Jason Weisman
@jlw12.bsky.social
#thisweeksfiddler
Miles Probability
3 17/256
3.5 32/256
4 24.75/256
4.5 72/256
5 9.1875/256
5.5 33/256
6 20.0625/256
6.5 48/256
Avg = 3*17/256+3.5*32/256+4*(24+3/4)/256+4.5*72/256+5*(9+3/16)/256+5.5*33/256+6*(20+1/16)/256+6.5*48/256
= 19933/4096 ~ 4.8665 miles
Miles Probability
3 17/256
3.5 32/256
4 24.75/256
4.5 72/256
5 9.1875/256
5.5 33/256
6 20.0625/256
6.5 48/256
Avg = 3*17/256+3.5*32/256+4*(24+3/4)/256+4.5*72/256+5*(9+3/16)/256+5.5*33/256+6*(20+1/16)/256+6.5*48/256
= 19933/4096 ~ 4.8665 miles
August 26, 2025 at 4:09 AM
#thisweeksfiddler
Miles Probability
3 17/256
3.5 32/256
4 24.75/256
4.5 72/256
5 9.1875/256
5.5 33/256
6 20.0625/256
6.5 48/256
Avg = 3*17/256+3.5*32/256+4*(24+3/4)/256+4.5*72/256+5*(9+3/16)/256+5.5*33/256+6*(20+1/16)/256+6.5*48/256
= 19933/4096 ~ 4.8665 miles
Miles Probability
3 17/256
3.5 32/256
4 24.75/256
4.5 72/256
5 9.1875/256
5.5 33/256
6 20.0625/256
6.5 48/256
Avg = 3*17/256+3.5*32/256+4*(24+3/4)/256+4.5*72/256+5*(9+3/16)/256+5.5*33/256+6*(20+1/16)/256+6.5*48/256
= 19933/4096 ~ 4.8665 miles
#ThisWeeksFiddler
EC: W= $90 cash with 50% likelihood from the outset.
First bet the entire $55 on one side. This has 50% probability of winning $55 cash while retaining the $55 of vouchers.
After winning use the same strategy as in Part 1 to add $35 or more cash guaranteed.
EC: W= $90 cash with 50% likelihood from the outset.
First bet the entire $55 on one side. This has 50% probability of winning $55 cash while retaining the $55 of vouchers.
After winning use the same strategy as in Part 1 to add $35 or more cash guaranteed.
August 19, 2025 at 4:34 AM
#ThisWeeksFiddler
EC: W= $90 cash with 50% likelihood from the outset.
First bet the entire $55 on one side. This has 50% probability of winning $55 cash while retaining the $55 of vouchers.
After winning use the same strategy as in Part 1 to add $35 or more cash guaranteed.
EC: W= $90 cash with 50% likelihood from the outset.
First bet the entire $55 on one side. This has 50% probability of winning $55 cash while retaining the $55 of vouchers.
After winning use the same strategy as in Part 1 to add $35 or more cash guaranteed.
#ThisWeeksFiddler
Arrange circles on a triangular lattice, each surrounded by six other circles.
Centers are integer linear combinations of: v1 =(1,0), v2 = (1/2, sqrt(3)/2).
Avg area contributed by each surrounded circle = sqrt(3)/2
For large N, min area of region is ~ sqrt(3)/2 N
Arrange circles on a triangular lattice, each surrounded by six other circles.
Centers are integer linear combinations of: v1 =(1,0), v2 = (1/2, sqrt(3)/2).
Avg area contributed by each surrounded circle = sqrt(3)/2
For large N, min area of region is ~ sqrt(3)/2 N
June 10, 2025 at 11:20 AM
#ThisWeeksFiddler
Arrange circles on a triangular lattice, each surrounded by six other circles.
Centers are integer linear combinations of: v1 =(1,0), v2 = (1/2, sqrt(3)/2).
Avg area contributed by each surrounded circle = sqrt(3)/2
For large N, min area of region is ~ sqrt(3)/2 N
Arrange circles on a triangular lattice, each surrounded by six other circles.
Centers are integer linear combinations of: v1 =(1,0), v2 = (1/2, sqrt(3)/2).
Avg area contributed by each surrounded circle = sqrt(3)/2
For large N, min area of region is ~ sqrt(3)/2 N