Let’s use math instead of just bickering about feelings, kids.
The board is 8x8, there are 64 gems. A 6x6 area (36 gems) will explode the full 9 gems. The non-corner 24 gems along the border will explode 6 gems. The 4 corner gems will explode 4.
So the 9-gem case happens 56% of the time and explodes 14% of the board. On average, 7.56 gems or 11.8% is exploded at the start of a round. That already makes me itchy for the 4/5 match.
Let’s imagine the board having columns A-H and rows 1-8. If we imagine a 4-match spanning from, say, D3 to D6, we know one gem at D4 or D5 has to be in C or D in order to have the match setup. That means, roughly, 25 gems around its perimeter including the involved 4 gems could disrupt the match. So that’s close enough to 30 of our 64 gems, putting us at about a 46% chance of a vertical 4-match being disrupted.
Vertical 5-match is worse, it ends up being exactly 50%, as comfortable as I am using the word “exactly” here.
Horizontal matches are more of a nightmare in terms of probability. Imagine a 4-match set up with gems at {A1, B2, C1, D1}. If the explosion happens in any column from A through E, that match is disrupted. That’s 40/64 = 62.5% of all possible explosions. Ouch. For a horizontal 5 match in row 1, it gets worse. That’s 6 columns or 48 gems = 75% chance of disruption.
The probabilities per row are (floored, not rounding, sue me):
- 1: 0.625 | 0.75
- 2: 0.625 | 0.75
- 3: 0.546 | 0.656
- 4: 0.468 | 0.562
- 5: 0.390 | 0.468
- 6: 0.312 | 0.375
- 7: 0.234 | 0.281
- 8: 0.156 | 0.187
(These are slightly off because I forgot to account for a 3-gem hump around the offset if and only if it’s above the match. Deal. It’s worth about 2% for the lower 6 rows and I’m already throwing lots of error and estimation around.)
This is harder to read, here’s my takeaways:
- If you think 46% is “close enough” to 50%, 62% of all horizontal 5-matches are going to be disrupted at least 50% of the time.
- 50% of all horizontal 4-matches are going to be disrupted at least 50% of the time.
- A row 8 4 or 5 match is “close enough” to 15% if we’re conservative. That’s only 12.5% of all horizontal 4/5 matches.
So, breaking it all down:
- Vertical 4 and 5 matches are roughly 50% likely to be disrupted.
- Top row horizontal matches are more likely to be disrupted than not.
- Bottom-row horizontal matches are safest and will only be disrupted 15% of the time.
- On average, horizontal matches are something between 40% and 50% likely to be disrupted.
So technically explosions don’t “hurt more often than help”. But theoretically “they are almost equally likely to hurt as help, with a very strong bias towards not hurting horizontal matches towards the bottom rows, which are less than half of all possibilities”.
But.
I haven’t even started to try and model “What are the odds of a 4/5 match being FORMED by the explosion”. I don’t know what that case is, it’s probably too hard to model. But if you’re comfy with considering your odds at about 45% - 50% for “hurt”, and you think there’s even a 5% chance of “help” in the aftermath, then the overall odds of “explosion doesn’t hurt” and “explosion helps” together give you a positive outcome. Someone else can try to work that one out.