Basically what it says on the tin. What do you think of replacing critical hits on the d20 with exploding* damage dice?
*For those unfamiliar with the term, it means if you roll the highest number possible on the damage die, you get to add another die. If that additional die is the maximum possible roll, then you add another die until you fail to roll the highest number on the die.
I'm assuming you mean replacing crits with exploding damage dice on all damage rolls.
This wonderful blog shows that an exploding fair die deals n/(n-1) times as much damage, where n is the number of sides.
In the games I've played, the exclamation point is used to indicate an exploding die.
1d4 = 2.5 avg
1d4 /w crits = 2.5 * 0.95 + 2.5 * 2 * 0.05 = 2.625 avg
1d4! = 2.5 * 4/3 = 3.33 avg
Result: +0.705 (+26%)
1d6 = 3.5 avg
1d6 /w crits = 3.5 * 0.95 + 3.5 * 2 * 0.05 = 3.675 avg
1d6! = 3.5 * 6/5 = 4.2 avg
Result: +0.525 (+14%)
1d8 = 4.5 avg
1d8 /w crits = 4.5 * 0.95 + 4.5 *2 * 0.05 = 4.725 avg
1d8! = 4.5 * 8/7 = 5.14 avg
Result: +0.415 (+8.8%)
1d10 = 5.5 avg
1d10 /w crits = 5.5 * 0.95 + 5.5 * 2 * 0.05 = 5.775 avg
1d10! = 5.5 * 10/9 = 6.11 avg
Result: +0.335 (+5.8%)
1d12 = 6.5 avg
1d12 /w crits = 6.5 * 0.95 + 6.5 * 2 * 0.05 = 6.825 avg
1d12! = 6.5 * 12/11 = 7.09 avg
Result: +0.265 (+3.9%)
2d6 = 1d6 + 1d6 = 7 avg
2d6 /w crits = 1d6 crit + 1d6 crit = 7.35 avg
2d6! = 1d6! + 1d6! = 8.4 avg
Result: +1.05 (+14%)
And, with Great Weapon Fighting Style, which is complicated because the dice stop being fair:
1d12 /w GWF = 7.33 avg
1d12 /w GWF & crits = 7.33 * 0.95 + 7.33 * 2 * 0.05 = 7.70 avg
1d12! /w GWF ~= 8.1 avg (calculated with a script and a pseudorandom number generator at 100,000 samples)
Result: ~+0.40 (+5.2%) (~+1.6 over base 1d12)
2d6 /w GWF = 8.33 avg
2d6 /w GWF & crits = 8.33 * 0.95 + 8.33 * 2 * 0.05 = 8.75 avg
2d6! /w GWF ~= 10.7 avg (calculated with a script and a pseudorandom number generator at 100,000 samples)
Result: ~+1.95 (+22%) (~+3.7 over base 2d6)
I'm assuming here that exploded dice can also be re-rolled on a 1 or a 2 (i.e., if you explode a die and then roll a 1 or a 2 on it, you can reroll that die once), and that re-rolls can still explode (i.e., if you reroll a 1 into a 6, it explodes). It'd be somewhat less significant if they don't do these things, but it will be less across the board. This is as powerful as you can make GWF and exploding dice, however, so it's a good upper bound.
You'd have to figure out what to do with abilities that use the crit rule (Great Weapon Master, Half-Orc and Barbarian bonus damage dice, Champion Fighter increased crit range, etc.).
You'd also have to decide if you want spells and sneak attack to explode.
Actual bottom line is that there's not much change, except 2d6 weapons look
much better than 1d12 weapons.