How to use if statements in a while loop?

I'm trying to compress all the if statements using a while loop but I don't know if there is a better way to do this. the program works without the while loop but I am just trying to make it shorter. I am new to Python please let me know if you think there is a better way to implement this.

value1=3
value2=3
value3=2
value4=4

#three same
while True:
    print("three same") 

    if value1 == value2 == value3 != value4:
        break
    elif value2 == value3 == value4 != value1:
        break

else: 
    print("not the same")

This is the code working without while loop (I just want to know if there is a way to avoid printing ("three same") twice)

value1=3
value2=3
value3=2
value4=4

#three same

if value1 == value2 == value3 != value4:
    print("three same")  
elif value2 == value3 == value4 != value1:
    print("three same")  

else: 
    print("not the same")