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Basic Arithmetic

5+6

## [1] 11

sqrt(64)

## [1] 8

5^2

## [1] 25

(5*2)^3

## [1] 1000

Variables

x <- (5*2)^3
y <- 5^2
x/y

## [1] 40

greeting <- "Hello!"
greeting

## [1] "Hello!"

Functions

Choose <- function (x,y) factorial(x)/(factorial(y)*factorial(x-y))
Choose(8,3)

## [1] 56

Sequences

xvec <- seq(1,10,0.5)
xvec

##  [1]  1.0  1.5  2.0  2.5  3.0  3.5  4.0  4.5  5.0  5.5  6.0  6.5  7.0  7.5
## [15]  8.0  8.5  9.0  9.5 10.0

number_of_heads <- 0:100
number_of_heads

##   [1]   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16
##  [18]  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33
##  [35]  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50
##  [52]  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65  66  67
##  [69]  68  69  70  71  72  73  74  75  76  77  78  79  80  81  82  83  84
##  [86]  85  86  87  88  89  90  91  92  93  94  95  96  97  98  99 100

Plots

number_of_sequences <- Choose(100,number_of_heads)
plot(number_of_heads,number_of_sequences)

plot(number_of_heads,number_of_sequences/2^100)

Random Numbers

runif(25,9,12) #generates 25 numbers between 9 and 12

##  [1] 11.331891  9.216436  9.082973 10.495313 10.865301 10.652609 11.586464
##  [8]  9.446740 11.467238 11.274991  9.269187  9.556835 11.400174 11.985929
## [15]  9.755771  9.879661 10.456782 10.096544 11.230864  9.761947 11.552647
## [22] 10.339227 11.120125 10.493780 11.274840

ceiling(runif(25,9,12))

##  [1] 11 12 12 10 10 10 11 12 10 11 11 12 12 12 10 11 11 12 12 11 11 12 12
## [24] 10 12

floor(runif(25,9,12))

##  [1] 10 10 11 11 11 11 10 11 10 11 11 11 10 10  9 11  9  9  9 10 10  9  9
## [24] 11 11

as.integer(runif(25,9,12))

