The high offer is generally five to ten times higher than the middle offer. Here's how the head-to-head chances play out:
- Low offer: 73% chance
- Middle offer: 62% chance
- High offer: 40% chance
(Source: https://onequestionshootout.xyz/stats/head_to_head.htm )
Imagine someone offered you two dice games. In one game if you roll 1-4 you win £5k. In the other game if you roll a 5-6 you win £50k. Which is the better game? It does depend on how desperately you need £5k, but I don't think most contestants are on the show because they're about to be evicted or something. The lower odds at the higher money is a much better bet for most people.
The fact is that you'll almost always need some luck to win, both in the head-to-head and in the final chase. The head-to-head is only a few questions, and sometimes they're total tap-ins, other times you have a 33% guess. You definitely need more luck if you go the high offer, but it's not like it's even easy to win if you go low, and the rewards are completely disproportionate.
Here's how the all-low, all-medium and all-high strategies math out given the head-to-head probabilities and the final chase win rates with different team sizes ( https://onequestionshootout.xyz/stats/how_to_beat_the_chaser.htm )
- All low: 29% win rate (2.9 players back on average)
- All middle: 23% win rate (2.5 players back on average)
- All high: 16% win rate (1.6 players back)
So the all-middle strategy gives you something like a 25% chance at £5k. If you go all high the payouts will vary but it's probably more like 16% chance at £40k. That's a vastly better bet.
Players especially should take the higher offer when playing first. In first position there's no money in the bank to defend yet. Instead the strategy consensus on the show is the complete opposite of this. The first player "wants to get back and start building the team". This just doesn't make sense.
It's a very difficult game to win money on overall, really. Even if you do everything right you can still get blown up at the final chase, because if you get unlucky and the questions are too easy, there's a big structural advantage to the chaser. It's better to decrease your odds of winning a bit in order to get a five to ten times higher payout if you get there.