There are numerous problems where the -0827 model succeeds in solving a problem that the -0801 model fails to solve. That makes -0827 a more capable model. There is one case where the -0827 model succeeds but fairly reliably goes into stuttering mode (repeats output). This is the problem statement:
A coffee can contains some black beans and white beans. The following process is to be repeated as long as possible:
Randomly select two beans from the can. If they are the same color, throw them out, but put another black bean in (enough extra black beans are available to do this). If they are different colors, place the white one back into the can and throw the black one away.
Executing a step in this process reduces the number of beans in the can by one. Repetition of this process must terminate with exactly one bean in the can, for then two beans cannot be selected.
There are 75 beans in the can when we start, 40 white and 35 black. What is the probability of the last remaining bean being white?