##  [1] 10 11 11  9 10 10 10 11 10 11  9 10  9 11 11 11 10 10 10 11 11 11  9
## [24] 11 11

Sampling

die <- 1:6
die

## [1] 1 2 3 4 5 6

sample(die,10, replace=TRUE) #sampling with replacement

##  [1] 5 1 6 5 2 5 6 4 1 2

sample(die,5, replace=FALSE) #sampling without replacement

## [1] 2 3 5 4 6

Simulation

num_sims <- 500

dieresults <- sample(die, num_sims, replace=TRUE)
dieresults

##   [1] 3 5 4 3 3 6 2 4 1 1 4 2 6 2 1 3 5 2 5 5 1 4 5 2 3 4 4 1 2 5 3 6 5 4 2
##  [36] 4 5 6 2 4 2 5 4 4 6 3 1 2 3 4 3 3 6 4 1 1 4 1 4 5 5 3 4 1 1 4 6 5 5 2
##  [71] 3 1 3 5 6 2 1 4 5 5 1 3 3 4 2 4 3 5 4 2 2 5 5 5 3 5 5 4 1 6 3 1 6 5 3
## [106] 5 4 3 6 2 6 3 3 3 2 1 1 3 5 4 2 5 5 5 3 4 2 1 1 1 2 1 6 3 5 5 3 5 4 5
## [141] 3 2 4 1 3 4 4 2 1 6 1 4 5 6 3 4 1 6 2 4 2 6 2 4 3 4 5 3 5 2 3 4 2 3 5
## [176] 5 4 5 4 1 6 3 5 1 6 6 1 2 3 1 5 1 6 1 4 3 1 6 1 5 6 1 1 3 2 3 6 1 1 3
## [211] 6 2 5 5 4 3 1 1 1 3 3 2 4 4 4 1 1 6 3 4 1 1 2 4 6 4 3 5 2 6 2 1 6 1 4
## [246] 1 6 6 3 5 4 1 2 2 2 4 4 3 2 6 1 4 4 1 6 4 2 6 1 6 6 4 1 5 6 6 2 5 3 4
## [281] 1 2 2 4 4 4 1 3 6 3 2 3 5 3 2 2 3 2 6 4 2 3 5 6 6 4 5 6 2 3 2 1 5 2 4
## [316] 4 2 3 3 2 3 4 3 6 5 1 1 2 2 2 1 2 2 3 4 5 2 2 3 3 5 6 4 4 4 2 5 4 3 4
## [351] 6 6 4 6 6 3 4 1 5 6 2 6 3 5 2 5 3 4 2 6 4 1 6 1 1 3 1 3 3 3 2 2 1 2 1
## [386] 5 6 6 2 3 4 6 6 6 2 4 6 3 1 4 4 3 2 5 3 5 1 4 3 1 1 5 3 1 6 1 4 1 2 4
## [421] 6 4 2 5 4 5 5 1 1 4 3 4 6 3 2 2 3 3 2 4 3 3 2 6 5 5 4 2 3 5 1 4 1 5 3
## [456] 2 5 4 2 2 4 5 3 1 5 5 2 5 6 5 4 3 1 5 2 1 1 5 5 2 6 6 2 4 6 6 2 2 5 3
## [491] 4 5 2 6 1 5 6 5 1 6

hist(dieresults, col="green")

hist(dieresults,main=paste(num_sims," roles of a single die"),breaks=seq(.5,6.5,1), col="pink")  

table(dieresults)

## dieresults
##  1  2  3  4  5  6 
## 83 86 87 91 82 71

Multiple Dice

num_sims <- 500
num_dice <- 5

dieresults <- sample(die, num_sims*num_dice, replace=TRUE)

