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Ask The Wizard #417
I know you used to be a government actuary. That said, are the figures in this table that allegedly show tariffs charged imports to the United States and exports of US products accurate?
No.
I was curious about the source of these statistics. To start with the column of tariffs charged to the U.S., I found they are not about tariffs at all but the trade deficit. The following table shows the value of imports and exports to the US by the top ten countries on the list in 2024. The "trade deficit ratio" column is the ratio of the imports minus exports to imports. Imports and Exports are shown in millions of dollars. Note that it agrees exactly with the figures on the table Trump was holding.
| Country | Exports | Imports | Trade Deficit Ratio |
"Tariffs Charged to the USA" |
|---|---|---|---|---|
| China | $143,546 | $438,947 | 67% | 67% |
| European Union | $370,189 | $605,760 | 39% | 39% |
| Vietnam | $13,098 | $136,561 | 90% | 90% |
| Taiwan | $42,337 | $116,264 | 64% | 64% |
| Japan | $79,741 | $148,209 | 46% | 46% |
| India | $41,753 | $87,416 | 52% | 52% |
| South Korea | $65,542 | $131,549 | 50% | 50% |
| Thailand | $17,719 | $63,328 | 72% | 72% |
| Switzerland | $24,962 | $63,425 | 61% | 61% |
| Indonesia | $10,202 | $28,085 | 64% | 64% |
Source of imports and exports: United States Census Bureau.
So, the "Tariffs Charged to the U.S.A." column in the president's chart has nothing to do with tariffs, but simply is the trade deficit as a percentage of imports.
"What about the gold column of 'U.S.A. Discounted Reciprocal Tariffs'?" column, you might ask. That is simply the greater of half the Tariffs Charged column and 10%. This can be seen by simply looking at the table.
It just goes to show that just because somebody throws a lot of numbers and statistics at you doesn't mean the speaker is truthful. In fact, it's a common method of fooling people to bombard them with numbers as if from a firehose and hope the listener is too lazy to fact check them. I haven't seen such blatant misuse of statistics since I saw this video on the man vs. bear debate. In fact, this "Reciprocal Tariffs" table is worse.
Suppose I bet $100 in an infinite-deck blackjack game and am dealt a pair of twos against a dealer three. Double after split is allowed and the player may re-split infinitely. What is the expected final total wager, assuming I re-split as much as possible and double if I have a two-card total of 9 to 11?
Let's first calculate how many hands you can expect to re-split to. Let n be the number of hands a single card will result in after re-splitting.
n=(12/13)×1 + (1/13)×2n
13n = 12 + 2n
11n = 12
n = 12/11 =~ 1.090909...
With two starting twos, the player can expect to re-split to 2×(12/11) = 24/11 =~ 2.181818 hands.
The probability of drawing a 7 to 9 to any given two is 3×(1/12) = 3/12 = 1/4. I am dividing by 12 and not 13 because if the player drew a 2 he would re-split the pair. So, the average units bet per hand after re-splitting is (3/4)×1 + (1/4)×2 = 5/4 = 1.25.
With a $100 base bet, the average final wager is $100×(24/11)×(5/4) = $272.73.
This question was asked and discussed in my forum at Wizard of Vegas.
Suppose two players wish to play Russian roulette under the following rules.
- Gun is a revolver with six chambers.
- One to five bullets must be put in the chambers for any given pull of the trigger.
- The number of bullets in the gun may changed before each pull.
- The gun must pass back and forth after every pull.
- No other randomization methods may be used other than the gun.
What is a method of ensuring each player has a 50% chance of surviving?
The following is just my answer. I'm sure there are others.
- Place two bullets in the gun for the first player. If he survives, go to step 2.
- Place three bullets in the gun for the second player. If he survives, go back to step 1.
If we let p be the probability player 1 loses, that can be calculated as follows:
p = (2/6) + (4/6)*(3/6)p
36p = 12 + 12p
24p = 12
p = 12/24 = 1/2
Suppose the sides of a square of side length a are extended onto a line below the square, creating distances of 2 and 5 onto the line.
What is the area of the square?
First, let's move up the line so it touches the corner of the square. This will not affect the distances on the line. Then, let's label the unknown sides of the two triangles.
The blue and yellow triangles are right triangles.
Using the Pythagorean formula on the blue triangle:
b2 + a2 = 4
b = sqrt(4-a2)
Using the Pythagorean formula on the yellow triangle:
c2 + a2 = 25
c = sqrt(25-a2)
The blue and yellow triangles are similar. Thus, the ratio of a to b equals the ratio of c to a:
a/sqrt(4-a2) = sqrt(25-a2)/a
a2 = sqrt(4-a2) * sqrt(25-a2)
Squaring both sides:
a4 = (4 - a2) * (25 - a2)
Let x = a2
x2 = (4-x)(25-x)
x2 = 100 - 29x + x2
29x = 100
x = 100/29
a = sqrt(x) = sqrt(100/29)
The question asked the area of the red square, which is a2 = (sqrt(100/29))2 = 100/29.