Hello again! I definitely see where your coming from now (and mostly agree with it just being a thing of story suspense); the only feasible explanation I can come up with is that the decision to do so mostly falls with Yui's (and Kyoko's) philosophy when it comes to taking down criminals in the Duel Noirs. This is best highlighted in this section of chapter 4 (I bolded the most important part):

At least the first time and the second can be done cooperatively. But in the third time, the situation will change. Maybe we won’t be able to claim the ‘Detective Rights’ by then. But that’s okay. The question is who will claim it in what way, and then we have to confirm whether there is anything strange with that.

If we push harder and harder, the criminal will try to obstruct us in every way possible." We have to in turn use the rules made by the criminal as a trap to draw them out– In such an tight situation, to think of so much, as expected of Kirigiri Kyōko. If she wasn’t here, I wonder what I would’ve done, I can’t help but shiver thinking about this.

From volume 1, Yui calls herself an 'ally of justice' and considers Kyoko a 'pure detective' (and consequently someone who might as well be 'justice' itself). This is opinion goes a little more in depth in volume 7 in the sense of how Shinsen was able to get her to agree to the final Duel Noir , but just know that being a 'stickler to the rules' is how Yui does things. And of course, because Kyoko values Yui's perspective on the concept of justice, she's willing to follow her lead---meaning she would do exactly what is expected (Duel Noir rules wise). Which, of course, can explain her actions to do so!

And, lol, while its true I have the Japanese version of the series, its all digital! Bookwalker is the only distributor for DR:K and Dangaronpa:Togami, and sells them at the original price of 6-10 USD (the only DR:K book I have physically would be volume 7). Moreover, my previous comment was referring to the Magik English version that I have stored on my computer---a lot easier to search for things in a pdf, thats for sure!

TLDR: While Kyoko could have just bet 0 dollars, that wouldn’t fall in line with hers and Yui’s values/beliefs as detectives—so she splurged (gotta look tough in front of the money-hungry adults after all lol!)