darray <- array(dieresults, c(num_sims,num_dice))
darray

##        [,1] [,2] [,3] [,4] [,5]
##   [1,]    3    1    1    3    1
##   [2,]    2    6    3    5    1
##   [3,]    5    4    4    5    4
##   [4,]    2    3    2    3    3
##   [5,]    1    3    4    1    6
##   [6,]    6    5    6    6    5
##   [7,]    1    1    1    3    4
##   [8,]    5    1    6    5    6
##   [9,]    6    5    4    2    4
##  [10,]    2    6    6    1    1
##  [11,]    6    6    4    2    3
##  [12,]    1    4    6    5    1
##  [13,]    3    3    4    5    6
##  [14,]    2    1    2    5    5
##  [15,]    4    1    2    4    1
##  [16,]    6    1    6    2    5
##  [17,]    1    4    5    5    6
##  [18,]    3    3    1    6    5
##  [19,]    5    2    6    2    2
##  [20,]    5    5    4    6    6
##  [21,]    5    2    4    1    2
##  [22,]    6    1    5    3    4
##  [23,]    2    4    4    4    3
##  [24,]    6    3    2    6    1
##  [25,]    4    3    1    1    3
##  [26,]    6    4    4    3    1
##  [27,]    2    1    5    3    3
##  [28,]    4    3    4    2    4
##  [29,]    3    2    6    3    3
##  [30,]    6    3    5    1    5
##  [31,]    4    4    1    3    2
##  [32,]    4    1    6    5    3
##  [33,]    2    3    5    2    4
##  [34,]    2    4    6    2    1
##  [35,]    1    1    4    3    2
##  [36,]    4    2    1    2    5
##  [37,]    2    2    2    4    2
##  [38,]    1    5    6    4    4
##  [39,]    6    4    1    4    4
##  [40,]    3    6    1    1    4
##  [41,]    1    3    5    1    1
##  [42,]    3    1    4    6    4
##  [43,]    2    5    3    6    6
##  [44,]    6    4    4    1    3
##  [45,]    5    1    4    6    2
##  [46,]    1    1    6    5    5
##  [47,]    4    3    6    6    2
##  [48,]    1    5    6    4    2
##  [49,]    4    5    4    6    1
##  [50,]    3    2    6    1    5
##  [51,]    2    3    3    5    6
##  [52,]    5    4    6    1    3
##  [53,]    6    2    4    5    5
##  [54,]    6    3    5    5    2
##  [55,]    5    2    2    4    6
##  [56,]    5    1    2    2    6
##  [57,]    6    1    6    2    5
##  [58,]    6    4    3    3    6
##  [59,]    2    2    4    2    5
##  [60,]    2    1    6    3    6
##  [61,]    1    3    3    5    6
##  [62,]    4    5    3    6    6
##  [63,]    2    6    6    3    2
##  [64,]    3    1    1    1    4
##  [65,]    5    3    6    5    2
##  [66,]    1    1    5    5    5
##  [67,]    2    1    2    3    4
##  [68,]    5    6    2    3    2
##  [69,]    6    1    5    2    2
##  [70,]    3    6    4    5    3
##  [71,]    2    2    5    1    4
##  [72,]    5    5    2    5    2
##  [73,]    6    5    2    5    1
##  [74,]    3    1    1    6    6
##  [75,]    3    4    1    4    3
##  [76,]    3    2    3    3    5
##  [77,]    6    1    2    4    5
##  [78,]    2    6    2    2    3
##  [79,]    3    2    4    4    5
##  [80,]    2    2    2    1    1
##  [81,]    4    4    4    3    1
##  [82,]    2    6    4    2    1
##  [83,]    6    2    6    6    5
##  [84,]    4    6    1    5    2
##  [85,]    2    5    6    6    3
##  [86,]    1    4    2    4    2
##  [87,]    4    4    5    2    6
##  [88,]    6    4    4    3    1
##  [89,]    5    6    4    4    3
##  [90,]    1    5    5    1    3
##  [91,]    3    4    2    1    3
##  [92,]    5    4    2    5    5
##  [93,]    5    1    4    2    4
##  [94,]    2    3    3    5    4
##  [95,]    6    4    2    1    3
##  [96,]    3    4    2    2    2
##  [97,]    5    3    4    5    2
##  [98,]    6    1    3    4    4
##  [99,]    4    2    4    2    6
## [100,]    2    2    6    5    2
## [101,]    6    3    6    2    1
## [102,]    5    1    4    2    2
## [103,]    5    2    6    5    5
## [104,]    2    3    4    4    3
## [105,]    6    4    3    4    6
## [106,]    6    4    3    6    5
## [107,]    6    1    5    2    5
## [108,]    5    6    1    3    3
## [109,]    4    3    6    4    3
## [110,]    6    2    1    4    2
## [111,]    6    3    6    4    2
## [112,]    3    6    6    3    4
## [113,]    2    4    3    2    4
## [114,]    1    1    5    4    3
## [115,]    3    2    3    3    1
## [116,]    5    1    3    2    2
## [117,]    5    4    6    4    2
## [118,]    4    1    5    4    2
## [119,]    6    5    1    4    5
## [120,]    4    6    4    5    2
## [121,]    1    6    4    4    6
## [122,]    4    6    2    6    5
## [123,]    2    2    4    2    6
