It’s been a closely followed competition on Greatest Hits Radio and like the distracting adverts, this post will be equally off-topic. It did, however, let me try out some ChatGPT assisted pondering and I wanted to see how my ‘logic’ stood up to the lure of quarter million daily prize pots from the Bauer / Planet Radio group of radio stations.
Can GPT help us make better decisions? Now I’ll be the first to disclaimer this by saying that these numbers are rough and, possibly in the case of GPTs data, plain false. Please check and do these calculations yourself for more accurate information; whilst I believe GPT can help us build the framework for better arguments, this needs to be done with a layer of ‘verification’ to check our homework.
So What are my Odds?
Rajar (RAJAR) provides quarterly info on listener ratings for radio in the UK. Whilst the BBC radio network still represents about 50% of all listeners in the UK, the group of stations under Bauer media group looks like about 10% so I passed this info into our friend GPT (as it has no stats beyond 2020) – we had to make a couple of assumptions but this was its summary of the competition;
- The total number of radio listeners in the UK is approximately 55.9 million.
- A competition is running on a popular group of radio stations that represent up to 10% of the total listenership, reaching approximately 5.59 million listeners.
- Based on the estimate that 36% of the UK population participates in paid competitions or lotteries, we can infer that around 2.01 million listeners from the network are likely to enter the competition.
- The entry fee for the competition is £2.
Winning Odds: Since the total number of entrants is not known, it is difficult to determine the precise odds of winning the £250,000 prize. However, with 2.01 million participants and a single prize, the odds are 1 in 2.01 million.
Revenue Generation: With an entry fee of £2 per participant, the network stands to generate approximately £4.02 million in revenue from applicants. This revenue can contribute to supporting the network’s operations, programming, and future competitions.
Now for some context
I asked more generally about the odds for the UK national lottery and finally I asked for some examples of probabilities that are equally similar to the chance of winning either (as both cost £2 to enter).
Roughly a 1 in 2 million chance:
- Being struck by lightning in your lifetime (source: National Weather Service).
- Being accepted into the Harvard University undergraduate program (historically, the acceptance rate has been below 5%).
- Winning a Nobel Prize in Physics, Chemistry, or Physiology/Medicine.
- Becoming a professional musician and achieving mainstream success with a hit song or album.
- Winning a ‘Greatest Hits Radio’ competition
Roughly a 1 in 45 million chance:
- Becoming a professional athlete in a major sport (e.g., football, basketball, soccer, etc.).
- Winning an Olympic gold medal in certain events.
- Being dealt a royal flush in a five-card poker hand (without drawing additional cards).
- Winning the UK National Lottery
There is a slight variation in this competition to others, in that it allows you to enter multiple times per day which I have ignored as it is impossible to know the probability without the exact number of entries.
However if we were to assume the odds were to average out to be the same 1 in 2 million, whilst each entry would be cheaper, the total expenditure and elapsed time won’t be favorable with more entries per day in any meaningful way:
Number of Entries | Cost per Entry | Total Expenditure per day | Total Expenditure | Number of Days Elapsed |
1 | £2.00 | £2.00 | £4,000,000 | 2,000,000 |
4 | £1.00 | £4.00 | £2,000,000 | 1,000,000 |
20 | £0.50 | £10.00 | £1,000,000 | 500,000 |
60 | £0.34 | £20.40 | £680,000 | 340,000 |
In conclusion and on average, you would need to enter the competition over 2 million times and spend approximately £4 million before you would win the £250,000 prize fund.
Now, the average human lifespan varies across different countries and populations, however according to the World Health Organization, the global average life expectancy at birth was around 73 years (in 2019). Average human lifespan in days ≈ 73 years * 365.25 days/year. That’s 26,723 days or in other words;
It would take approximately 75 lifetimes to win this competition.
So whilst the competition odds of winning look great compared to something like the national lottery, when viewed in real-world terms, just as with most competitions, the probability is still incredibly low. Meanwhile, the competition hosts always come out better off, in this example it looks like Bauer Media Group are making upwards of £4 million every single day from competition entries.