, inelegant and probably buggy. I should (almost) feel ashamed of it
I'm gonna post it anyway, just to show the results.
The results:
- generate every possible board;
- for each board evaluate which are the couple of card that make the nut low (getNutLow function in the code);
- check if the given hand has that couple of cards (checkLow function).
The code I wrote is very slow, inelegant and probably buggy. I should (almost) feel ashamed of it
I'm gonna post it anyway, just to show the results.Code:
getNutLow<-function(board)
{
hand<-unique(board)
low<-hand[which(hand<=8)]
if (length(low)<3) return(NULL)
below6<-hand[which(hand<6)]
if (length(below6)==5) return(combn(5,2))
if (length(below6)==4) return(matrix(c(rep(setdiff(1:5,low),4),sort(low)[1:4]),nrow=2,byrow=TRUE))
matrix(setdiff(1:5,low)[1:2],ncol=1)
}
checkLow<-function(lowMatrix,hand)
{
if (is.null(lowMatrix)) FALSE else any(apply(lowMatrix,2,function(x) all(x %in% hand)))
}
getNutLowProb<-function(hand)
{
deck <- c(1:13,101:113,1001:1013,10001:10013)
cards.out <- hand
deck <- deck[-which(deck %in% cards.out)]%%100
boards <- combn(deck,5,simplify=FALSE)
hand<-hand%%100
allNutLow<-lapply(boards,getNutLow)
res<-vapply(allNutLow,checkLow,TRUE,hand=hand)
sum(res)/length(boards)
}
Code:
> getNutLowProb(c(1,2,13,113)) [1] 0.2479186 > getNutLowProb(c(1,2,3,13)) [1] 0.4313767 > getNutLowProb(c(2,3,4,13)) [1] 0.2250628
07-29-2014
, 08:28 PM
07-31-2014
, 04:25 AM
Finally I produced something I shouldn't be ashamed of!
I dramatically improved my code just by nothing a couple of things.
First, in this problem just the rank matters. By generating all the boards, the old code evaluated the nut low for many basically identical boards.
So, you just need to do that for every different (in the sense of having different ranks) board. A board can contain 2,3,4 or 5 different ranks. You discard immediately the 2 rank boards (can't be any low). For the others, you have to evaluate the "cardinality" (i.e. the number of different boards with those ranks). A board with 5 ranks can be realized in n_1*n_2*n_3*n_4*n_5 ways, n_i being the number of cards that rank has (you have to remove your hand). A 4 rank board must contain a pair; a 3 rank board can contain either a trips or two pair. In any case, it's easy to evaluate the number of combos corresponding to a board type. For doing so I added the getBoardCardinality function.
Here is the code:
And here we are:
Same old results, but a speed up of a factor ~ 1500 on my PC.
I dramatically improved my code just by nothing a couple of things.
First, in this problem just the rank matters. By generating all the boards, the old code evaluated the nut low for many basically identical boards.
So, you just need to do that for every different (in the sense of having different ranks) board. A board can contain 2,3,4 or 5 different ranks. You discard immediately the 2 rank boards (can't be any low). For the others, you have to evaluate the "cardinality" (i.e. the number of different boards with those ranks). A board with 5 ranks can be realized in n_1*n_2*n_3*n_4*n_5 ways, n_i being the number of cards that rank has (you have to remove your hand). A 4 rank board must contain a pair; a 3 rank board can contain either a trips or two pair. In any case, it's easy to evaluate the number of combos corresponding to a board type. For doing so I added the getBoardCardinality function.
Here is the code:
Code:
# Function to check if hand has nuts for board
checkNutLow = function(board,hand) {
board.u = unique(board) # get unique ranks
low = board.u[which(board.u <= 8)] # get ranks <= 8
if (length(low) < 3) { # if fewer than 3, no nuts
return(FALSE)
} else {
below6 = length(board.u[which(board.u < 6)]) # number of ranks < 6
if (below6 < 4) { # if fewer than 4, nuts is 2 lowest not on board
nuts<-setdiff(1:5,low)[1:2]
} else if (below6 == 4) { # if exactly 4, nuts is missing rank and any other A-5
nuts<-setdiff(1:5,low)
} else { # if exactly 5, nuts is any two A-5
return(TRUE)
}
return(all(nuts %in% hand)) # return TRUE if hand has nuts
}
}
getBoardCardinality<-function(board,cardNumber)
{
tavola<-cardNumber[board]
if (length(board)==5) return(prod(tavola))
if (length(board)==4)
{
res<-numeric(4)
for (i in 1:4) res[i]<-choose(tavola[i],2)*prod(tavola[-i])
return(sum(res))
}
if (length(board)==3)
{
res<-numeric(3)
for (i in 1:3)
{
res[i]<-choose(tavola[i],3)*prod(tavola[-i])+tavola[i]*prod(choose(tavola[-i],2))
}
return(sum(res))
}
}
getNutLowProb <- function(hand)
{
deck <- c(1:13,101:113,1001:1013,10001:10013)
deck<-sort(setdiff(deck,hand)%%100)
cardNumber<-table(deck)
hand<-unique(hand%%100)
if (sum(hand<6)<2) return(0)
deck<-1:13
boardRanks<-choose(13,3:5)
intervals<-c(0,cumsum(boardRanks))
boards<-vector(sum(boardRanks),mode="list")
for (i in 1:3) boards[(intervals[i]+1):intervals[i+1]]<-combn(deck,i+2,simplify=FALSE)
mandatory.on.boards<-(1:min(hand))[-min(hand)]
boards <- boards[which(vapply(boards,function(x) sum(x<= 8) >= 3 && all(mandatory.on.boards %in% x),TRUE))]
numerosity<-vapply(boards,getBoardCardinality,1,cardNumber=cardNumber)
isLow<-vapply(boards,checkNutLow,TRUE,hand)
sum(isLow*numerosity)/choose(48,5)
}
Code:
> system.time(res<-getNutLowProb(c(1,2,13,113))) user system elapsed 0.076 0.000 0.075 > res [1] 0.2479186 > getNutLowProb(c(1,2,3,13)) [1] 0.4313767 > getNutLowProb(c(2,3,4,13)) [1] 0.2250628