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In basic D&D Clerics' primal Stat is wisdom. But it does not effect neither turn undead nor their spells. So why do they need a high wisdom? Just for the exp bonus?

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In older D&Ds, not everything is tied tightly into things written on your sheet. Assuming that it works like modern D&D and that you can bring in modern D&D assumptions about what matters most—what's on your sheet—is a common mistake that can lead to de-optimising a character. There are mechanics that only appear within the adventure notes, there are ad hoc situations that will be judged by eyeballing the PCs' stats or testing them with a d20 roll, there are monster abilities that trigger off PC stats.

Your stats, therefore, should not be considered merely a source of bonuses. Your stats are what you are capable of, just yourself, when all of your abilities, gear, spells, and friends are missing, damaged, irrelevant, or stripped away by misfortune or misadventure. They are what lies between you and the unknown when you're in dire straits. A cleric is known for their wisdom, so a less-wise cleric will always be at a slight disadvantage, but whether that matters and makes any difference when the chips are down is something you can't know until you're tested by adventure.

So yeah, you don't "need" a Wisdom of 15 compared to a Wisdom of 13, but that's not the point. When you write down 13, you are saying "I am not as wise as the next cleric." Similarly, a lower strength means you're not as strong. There's no such thing as optimising here, just making a statement and then living or dying by it. You're making trade offs, with neither being better than the other. After all, you can't optimise for what you don't know, and old D&D is all about venturing into the unknown to see if you can come back better off. You can optimise for the short-term mechanical bonuses that are immediately obvious, but that's not wise, that's just making a wager that you won't need the other stat more and higher later.

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First, your question doesn't really fit the mindset that B/X embodies. Asking:

So why do they need a high wisdom?

is incorrect. Clerics benefit from a high wisdom but there is no reason in B/X you can't run a character with a wisdom of 3 as a cleric. You'll just advance slower than other clerics.

3.x and on have been games about playing optimized characters much more than earlier editions although the trend started with AD&D where the four classes needed a minimum of 9 in their prime requesites and gained special class related advantages (such as extra clerical spells). In fact, if you go to OD&D you get the following bit:

Name: Xylarthen Class: Magic-User

Strength: 6 Intelligence: 11 Wisdom: 13

Constitution: 12 Dexterity: 9 Charisma: 0

Gold Pieces: 70 Experience: Nil

This supposed player would have progressed faster as a Cleric , but because of a personal preference for magic opted for that class.

As SevenSidedDie has pointed out a lot of ad hoc tests of attributes were common when B/X was current such as roll a d20 or 3d6 under a stat.

The advantage of this is you can play a character against type without a mountain of mechanical penalties. A B/X version of Peter the Hermit, a very unwise holy man who was very influential in the First Crusade, would just advance a bit slower than a B/X version of the Buddha. A 3.x version of Peter would be unplayable.

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I just browsed both books and although later editions have rules for primary attributes, the classic D&D rules seem to have only the experience bonus for high attributes. Neither turning, nor spellcasting, nor maximum spell level nor anything else is changed by high (or low) wisdom.

UPDATE:

I seem to have overlooked the character sheet where it says that wisdom modifier is added to the saves against spells, wands and staves. I have browsed the books again but did not find it in the text. I do have a German translation though, so maybe it's an error.

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Pretty disappointing. So since my wisdom is 15 and my strength is 12, it would be wise to lower my wis to 13 and enhance str to 13, wouldn't it? So I'd get a higher to hit and damage mod without lowering my % of exp. –  NetHacker Jun 17 at 14:45
    
(it's Moldvay's Basic) –  NetHacker Jun 17 at 14:47
    
@NetHacker just looked at an old character sheet, see the update. –  nvoigt Jun 17 at 15:57
    
I knew that, yes, but it is not a cleric special feature. –  NetHacker Jun 17 at 16:39
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Well, for one, you cannot drop your wisdom to raise your strength as a cleric. You can only trade to increase your PR. –  HerbN Jun 17 at 19:57
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