Regulation

masonic

mebu60 said:

Interesting! And that's on the current prize matrix which is considerably more generous than most of the previous four years in question. 

Yes, but the odds of winning a prize have been the same for ages, they've just altered the distribution of prizes, with more of the higher prizes available and fewer £25 prizes in recent months. I guess that would make it a little less likely for two holdings to generate the same winnings and reset the streak, so the odds of a winning streak may be a little longer when including historic draws.

Incidentally, as I've generated the data as a side effect of this experiment, the median winnings for a £50k holding were determined to be 4.1% (equivalent to 5.12% taxed at BR) with IQR of 3.4-4.9% (4.3-6.1% taxed at BR).

eskbanker

masonic said:

mebu60 said:

Interesting! And that's on the current prize matrix which is considerably more generous than most of the previous four years in question. 

Yes, but the odds of winning a prize have been the same for ages, they've just altered the distribution of prizes, with more of the higher prizes available and fewer £25 prizes in recent months.

Not really, there have been quite a few changes over the period under discussion:

September 2023		21,000 to 1
August 2023		22,000 to 1
October 2022		24,000 to 1
June 2022		24,500 to 1
December 2020		34,500 to 1
December 2017		24,500 to 1

https://www.nsandi.com/historical-interest-rates

masonic

eskbanker said:

masonic said:

mebu60 said:

Interesting! And that's on the current prize matrix which is considerably more generous than most of the previous four years in question. 

Yes, but the odds of winning a prize have been the same for ages, they've just altered the distribution of prizes, with more of the higher prizes available and fewer £25 prizes in recent months.

Not really, there have been quite a few changes over the period under discussion:

September 2023		21,000 to 1
August 2023		22,000 to 1
October 2022		24,000 to 1
June 2022		24,500 to 1
December 2020		34,500 to 1
December 2017		24,500 to 1

https://www.nsandi.com/historical-interest-rates

So it has! I even updated the odds in my simulator script last month while adding the new prize distribution without even registering that I'd done it, doh.

At odds of 34,500 to 1, the chance of avoiding winning nothing with a full holding over those 18 draws is about 0.8%, whereas at the most recent odds it's 17% That's just one of the ways a streak could be lost. So it seems at first blush to be a lot less likely for one person to consistently beat another under the longer odds, and probably worth simulating for comparison...

Using the 34,500 to 1 odds and prize information from https://web.archive.org/web/20210120005936/https://www.nsandi.com/get-to-know-us/monthly-prize-allocation I've rerun the analysis and the longest streak in 100,000 draws under that regime was only 21, while there were only 26 streaks of at least 18 months, making the chance of getting through that period alone without losing the streak close to 4,000 to 1 (i.e. considerably less likely than a 50 win streak going forward with current odds). This is largely due to the probability of the two people getting the same winnings rising from 7.6% to a whopping 24% (combination of more chance of winning nothing and much greater chance of winning £25 vs any other prize [£25 prizes made up almost 98% of the prizes available vs 40% of the prizes now being £50 and another 40% being £100]).

As a very crude approximation of the effect that might have on the OP's scenario, taking the 5 in 100,000 of a twenty month streak in combination with the 765 in 100,000 streaks of a thirty month streak under the current odds and prize matrix, would give odds of order 10^6 to 1, so beginning to look a lot less believable. That said, in the context of the likely number of people playing with full holdings in a position to compare results and post about them here...