Seemingly simple loop

[BashBedlam]

Here's one way to go about it but if you are going to control input throughout the whole game, I would consider writing a function that would accept a prompt and list or tuple of acceptable answers.

name = input("Hello, What is your name? ")
player = name
print ("Would you like to play a game " + player + "?")
prompt1 = 'BashBedlam was here.'
while prompt1 not in ('yes', 'no', 'y', 'n') :
	prompt1 = input ("yes or no?").lower ()
	if prompt1 == "yes":
		print("let's play!")
	elif prompt1 == "no":
		print("You're no fun! Goodbye.")