# Example 934 — The hundred year flood in a thirty year mortgage `the_hundred_year_flood_in_a_thirty_year_mortgage.eml` - A buyer takes a thirty-year mortgage on a house in the hundred-year floodplain, the flood map is correct, and the buyer reasons that a hundred-year flood is not a thirty-year problem. What one percent a year adds up to over thirty years is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A buyer takes a # thirty-year mortgage on a house in the hundred-year floodplain, the flood # map is correct, and the buyer reasons that a hundred-year flood is not a # thirty-year problem. What one percent a year adds up to over thirty years is # computed below. # # The reasoning is careful. The map's annual probability is the real, # well-estimated one percent; thirty is genuinely less than a hundred; the # mortgage term is exactly thirty years; and the intent is exactly 'will this # house flood while I own it'. # # A hundred-year flood is a one-percent chance every year, and thirty draws at # one percent leave a seventy-four percent chance of no flood - so the chance of # at least one flood during the mortgage is twenty-six percent, not zero and not # thirty percent of the way to certain. 100 => annual_flood_chance_per_myriad 30 => mortgage_years 7397 => chance_of_no_flood_in_thirty_years_per_myriad 9044 => chance_of_no_flood_in_ten_years_per_myriad 10000 - chance_of_no_flood_in_thirty_years_per_myriad => chance_of_at_least_one_flood_in_thirty_years_per_myriad 10000 - chance_of_no_flood_in_ten_years_per_myriad => chance_of_at_least_one_flood_in_ten_years_per_myriad annual_flood_chance_per_myriad * mortgage_years => expected_floods_in_thirty_years_per_myriad int(chance_of_at_least_one_flood_in_thirty_years_per_myriad / annual_flood_chance_per_myriad) => times_the_single_year_chance "annual chance of a flood : " + str(annual_flood_chance_per_myriad) + " per ten thousand (a hundred-year flood)" ^0 "years of the mortgage : " + str(mortgage_years) ^0 "" ^0 "chance of no flood in ten years : " + str(chance_of_no_flood_in_ten_years_per_myriad) + " per ten thousand" ^0 "chance of at least one, ten years : " + str(chance_of_at_least_one_flood_in_ten_years_per_myriad) + " per ten thousand" ^0 "chance of no flood in thirty years : " + str(chance_of_no_flood_in_thirty_years_per_myriad) + " per ten thousand" ^0 "chance of at least one, thirty years : " + str(chance_of_at_least_one_flood_in_thirty_years_per_myriad) + " per ten thousand" ^0 "expected floods over the term : " + str(expected_floods_in_thirty_years_per_myriad) + " per ten thousand of a flood" ^0 "thirty years is : " + str(times_the_single_year_chance) + " times the single-year chance" ^0 "" ^0 # ---- what the reasoning verified ---- "the not-my-problem reasoning" ^0 " annual probability : the map's real one percent" ^0 " arithmetic : thirty is less than a hundred" ^0 " term : exactly thirty years" ^0 " intent : will this house flood while I own it" ^0 " facts wrong : 0" ^0 " verdict : A HUNDRED-YEAR EVENT WILL NOT FALL IN THIRTY YEARS" ^0 "" ^0 " taking the map's real annual probability is the part" ^0 " done right here, and it is why one percent a year is a" ^0 " true statement about every single year" ^0 "" ^0 # ---- what one percent a year adds up to ---- "thirty draws at one percent" ^0 " each year : a fresh one-in-a-hundred" ^0 " no flood in a year : ninety-nine in a hundred" ^0 " no flood in thirty years : ninety-nine in a hundred, thirty" ^0 " times over, " + str(chance_of_no_flood_in_thirty_years_per_myriad) + " per ten thousand" ^0 " at least one flood : the rest, " + str(chance_of_at_least_one_flood_in_thirty_years_per_myriad) + " per ten thousand" ^0 " what a hundred-year flood is : a rate, not an appointment" ^0 "" ^0 # ---- what the buyer got ---- "the exposure" ^0 " believed : no meaningful chance" ^0 " actual : about one in four over the mortgage" ^0 " is the map wrong : no; one percent a year is right" ^0 " is a hundred-year flood a hundred years away : no; it is" ^0 " one percent away, every year, and thirty of those add up" ^0 "" ^0 # ---- null control ---- # The same question answered with the compounded probability over the term # instead of by comparing the return period with the term. 0 => nc_chance_read_by_comparing_a_hundred_to_thirty_per_myriad 2603 => nc_chance_read_by_compounding_per_myriad 2603 => nc_exposure_the_compounding_reveals_per_myriad "null control - compound the annual chance over the term" ^0 " chance, comparing 100 to 30 : " + str(nc_chance_read_by_comparing_a_hundred_to_thirty_per_myriad) + " per ten thousand" ^0 " chance, compounded over 30 years : " + str(nc_chance_read_by_compounding_per_myriad) + " per ten thousand" ^0 " exposure the compounding reveals : " + str(nc_exposure_the_compounding_reveals_per_myriad) + " per ten thousand" ^0 " no map and no term changed; the return period stopped" ^0 " being read as a countdown" ^0 "" ^0 # ---- the rule ---- "what a correct hundred-year flood map guarantees" ^0 " the chance in any one year is one percent : exactly, the" ^0 " map's real estimate" ^0 " a thirty-year owner will not see one : not addressed;" ^0 " thirty independent one-percent years leave a " + str(chance_of_at_least_one_flood_in_thirty_years_per_myriad) + "-per-" ^0 " ten-thousand chance of at least one flood" ^0 "" ^0 "a return period is a rate wearing the costume of a date; nothing about the" ^0 "river remembers the calendar, and a small chance repeated every year for a" ^0 "working lifetime is not a small chance" ^0 "" ^0 "The map's one percent a year is right - every year. But thirty such years" ^0 "compound: the chance of no flood is " + str(chance_of_no_flood_in_thirty_years_per_myriad) + " per ten thousand, so the chance of at" ^0 "least one during the mortgage is " + str(chance_of_at_least_one_flood_in_thirty_years_per_myriad) + ", " + str(times_the_single_year_chance) + " times the single-year figure the" ^0 "buyer compared with the term, until the rate is compounded over the years held." ^0 ``` ## Python (deterministic transpilation) ```python annual_flood_chance_per_myriad = 100 mortgage_years = 30 chance_of_no_flood_in_thirty_years_per_myriad = 7397 chance_of_no_flood_in_ten_years_per_myriad = 9044 chance_of_at_least_one_flood_in_thirty_years_per_myriad = 10000 - chance_of_no_flood_in_thirty_years_per_myriad chance_of_at_least_one_flood_in_ten_years_per_myriad = 10000 - chance_of_no_flood_in_ten_years_per_myriad expected_floods_in_thirty_years_per_myriad = annual_flood_chance_per_myriad * mortgage_years times_the_single_year_chance = int(chance_of_at_least_one_flood_in_thirty_years_per_myriad / annual_flood_chance_per_myriad) print("annual chance of a flood : " + str(annual_flood_chance_per_myriad) + " per ten thousand (a hundred-year flood)") print("years of the mortgage : " + str(mortgage_years)) print("") print("chance of no flood in ten years : " + str(chance_of_no_flood_in_ten_years_per_myriad) + " per ten thousand") print("chance of at least one, ten years : " + str(chance_of_at_least_one_flood_in_ten_years_per_myriad) + " per ten thousand") print("chance of no flood in thirty years : " + str(chance_of_no_flood_in_thirty_years_per_myriad) + " per ten thousand") print("chance of at least one, thirty years : " + str(chance_of_at_least_one_flood_in_thirty_years_per_myriad) + " per ten thousand") print("expected floods over the term : " + str(expected_floods_in_thirty_years_per_myriad) + " per ten thousand of a flood") print("thirty years is : " + str(times_the_single_year_chance) + " times the single-year chance") print("") print("the not-my-problem reasoning") print(" annual probability : the map's real one percent") print(" arithmetic : thirty is less than a hundred") print(" term : exactly thirty years") print(" intent : will this house flood while I own it") print(" facts wrong : 0") print(" verdict : A HUNDRED-YEAR EVENT WILL NOT FALL IN THIRTY YEARS") print("") print(" taking the map's real annual probability is the part") print(" done right here, and it is why one percent a year is a") print(" true statement about every single year") print("") print("thirty draws at one percent") print(" each year : a fresh one-in-a-hundred") print(" no flood in a year : ninety-nine in a hundred") print(" no flood in thirty years : ninety-nine in a hundred, thirty") print(" times over, " + str(chance_of_no_flood_in_thirty_years_per_myriad) + " per ten thousand") print(" at least one flood : the rest, " + str(chance_of_at_least_one_flood_in_thirty_years_per_myriad) + " per ten thousand") print(" what a hundred-year flood is : a rate, not an appointment") print("") print("the exposure") print(" believed : no meaningful chance") print(" actual : about one in four over the mortgage") print(" is the map wrong : no; one percent a year is right") print(" is a hundred-year flood a hundred years away : no; it is") print(" one percent away, every year, and thirty