## [124,]    2    2    5    1    6
## [125,]    1    3    3    3    2
## [126,]    3    4    4    1    4
## [127,]    4    4    2    1    2
## [128,]    4    3    2    2    4
## [129,]    5    3    2    2    1
## [130,]    6    1    5    2    5
## [131,]    3    2    3    2    1
## [132,]    5    5    5    6    4
## [133,]    1    2    1    3    5
## [134,]    5    3    5    4    5
## [135,]    1    1    3    6    2
## [136,]    5    2    1    2    2
## [137,]    6    5    4    6    1
## [138,]    4    4    1    3    6
## [139,]    6    4    2    3    4
## [140,]    4    3    5    6    3
## [141,]    4    3    6    1    1
## [142,]    3    4    3    6    5
## [143,]    4    3    5    6    3
## [144,]    4    4    1    4    4
## [145,]    1    5    5    6    2
## [146,]    6    1    2    1    4
## [147,]    6    5    1    6    6
## [148,]    2    3    5    2    1
## [149,]    3    2    5    1    6
## [150,]    3    5    1    6    4
## [151,]    4    1    5    6    6
## [152,]    1    2    4    6    5
## [153,]    5    6    6    1    2
## [154,]    6    5    5    4    5
## [155,]    3    4    5    3    4
## [156,]    1    6    4    1    3
## [157,]    3    4    2    3    2
## [158,]    3    2    3    5    6
## [159,]    3    1    6    3    6
## [160,]    5    3    4    2    3
## [161,]    1    1    1    5    5
## [162,]    1    6    1    6    1
## [163,]    2    1    4    5    1
## [164,]    3    1    4    4    5
## [165,]    3    3    1    4    6
## [166,]    2    3    5    2    3
## [167,]    6    2    6    1    3
## [168,]    6    6    5    5    4
## [169,]    2    2    1    3    1
## [170,]    6    6    5    5    2
## [171,]    3    2    4    6    6
## [172,]    6    3    1    1    6
## [173,]    6    3    3    2    2
## [174,]    5    3    5    4    5
## [175,]    6    1    2    5    2
## [176,]    2    2    4    2    5
## [177,]    1    2    3    4    1
## [178,]    5    4    2    3    6
## [179,]    3    6    6    6    6
## [180,]    3    4    5    2    4
## [181,]    4    4    1    2    1
## [182,]    2    4    3    2    6
## [183,]    2    6    5    2    1
## [184,]    5    4    6    4    1
## [185,]    6    5    6    1    4
## [186,]    4    5    5    2    1
## [187,]    3    5    5    4    1
## [188,]    6    5    4    6    6
## [189,]    1    2    4    1    6
## [190,]    2    4    4    6    6
## [191,]    2    1    5    6    1
## [192,]    2    4    6    5    1
## [193,]    3    1    2    3    4
## [194,]    1    6    6    2    4
## [195,]    5    2    6    1    6
## [196,]    6    4    4    2    4
## [197,]    3    3    6    2    6
## [198,]    1    3    1    4    6
## [199,]    3    3    6    1    1
## [200,]    5    2    3    5    3
## [201,]    2    4    3    5    1
## [202,]    4    5    5    5    6
## [203,]    5    6    1    6    3
## [204,]    2    3    1    4    1
## [205,]    6    5    1    6    5
## [206,]    3    1    3    5    3
## [207,]    4    6    3    5    2
## [208,]    5    4    5    2    5
## [209,]    5    3    4    1    3
## [210,]    1    1    3    3    1
## [211,]    4    2    6    5    5
## [212,]    6    5    2    1    2
## [213,]    2    6    1    1    6
## [214,]    4    1    5    4    6
## [215,]    2    4    1    4    6
## [216,]    1    5    2    2    3
## [217,]    6    3    4    2    2
## [218,]    4    1    1    1    2
## [219,]    3    6    2    1    5
## [220,]    5    3    6    4    2
## [221,]    6    2    6    3    6
## [222,]    5    3    3    6    1
## [223,]    3    1    1    4    6
## [224,]    2    4    1    6    1
## [225,]    6    2    1    6    4
## [226,]    6    6    2    6    2
## [227,]    2    4    6    3    4
## [228,]    3    4    4    1    1
## [229,]    1    2    4    3    1
## [230,]    5    1    4    2    1
## [231,]    4    2    4    1    4
## [232,]    3    3    5    5    4
## [233,]    5    6    1    5    3
## [234,]    6    4    5    5    5
## [235,]    1    1    2    5    1
## [236,]    2    1    3    1    5
## [237,]    4    5    5    5    2
## [238,]    5    6    2    5    2
## [239,]    5    5    5    4    5
## [240,]    6    6    6    5    5
## [241,]    2    3    4    6    1
## [242,]    3    2    1    2    2
## [243,]    2    1    6    4    3
## [244,]    1    3    2    3    2
## [245,]    1    2    5    6    1
## [246,]    5    4    5    2    6
## [247,]    1    3    3    6    2
## [248,]    2    2    1    4    5
## [249,]    4    1    