```
#' Calculate the odds that a bookie will likely give for a certain trifecta pick.
#' Also calculate the probability of a trifecta pick happening, using the same
#' method that we do in the win function. We make these calculations using the
#' Harville method (Journal of the Amer. Stat. Assn. 1973), which states that
#' trifecta probability can be calculated by the formula:
#'
#' (p1 * p2 * p3)/((1 - p1)*(1 - p1 - p2))
#'
#' where p1, p2, and p3 are the odds that horse 1, horse 2, and horse 3 have to
#' win first place. Making this calculation using the bookies' p1, p2, and p3 will
#' give us odds that we would likely see from a bookie. We will perform the same
#' calculation substituting the sum of all bookies' odds for 1 (which is always
#' greater than 1). This is analagous to the calculations we perform to find
#' the true probability of an individual horse winning in the win function.
#'
#' @param race_df, a data frame that has been passed through generate_psodds, so it has columns
#' for each horse's odds of winning 1st, 2nd, and 3rd
#' @param picks character vector containing the better's picks for 1st, 2nd,
#' and 3rd place, in that order
#' @return a vector containing odds and our calculation of probability
#' @examples
#' trifecta(Kentucky_derby, c('Nyquist','Exaggerator','Big Brown'))
#' trifecta(race, my_picks)
#' @export
trifecta <- function(race_df, picks) {
## Ensure data frame is in right format; if not, run generate_psodds on it to correct
if (length(names(race_df)) == 3) race_df <- generate_psodds(race_df)
if (length(picks) != 3)
stop("Must pick three horses", call. = FALSE)
if (picks[1] == picks[2])
stop("Cannot pick same horse", call. = FALSE)
if (picks[2] == picks[3])
stop("Cannot pick same horse", call. = FALSE)
if (picks[1] == picks[3])
stop("Cannot pick same horse", call. = FALSE)
option1 <- race_df[which(race_df[,1] == picks[1]), 'psoddsFirst'] * race_df[which(race_df[,1] == picks[2]), 'psoddsSecond'] * race_df[which(race_df[,1] == picks[3]), 'psoddsThird']
}
```

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