Brainteasers
Brainteasers focused on dice, coins and poker cards.
Basic information:
For X ~ U(a, a+1, …, b),
\[
\mathbb{E}[X] = \frac{a+b}{2}.
\]
\[
\text{Var}(X) = \frac{(b-a+1)^2 - 1}{12}.
\]
95% CI \(\approx\) EV \(\pm \) 1.96 std
Dice
EV = 3.5
Var = 35/12
std = 1.71
95% CI = (0.15, 6.85)
10 dice:
EV = 35
std = 5.4
95% CI = (24.4, 45.6)
100 dice:
EV = 350
std = 17.1
95% CI = (316.5, 383.5)
Poker
EV = 7
var = 14
std = 3.74
10 card:
EV = 70
std = 11.8
95% CI = (46.8, 93.2)