1    4    4
## [250,]    6    5    1    4    1
## [251,]    2    2    4    1    2
## [252,]    6    4    5    5    5
## [253,]    5    3    2    5    6
## [254,]    3    4    3    2    1
## [255,]    3    5    6    2    6
## [256,]    1    2    6    3    3
## [257,]    2    5    4    1    1
## [258,]    6    4    3    2    4
## [259,]    6    4    6    3    2
## [260,]    2    4    4    4    1
## [261,]    1    3    4    6    4
## [262,]    5    5    4    3    6
## [263,]    6    6    1    5    2
## [264,]    3    6    2    2    3
## [265,]    5    2    6    1    5
## [266,]    6    4    6    3    3
## [267,]    2    1    3    4    1
## [268,]    6    1    4    6    6
## [269,]    5    6    1    5    6
## [270,]    4    4    4    3    1
## [271,]    5    4    1    5    1
## [272,]    4    4    2    2    1
## [273,]    2    1    4    4    4
## [274,]    4    6    1    5    4
## [275,]    6    1    3    3    5
## [276,]    3    5    6    6    4
## [277,]    1    1    4    1    2
## [278,]    1    3    3    2    1
## [279,]    6    6    1    4    6
## [280,]    5    4    1    6    5
## [281,]    4    6    6    3    2
## [282,]    4    6    5    1    1
## [283,]    5    5    5    6    3
## [284,]    1    5    1    2    3
## [285,]    4    6    5    1    1
## [286,]    6    3    2    4    2
## [287,]    1    1    1    1    1
## [288,]    6    3    3    5    5
## [289,]    2    1    4    2    1
## [290,]    6    3    2    2    5
## [291,]    1    5    6    1    2
## [292,]    4    5    2    4    3
## [293,]    4    5    3    4    4
## [294,]    6    1    4    5    5
## [295,]    1    4    4    6    2
## [296,]    1    3    6    1    1
## [297,]    3    5    1    3    2
## [298,]    2    2    6    1    2
## [299,]    6    6    2    5    3
## [300,]    1    3    4    5    5
## [301,]    6    3    2    1    1
## [302,]    5    1    3    2    6
## [303,]    5    3    5    2    4
## [304,]    4    2    5    2    4
## [305,]    6    4    5    6    3
## [306,]    6    3    1    3    5
## [307,]    6    1    2    5    1
## [308,]    6    2    5    2    1
## [309,]    3    3    4    2    2
## [310,]    6    5    4    1    5
## [311,]    5    1    2    1    4
## [312,]    5    1    5    4    1
## [313,]    4    3    1    5    5
## [314,]    6    6    3    4    3
## [315,]    2    1    3    1    4
## [316,]    2    4    3    4    1
## [317,]    3    6    1    5    1
## [318,]    3    6    2    4    6
## [319,]    1    3    5    5    2
## [320,]    3    6    6    6    6
## [321,]    1    3    1    1    6
## [322,]    4    1    2    1    4
## [323,]    5    5    5    6    5
## [324,]    1    1    4    6    5
## [325,]    4    3    1    2    6
## [326,]    1    5    2    3    4
## [327,]    1    2    6    3    6
## [328,]    4    3    4    6    3
## [329,]    3    2    1    4    4
## [330,]    4    2    1    6    4
## [331,]    2    6    3    4    1
## [332,]    4    1    1    1    6
## [333,]    6    3    6    6    5
## [334,]    6    2    1    4    4
## [335,]    1    1    4    4    6
## [336,]    1    5    2    2    5
## [337,]    2    2    1    1    1
## [338,]    4    3    2    2    2
## [339,]    3    6    1    6    5
## [340,]    6    4    1    5    2
## [341,]    1    1    5    5    4
## [342,]    6    1    4    5    1
## [343,]    6    4    6    1    5
## [344,]    3    6    6    2    1
## [345,]    5    3    4    4    4
## [346,]    4    1    3    4    5
## [347,]    3    5    4    2    5
## [348,]    5    6    3    2    6
## [349,]    1    1    2    6    3
## [350,]    4    4    3    4    2
## [351,]    3    6    5    4    5
## [352,]    6    2    2    4    4
## [353,]    2    6    3    1    5
## [354,]    5    6    3    6    4
## [355,]    3    3    1    6    5
## [356,]    1    2    3    5    1
## [357,]    2    3    3    5    3
## [358,]    5    4    5    3    4
## [359,]    1    2    5    4    6
## [360,]    5    6    5    3    2
## [361,]    1    2    5    2    3
## [362,]    3    5    6    2    3
## [363,]    4    3    5    2    3
## [364,]    6    3    4    6    5
## [365,]    6    2    3    1    4
## [366,]    6    6    4    5    1
## [367,]    2    1    1    3    2
## [368,]    3    5    6    4    2
## [369,]    3    6    4    4    3
## [370,]    5    4    1    6    4
## [371,]    1    4    5    5    5
## [372,]    2    2    1    4    6
## [373,]    5    2    5    1    5
## [374,]    6    5    4    5    5
## [375,]    