[R] Offtopic, HT vs. HH in coin flips
Erik Iverson
eiverson at NMDP.ORG
Mon Aug 31 22:35:11 CEST 2009
Part of my issue was that I was not answering my original question. "What is more likely to show up first, HT or HH?" The answer to that turns out to be "neither", or "identical chances".
ht <- replicate(2500,
paste(sample(c("H", "T"), 100, replace = TRUE),
collapse = ""))
hts <- regexpr("HT", ht) + 1
hhs <- regexpr("HH", ht) + 1
## which is first?
table(hts < hhs) # about 50/50
summary(hts) #mean of 4
summary(hhs) #mean of 6
So, "What is more likely to show up first, HH or HT?" is of course a different question than "Are the expected values of the positions for the first HT or HH the same?" I suppose that's where confusion set in. It seems that if HH appears later in the string on average (i.e., after 6 tosses instead of 4), that the probability of it being first would be lower than HT, which is obviously wrong!
A quick graphic that helps show this (you must run the above code first):
library(lattice)
ht.df <- data.frame(count = c(hts, hhs),
type = gl(2, 1250, labels = c("HT", "HH")))
barchart(prop.table(xtabs(~ count + type, data = ht.df)),
stack = FALSE, horizontal = FALSE,
box.ratio = .8, auto.key = TRUE)
Thanks to all those who replied, and also someone sent me the following link off list, it also clears up the confusion:
http://www.mit.edu/~emin/writings/coinGame.html
Best,
Erik
-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Erik Iverson
Sent: Monday, August 31, 2009 2:17 PM
To: r-help at r-project.org
Subject: [R] Offtopic, HT vs. HH in coin flips
Dear R-help,
Could someone please try to explain this paradox to me? What is more likely to show up first in a string of coin tosses, "Heads then Tails", or "Heads then Heads"?
##generate 2500 strings of random coin flips
ht <- replicate(2500,
paste(sample(c("H", "T"), 100, replace = TRUE),
collapse = ""))
## find first occurrence of HT
mean(regexpr("HT", ht))+1 #mean of HT position, 4
## find first occurrence of HH
mean(regexpr("HH", ht))+1 #mean of HH position, 6
FYI, this is not homework, I have not been in school in years. I saw a similar problem posed in a blog post on the Revolutions R blog, and although I believe the answer, I'm having a hard time figuring out why this should be?
Thanks,
Erik Iverson
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