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No Game No Life pledge 4:

As long as it doesn't violate pledge 3, anything may be bet, and any game may be played.

  1. What happens when we delete the hypothesis (aka assumption) 'As long as it doesn't violate pledge 3' ?

Of course, if we delete the hypothesis, then we might as well delete the 4th pledge altogether. Thus, pledge 4 may be restated:

Anything may be bet, and any game may be played unless it violates pledge three.

I guess my question may be rephrased to ask for (counter)examples of bets or games that would violate pledge 3.

  1. I actually feel there's some

This might be resolved by question 1, but if not, then what's going on?

Pledge 4 actually seems to point out that the 'game' and that which players bet in pledges 2 and 3 are kinda not quite defined at least in terms of the scope. I mean, what's the scope of the games or that which players bet? It seems pledge 4 is precisely defining the scope, but pledge 4 refers to pledge 3. My understanding is:

Pledge 2: All conflict in this world will be resolved through games, where games are defined in scope in pledge 4.

Pledge 3: In games, each player will bet something that they agree is of equal value, where games and that which players bet are defined in scope in pledge 4.

Pledge 4: The scope of games and that which players bet is that which does not violate pledge 3.

What am I misunderstanding?

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The pledges were created by Tet in order to stop the violent wars in Disboard, while also providing a formal way for the races to compete with each other.

The pledges in question as stated in the wiki are:

Third Pledge: In games, each player will bet something that they agree is of equal value.

Fourth Pledge: As long as it doesn't violate pledge three, anything may be bet, and any game may be played.

So the 4th pledge states that anything can be wagered, while the 3rd one makes certain that the wagered items are agreed to be of equal worth by both parties involved.

The lack of the third pledge would lead to extremely unbalanced bets, where the challenged party can wager something of very little value, or disagree to the game entirely. This would make it hard for the challengers to gain significant resources to overtake other races.

Considering that the pledges are aiming to stop violence, unbalanced bets would lead to further disagreements and the races would turn violent instead of playing a game. Hence, the third pledge is necessary to maintain fairness.

Now, the 4th pledge then mentions that as long as the items are considered to be equal in value (i.e. does not violate Pledge 3), they may be anything. Considering that the Ten Pledges are always taken in conjunction, it is indeed redundant to reiterate that Pledge 3 should not be violated. However, this does not lead to any major errors as far as I can see. It is just a case of repeating something that is already being ensured.

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Let's suppose pledge 3 doesn't exist. Person A challenges person B to a game. Person B decided the rules as they are the challenged party. Person B decides that if he/she wins, person A must give him/her everything they have. If person A wins, person B must give him/her their glove. Person A objects, as they don't even want a glove. Person B states that they can't drop out as they have already issued the challenge.

Suppose pledge 4 didn't exist; someone could say that they can't bet something, because it's a part of who they are.

With the absence of pledge 3 it would be impossible to gain anything by challenging someone. Pledge 4 makes psychological bets such as "becoming dog for the day", betting your existence and betting your memories possible. I'm not sure what you mean by "delete the hypothesis (aka assumption)", but I hope I've answered your question.

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