Does not matter. Your expected return from sticking is the same as your expected return from twisting.
3 out of 4 of the numbers on the cards are even. Of those even numbers, only 1 out of 3 are low numbers (good for twisting) while 2 out of 3 are high numbers (bad for twisting). So, if we twist all cards, 1/3 are good twists and 2/3 are bad twists.
If we know nothing about the odds and evens, just that twisting (I prefer "flipping"
either pays twice as much or half a much as is shown on the face, then the expected return from twisting is ((2 * facevalue) + (1/2 * facevalue)) / 2 = (1 + 1/4) * facevalue = 5/4 of facevalue. So, over time, you will get 25% more from always flipping the card if we know nothing else.
But we know that the likelihood of a good twist is 1/3 and the likelihood of a bad twist is 2/3 so our expected return from always flipping is 1/3 * 2 * facevalue + 2/3 * 1/2 * facevalue = 2/3 * facevalue + 1/3 * facevalue = facevalue.