of those add up") print("") nc_chance_read_by_comparing_a_hundred_to_thirty_per_myriad = 0 nc_chance_read_by_compounding_per_myriad = 2603 nc_exposure_the_compounding_reveals_per_myriad = 2603 print("null control - compound the annual chance over the term") print(" chance, comparing 100 to 30 : " + str(nc_chance_read_by_comparing_a_hundred_to_thirty_per_myriad) + " per ten thousand") print(" chance, compounded over 30 years : " + str(nc_chance_read_by_compounding_per_myriad) + " per ten thousand") print(" exposure the compounding reveals : " + str(nc_exposure_the_compounding_reveals_per_myriad) + " per ten thousand") print(" no map and no term changed; the return period stopped") print(" being read as a countdown") print("") print("what a correct hundred-year flood map guarantees") print(" the chance in any one year is one percent : exactly, the") print(" map's real estimate") print(" a thirty-year owner will not see one : not addressed;") print(" thirty independent one-percent years leave a " + str(chance_of_at_least_one_flood_in_thirty_years_per_myriad) + "-per-") print(" ten-thousand chance of at least one flood") print("") print("a return period is a rate wearing the costume of a date; nothing about the") print("river remembers the calendar, and a small chance repeated every year for a") print("working lifetime is not a small chance") print("") print("The map's one percent a year is right - every year. But thirty such years") print("compound: the chance of no flood is " + str(chance_of_no_flood_in_thirty_years_per_myriad) + " per ten thousand, so the chance of at") print("least one during the mortgage is " + str(chance_of_at_least_one_flood_in_thirty_years_per_myriad) + ", " + str(times_the_single_year_chance) + " times the single-year figure the") print("buyer compared with the term, until the rate is compounded over the years held.") ``` ## stdout (executed) ```text annual chance of a flood : 100 per ten thousand (a hundred-year flood) years of the mortgage : 30 chance of no flood in ten years : 9044 per ten thousand chance of at least one, ten years : 956 per ten thousand chance of no flood in thirty years : 7397 per ten thousand chance of at least one, thirty years : 2603 per ten thousand expected floods over the term : 3000 per ten thousand of a flood thirty years is : 26 times the single-year chance the not-my-problem reasoning annual probability : the map's real one percent arithmetic : thirty is less than a hundred term : exactly thirty years intent : will this house flood while I own it facts wrong : 0 verdict : A HUNDRED-YEAR EVENT WILL NOT FALL IN THIRTY YEARS taking the map's real annual probability is the part done right here, and it is why one percent a year is a true statement about every single year thirty draws at one percent each year : a fresh one-in-a-hundred no flood in a year : ninety-nine in a hundred no flood in thirty years : ninety-nine in a hundred, thirty times over, 7397 per ten thousand at least one flood : the rest, 2603 per ten thousand what a hundred-year flood is : a rate, not an appointment the exposure believed : no meaningful chance actual : about one in four over the mortgage is the map wrong : no; one percent a year is right is a hundred-year flood a hundred years away : no; it is one percent away, every year, and thirty of those add up null control - compound the annual chance over the term chance, comparing 100 to 30 : 0 per ten thousand chance, compounded over 30 years : 2603 per ten thousand exposure the compounding reveals : 2603 per ten thousand no map and no term changed; the return period stopped being read as a countdown what a correct hundred-year flood map guarantees the chance in any one year is one percent : exactly, the map's real estimate a thirty-year owner will not see one : not addressed; thirty independent one-percent years leave a 2603-per- ten-thousand chance of at least one flood a return period is a rate wearing the costume of a date; nothing about the river remembers the calendar, and a small chance repeated every year for a working lifetime is not a small chance The map's one percent a year is right - every year. But thirty such years compound: the chance of no flood is 7397 per ten thousand, so the chance of at least one during the mortgage is 2603, 26 times the single-year figure the buyer compared with the term, until the rate is compounded over the years held. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done