Instead of generating a random number, use a randomizer to pick one of ten embedded data blocks with the recode and choice text. Here is an example with 2 embedded data blocks:
Then pipe randRecode and randChoice into JavaScript, parse randChoice with split() and then use randRecode to choose the left or right string.

Ok, great. Thanks for the tip. Can you also provide me with the JS code? I'm a novice to JS and I've no clue how to use the split function.

https://www.qualtrics.com/community/discussion/comment/27105#Comment_27105var rcArr = "${e://Field/randChoice}".split("||QBipolarDelim||");

As a follow-up: I would like to then use the decision of the participant (A or in a randomly drawn decision situation (1-10) and calculate his prize in that lottery.
To do so, I need another random draw. Either drawing I or II with different probabilities (depending on the randomly drawn decision situation 1-10) or drawing 1 - 10 in which e.g. (decision situation 2) 1 and 2 represent I and 3-10 represent II.

I got the first bit, the random draw of a decision situation:
We randomly drew decision number ${e://Field/randRecode}, in which you selected lottery ${e://Field/randChoice}
With the JS code looking as follows:
var rcArr = "${e://Field/randChoice}".split("||QBipolarDelim||"); 
Yet, as you see in the screenshot, the random decision number is not followed by the correct description text (needs to be linked) and I don't know how to display the actual decision of the participant (A or B/left or right).
Any ideas how to link randRecode and randChoice and how to display randChoice and not the descriptive text?

https://www.qualtrics.com/community/discussion/comment/27231#Comment_27231rcArr is an array where rcArr[0] is the left label and rcArr[1] is the right label. randRecode is the answer selected where 1 is left and 2 is right (you could recode them to 0 and 1 to match the rcArr indices).
To show what they selected you need some html and JS.
html where you want to pipe the selected choice text:

JS:
jQuery("#choiceText").html(rcArr[parseInt("${e://Field/randRecode}")-1]);
If you want to pipe the random row number, you need to add another field to your embedded data blocks (e.g., randRow = 1).