Maximum initiative possible (5e Optimized Character Build)
start by choosing the harengon race for the hair trigger ability (lets you add your proficiency bonus to your initiative) and to get a +1 bonus in three different stats, we will be choosing intelligent's, wisdom, and dexterity.
then, using the point by system, make your wisdom 15, your intelligent's 15, and your dexterity 15 (with racial bonuses they will all become 16's). then, get four levels in war magic wizard subclass(lets you add your intelligent's to initiative) and four levels in gloom stalker ranger(lets you add your wisdom to your initiative), then put the rest of your levels in fighter(probably battle master subclass for the "ambush" ability but we will not be using that right now). You will now have a +13 to initiative and get to choose 6 feats. For your feats you will want to choose alert for the +5 to initiative and the rest should be spent to increase your wisdom and dexterity to 20 then your intelligent's to 18. finally, cast gift of Alacrity to add a d8 to your initiative. so in the end your stats will be:
str 8(-1)
dex 20(+5)
con 8(-1)
int 20(+5)
wis 18(+4)
cha 8(-1)
hair trigger +4
gift of alacrity 1d8 (average 4.5) +1 min
alert +5
total: +24 (max +31) (max roll 51). And that is the highest possible (long lasting) initiative you can have without outside assistance(or magic items).
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