3    1    2    4    5
## [376,]    3    3    2    2    5
## [377,]    2    1    6    6    6
## [378,]    1    4    5    3    5
## [379,]    5    3    2    6    3
## [380,]    1    5    4    4    2
## [381,]    2    1    6    1    3
## [382,]    3    1    2    2    5
## [383,]    4    4    6    2    1
## [384,]    2    5    4    6    1
## [385,]    2    4    1    1    2
## [386,]    6    6    4    5    6
## [387,]    1    2    2    6    1
## [388,]    5    1    2    3    1
## [389,]    2    4    2    6    5
## [390,]    1    6    1    4    1
## [391,]    1    5    5    2    5
## [392,]    4    2    4    2    5
## [393,]    4    5    1    6    2
## [394,]    5    3    5    6    2
## [395,]    2    4    2    5    2
## [396,]    5    4    2    6    2
## [397,]    1    5    1    3    6
## [398,]    4    5    6    2    5
## [399,]    4    2    6    3    4
## [400,]    3    4    4    4    3
## [401,]    5    2    6    5    1
## [402,]    3    3    1    4    2
## [403,]    5    4    6    2    3
## [404,]    5    4    6    4    3
## [405,]    1    2    2    1    3
## [406,]    4    6    3    6    2
## [407,]    2    4    3    3    3
## [408,]    5    5    3    1    1
## [409,]    2    5    6    4    2
## [410,]    1    1    6    1    3
## [411,]    4    2    2    3    4
## [412,]    5    2    6    3    2
## [413,]    6    3    2    6    6
## [414,]    1    1    5    1    3
## [415,]    6    3    3    2    1
## [416,]    4    6    3    5    4
## [417,]    1    3    6    5    5
## [418,]    2    4    4    3    3
## [419,]    4    5    1    2    3
## [420,]    5    1    6    4    3
## [421,]    6    6    6    1    4
## [422,]    1    2    5    6    6
## [423,]    6    4    2    5    2
## [424,]    3    6    1    3    3
## [425,]    5    4    1    4    3
## [426,]    3    5    6    1    6
## [427,]    1    3    6    1    6
## [428,]    2    3    2    3    3
## [429,]    5    2    4    4    1
## [430,]    3    2    3    5    5
## [431,]    1    1    1    5    3
## [432,]    2    6    5    2    3
## [433,]    3    6    3    4    1
## [434,]    5    3    5    5    1
## [435,]    1    2    4    3    3
## [436,]    3    6    4    2    1
## [437,]    6    6    5    6    2
## [438,]    4    2    1    5    5
## [439,]    1    6    4    3    3
## [440,]    3    6    6    5    3
## [441,]    2    3    4    2    1
## [442,]    1    6    3    3    3
## [443,]    5    2    5    4    3
## [444,]    3    6    2    2    2
## [445,]    2    4    4    6    5
## [446,]    6    2    3    4    6
## [447,]    4    4    3    1    5
## [448,]    1    4    1    3    4
## [449,]    5    4    6    4    6
## [450,]    4    5    2    6    2
## [451,]    2    1    5    1    6
## [452,]    6    5    6    5    4
## [453,]    5    5    4    6    3
## [454,]    2    5    3    1    6
## [455,]    5    4    3    2    3
## [456,]    4    2    6    5    4
## [457,]    1    3    2    6    5
## [458,]    5    1    5    3    6
## [459,]    3    1    6    1    4
## [460,]    5    1    6    6    3
## [461,]    6    1    3    2    2
## [462,]    6    1    1    5    5
## [463,]    3    5    5    3    4
## [464,]    5    1    6    5    3
## [465,]    6    6    4    4    1
## [466,]    1    5    2    5    1
## [467,]    1    2    3    3    1
## [468,]    1    4    3    5    5
## [469,]    6    1    4    3    5
## [470,]    3    3    3    1    4
## [471,]    3    2    3    4    5
## [472,]    3    6    5    1    3
## [473,]    6    4    5    4    5
## [474,]    3    1    2    3    6
## [475,]    1    3    1    6    4
## [476,]    1    5    4    5    3
## [477,]    2    6    5    5    1
## [478,]    2    1    5    3    6
## [479,]    5    3    3    4    4
## [480,]    1    4    5    3    3
## [481,]    4    2    6    4    3
## [482,]    1    6    3    3    3
## [483,]    1    3    1    4    5
## [484,]    5    3    2    3    1
## [485,]    3    1    5    2    3
## [486,]    5    2    5    1    1
## [487,]    5    2    4    1    1
## [488,]    5    1    2    3    1
## [489,]    2    3    3    4    4
## [490,]    3    3    6    1    1
## [491,]    2    3    1    2    5
## [492,]    1    3    3    4    3
## [493,]    5    3    3    6    5
## [494,]    1    6    1    2    2
## [495,]    2    2    6    1    2
## [496,]    4    5    1    2    5
## [497,]    3    6    2    6    2
## [498,]    6    6    5    2    3
## [499,]    6    5    2    2    3
## [500,]    2    4    1    1    5

