If $Y_n$ is 1 or 0 depending on whether the $n$th ball drawn in a Polya urn scheme is red or not, then the variables $Y_1, Y_2,\ldots$ are exchangeable. It is shown for a generalized class of urn models that no other scheme gives rise to exchangeable variables unless the $Y_n$ are either independent and identically distributed, or deterministic (that is, all of the $Y_n$'s have the same value with probability 1).
Bruce M. Hill. David Lane. William Sudderth. "Exchangeable Urn Processes." Ann. Probab. 15 (4) 1586 - 1592, October, 1987. https://doi.org/10.1214/aop/1176991995