The 4th girl in the poker mini game knows our hand. She will immediately fold if we have a good hand and immediately fold if we swap for a good hand so its impossible to bet big without pure luck because she knows our hand. The best strategy for beating her I found was just spam clicking next until I got lucky.

I finally managed to beat her. For anyone else trying to complete it like I was the best strategy is to press next until you can swap cards and try to swap for a good hand. Then she will instantly fold. If she allows you to bet high she has already won. She won't let you bet high if you have the better hand. Unfortunately, this is the only consistent way to beat her at the moment. You can try to bet high on the first hand, but you are required to get a swap that beats her hand or its a guaranteed loss. Sometimes it is impossible to win if she draws the golden card.