darray[2,1]

## [1] 2

darray[5,]

## [1] 1 3 4 1 6

darray[1:5,1:2]

##      [,1] [,2]
## [1,]    3    1
## [2,]    2    6
## [3,]    5    4
## [4,]    2    3
## [5,]    1    3

hist(rowMeans(darray))

hist(rowSums(darray))

n1 <- NULL
n2 <- NULL
n3 <- NULL
n4 <- NULL
n5 <- NULL
n6 <- NULL
high <- NULL

for (i in 1:num_sims){
  n1 <- rbind(n1,sum(darray[i,]%in%1))
  n2 <- rbind(n2,sum(darray[i,]%in%2))
  n3 <- rbind(n3,sum(darray[i,]%in%3))
  n4 <- rbind(n4,sum(darray[i,]%in%4))
  n5 <- rbind(n5,sum(darray[i,]%in%5))
  n6 <- rbind(n6,sum(darray[i,]%in%6))
  high <-  rbind(high,max(n1[i],n2[i],n3[i],n4[i],n5[i],n6[i]))
}
table(n1); mean(n1)

## n1
##   0   1   2   3   5 
## 187 211  83  18   1

## [1] 0.872

table(high); mean(high)

## high
##   1   2   3   4   5 
##  41 354  98   6   1

## [1] 2.144

hist(high,main=paste(num_sims,"First Yatzee rolls"),xlab="#-of-a-kind",breaks=seq(.5,5.5,1))