What are the odds? -- Unusual set of 5/39 QPs (California Fantasy 5)

Reply #11

cottoneyedjoe — Mon, 02 Mar 2020 08:38:10 GMT

Habit.

Reply #10

lucky1day — Mon, 02 Mar 2020 04:30:11 GMT

Just curious, Why import secrets instead of import random

Reply #9

cottoneyedjoe — Sun, 01 Mar 2020 23:12:12 GMT

Neat find, db101. This is a python script for a simulation, it runs very slowly, maybe someone can optimize it.

import secrets

def t():

listy = [[],[],[],[],[]]

for i in range(5):

while len(listy[i]) 5:

w = secrets.randbelow(39)+1

if w not in listy[i]:

listy[i].append(w)

c = []

for i in range(5):

c.append(min(listy[i]))

return set(c)

counter = 0

simulations = 200000

for i in range(simulations):

a = t()

if a == set([1,2,3,4,5]):

counter

Reply #8

db101 — Wed, 26 Feb 2020 06:50:18 GMT

I worked it out for Florida Fantasy 5 which is a 36 ball game. Works out to 2427128628125/1369923289168896 exactly on Wolfram A, which is about 0.001772, or about odds of 1 in 564. It is an interesting problem, but if I got such a ticket I honestly wouldn't even notice if the first digits were 12345 unless they were in exact order.

Im surprised this phenomenon in the 39 ball abd 36 ball games is more likely than hitting straight in Pick 3. But if you up it to 42 balls the probability is ab... [ More ]

Reply #7

KY Floyd — Wed, 19 Feb 2020 19:08:24 GMT

Interesting question.

I've frequently said that a lot of what people offer as evidence of rigged games is just being wrong about how often things should happen as a result of random probability. In this case that 1 in 756 struck me as happening too often . I see the logic of the approach used by Tucker, but it felt off so I played with it in a different way.

The line starting with 1 is of course the easiest, but instead of starting with the simple 5/39 probability = 0.128205128205128205128... [ More ]

Reply #6

Tucker Black — Sun, 16 Feb 2020 21:58:15 GMT

Reply #5

cottoneyedjoe — Sun, 16 Feb 2020 17:08:23 GMT

Hey Tucker, I'm happy a math brain came to take up the challenge. I'm also glad you got the same answer I did, because I did it analytically and then tested the solution with a simulation, but the simulation always returned a lower probability even with millions of runs. For the longest time I couldn't tell if my math was bad or if my code had squirrels in the attic. Turned out to be a very small but very pernicious squirrel.

I did it pretty much the same way. There are (38 choose 4) tickets... [ More ]

Reply #4

cottoneyedjoe — Sun, 16 Feb 2020 16:46:36 GMT

B is something I didn't consider, but could always have some truth to it. I just operate on the assumption that the RNGs in the lottery terminals that generate QPs work as intended. The recipient of the tickets thinks QPs are lucky

Reply #3

Tucker Black — Sun, 16 Feb 2020 08:19:43 GMT

As you can see in my post above, the probability that the first number is n goes down as n goes up. So the probability of the smallest number of the 5 lines being 2,7,12,15,21 is far less than 1,2,3,4,5.

If you want to buy 5 QP tickets with first numbers 1,2,3,4,5, you will have to pick the numbers yourself. It's QP or self-pick, no in between. Fill out a ticket and choose 1 then randomly choose 4 more numbers (using Excel or just guess or whatever you like). Then for the second one choose 2... [ More ]

Reply #2

Tucker Black — Sun, 16 Feb 2020 08:07:27 GMT

Probability of the 1st number of a QP being 1 is:

1/39*5

The reason is if you pick a random number between 1 and 39, the chance of picking 1 is 1 in 39. Since 5 numbers are chosen and then printed in ascending order, where 1 would always be first since it's the smallest, there are 5 choose 1 (which is 5) different ways to do that.

Another way to look at this is:

prob(choose 1 then choose 4 more numbers) = 1/39 since after picking for the 1st number, the other 4 numbers must be larger... [ More ]

Reply #1

nibor200 — Sat, 15 Feb 2020 22:23:59 GMT

A very interesting question to ponder,

a. I'm assuming if those 5 QP tickets had first numbers of 2,7,12,15,21 you would not have asked the question even though the odds of each set happening is probably the same.

b. Many believe QP tickets generated by lottery computers have biases and don't come close to matching the expected mathematical combination probabilities, so I'm not sure how to figure out odds within that belief circle.

c. Then I was wondering if I walked up to a lottery cou... [ More ]

What are the odds? -- Unusual set of 5/39 QPs (California Fantasy 5)

cottoneyedjoe — Sat, 15 Feb 2020 18:54:10 GMT

I picked up 5 lines of CA Fantasy 5 quick picks for someone who's been housebound for a while. (Too bad you can't buy them online here.) The first numbers of the lines were 1, 2, 3, 4 5, although not in that order. It's a choose 5 out of 39 game and the numbers in a line are printed out in increasing order, standard stuff.

What are the odds of getting 5 quick picks like that