Analysis of spans in 5/N and 6/N games

Reply #2

cottoneyedjoe — Wed, 23 Dec 2020 06:17:17 GMT

Here's how I found the 50-ish percentile. Let's take the 5/N game and fix N=60 like your Cash4Life example, ignoring the extra ball. There are 60 choose 5 = 5461512 different ticket combinations ignoring the extra ball. Half of 5461512 is 2730756.

In a 5/60 game, the span of a combo can be as small as 4, or as large as 59. What I did first is find the number of combos for each span from 4 to 59:

span of 4: 56 combinations

span of 5: 220 combinations

span of 6: 540 combinations

sp... [ More ]

Reply #1

GoogilyMoogily — Wed, 23 Dec 2020 02:22:37 GMT

With 974 Cash4Life draws since the last format change for real world data, a 5/60-4 game, the 50th percentile of the drawn numbers span (max - min, not the extra ball) is 41.

If one were to calculate the number of times a ball appears in positions 1 thru 5 for every possible combination, exclude the range that most closely gets to the 50th percentile, the span is 44.

How did you calculate your span

Analysis of spans in 5/N and 6/N games

cottoneyedjoe — Mon, 21 Dec 2020 06:11:41 GMT

For this post, the span of a combination is the difference between the largest and smallest numbers drawn. E.g., the Fantasy Five ticket 2-11-21-24-29 has a span of 27. In 5/N and 6/N style games, for a given N, I found a number K such that about 50% of the time (or as close to 50% as I can get) the span is at most K.

These findings are given below.

5/N games

span is max - min

N = 32: 49.402% chance span is at most 22

N = 33: 51.488% chance span is at most 23

N = 34: 47.098% ch... [ More ]