Table 2.

Comparison of conditional allocation probabilities of the BUD and PBD (Three-treatment unbalanced allocation w₁:w₂:w₃=1:2:2 Block size = 10)

i	Randi	Block urn design (BUD)							Permuted block design (PBD)
		Ni-1,1	Ni-1,2	Ni-1,3	ki-1	Pi1	Pi2	$T_i^{\&}$	Ni-1,1	Ni-1,2	Ni-1,3	Pi1	Pi2	$T_i^{\&}$
1	0.8290	0	0	0	0	2/10	4/10	3	0	0	0	2/10	4/10	3
2	0.4852	0	0	1	0	2/9	4/9	2	0	0	1	2/9	4/9	2
3	0.7767	0	1	1	0	2/8	3/8	3	0	1	1	2/8	3/8	3
4	0.0069	0	1	2	0	2/7	3/7	1	0	1	2	2/7	3/7	1
5	0.9145	1	1	2	0	1/6	3/6	3	1	1	2	1/6	3/6	3
6	0.5337	1	1	3	0	1/5	3/5	2	1	1	3	1/5	3/5	2
7	0.7652	1	2	3	1	2/9§	4/9§	3	1	2	3	1/4	2/4	3
8	0.1473	1	2	4	1	2/8	4/8	1	1	2	4	1/3	2/3	1
9	0.2346	2	2	4	1	1/7	4/7	2	2	2	4	0/2	2/2	2*
10	0.0684	2	3	4	1	1/6	3/6	1	2	3	4	0/1	1/1	2*
11	0.9372	3	3	4	1	0/5	3/5	3	2	4	4	2/10§	4/10§	3
12	0.8102	3	3	5	1	0/4	3/4	3	2	4	5	2/9	4/9	3
13	0.6827	3	3	6	1	0/3	3/3	2*	2	4	6	2/8	4/8	2
14	0.3290	3	4	6	2	1/7§	4/7§	2	2	5	6	2/7	3/7	2
15	0.6940	3	5	6	2	1/6	3/6	3	2	6	6	2/6	2/6	3
16	0.6481	3	5	7	2	1/5	3/5	2	2	6	7	2/5	2/5	2
17	0.9090	3	6	7	3	2/9§	4/9§	3	2	7	7	2/4	1/4	3
18	0.4940	3	6	8	3	2/8	4/8	2	2	7	8	2/3	1/3	1
19	0.3266	3	7	8	3	2/7	3/7	2	3	7	8	1/2	1/2	1
20	0.1690	3	8	8	3	2/6	2/6	1	4	7	8	0/1	1/1	2*
21	0.4618	4	8	8	4	2/10§	4/10§	2	4	8	8	2/10§	4/10§	2
22	0.4423	4	9	8	4	2/9	3/9	2	4	9	8	2/9	3/9	2

^&T_i = iif (Rand_i < P_i1, 1, iif (Rand_i < (P_i1 + P_i2), 2, 3))

^*: Deterministic assignment.

^§The active urn is updated by returning balls from the inactive urn.