Twixt Commentator

Twixt Commentator — First Moves

Elo-adjusted expected-score residuals for board size 24.

This page shows how White's actual win rate compares to what Elo ratings would predict, for each first move, normalized to the upper-left quadrant of a 24×24 board.

Residual: White underperforms Elo ≈ expected White overperforms Elo stripes = <100 games thick stripes = <20 games

First Move Heatmap

	b, w	c, v	d, u	e, t	f, s	g, r	h, q	i, p	j, o	k, n	l, m
1, 24	b1 −8.8% 2.1% swap	c1 −8.1% 0.0% swap	d1 −14.7% 0.0% swap	e1 −12.4% 0.0% swap	f1 −16.7% 0.0% swap	g1 −23.5% 0.0% swap	h1 −13.6% 3.4% swap	i1 −4.1% 3.2% swap	j1 −4.2% 4.5% swap	k1 −13.6% 0.0% swap	l1 −13.4% 1.8% swap
2, 23	b2 −9.3% 0.9% swap	c2 −8.8% 3.6% swap	d2 −4.1% 3.2% swap	e2 −8.2% 7.2% swap	f2 −2.3% 9.5% swap	g2 −23.3% 5.9% swap	h2 −25.6% 4.5% swap	i2 −16.1% 6.3% swap	j2 −13.2% 0.0% swap	k2 −22.0% 0.0% swap	l2 −16.8% 4.0% swap
3, 22	b3 +1.8% 3.0% swap	c3 −0.7% 18.8% swap	d3 +1.4% 24.9% swap	e3 +0.8% 24.9% swap	f3 −1.6% 23.3% swap	g3 +0.4% 26.3% swap	h3 −1.6% 23.7% swap	i3 −6.8% 20.9% swap	j3 −7.9% 22.1% swap	k3 −9.1% 25.3% swap	l3 −0.8% 20.1% swap
4, 21	b4 +0.2% 4.8% swap	c4 +2.5% 29.0% swap	d4 +1.9% 38.8% swap	e4 +1.8% 42.8% swap	f4 +0.8% 44.6% swap	g4 +4.0% 47.0% swap	h4 −1.2% 37.3% swap	i4 +0.5% 34.8% swap	j4 −0.6% 28.7% swap	k4 −5.8% 27.7% swap	l4 −2.8% 20.1% swap
5, 20	b5 −3.4% 9.0% swap	c5 +2.6% 26.9% swap	d5 +2.1% 39.6% swap	e5 +0.9% 46.3% swap	f5 −2.3% 47.8% swap	g5 −0.6% 45.0% swap	h5 +0.5% 44.2% swap	i5 +1.0% 44.9% swap	j5 −1.5% 49.5% swap	k5 −1.0% 35.6% swap	l5 −10.4% 35.0% swap
6, 19	b6 +3.1% 38.2% swap	c6 +4.4% 29.1% swap	d6 +1.4% 44.5% swap	e6 −2.2% 48.3% swap	f6 −3.0% 49.9% swap	g6 −2.2% 49.4% swap	h6 +3.0% 54.1% swap	i6 −2.0% 49.1% swap	j6 −5.8% 49.5% swap	k6 −1.6% 40.9% swap	l6 −4.6% 46.1% swap
7, 18	b7 −2.3% 43.6% swap	c7 +3.6% 23.9% swap	d7 +1.8% 48.0% swap	e7 +0.2% 52.0% swap	f7 −3.3% 58.7% swap	g7 −4.3% 57.0% swap	h7 −1.7% 52.2% swap	i7 −3.5% 47.1% swap	j7 −8.1% 54.9% swap	k7 −0.2% 53.3% swap	l7 −5.3% 42.6% swap
8, 17	b8 −0.9% 16.7% swap	c8 +3.4% 26.4% swap	d8 +1.5% 45.1% swap	e8 −5.5% 51.6% swap	f8 −2.3% 53.8% swap	g8 −8.1% 57.2% swap	h8 −4.7% 53.8% swap	i8 −7.1% 52.5% swap	j8 −2.5% 56.7% swap	k8 −6.0% 60.3% swap	l8 −0.3% 46.9% swap
9, 16	b9 −0.9% 38.2% swap	c9 −2.0% 28.6% swap	d9 −1.2% 47.5% swap	e9 +7.9% 47.9% swap	f9 −2.1% 52.9% swap	g9 −7.2% 61.2% swap	h9 −5.0% 53.6% swap	i9 −3.8% 56.5% swap	j9 −4.7% 56.1% swap	k9 −2.6% 43.2% swap	l9 −1.8% 53.1% swap
10, 15	b10 −2.1% 13.3% swap	c10 +1.7% 24.7% swap	d10 −7.4% 42.5% swap	e10 −0.2% 40.2% swap	f10 −6.6% 54.2% swap	g10 −5.8% 58.5% swap	h10 −3.9% 57.1% swap	i10 −1.0% 52.1% swap	j10 −1.4% 48.0% swap	k10 −2.9% 45.0% swap	l10 −9.1% 50.0% swap
11, 14	b11 −9.9% 7.1% swap	c11 +4.2% 29.6% swap	d11 −6.0% 46.0% swap	e11 −5.7% 45.5% swap	f11 −6.9% 45.0% swap	g11 −1.5% 46.5% swap	h11 −6.3% 52.7% swap	i11 −2.5% 53.2% swap	j11 −5.5% 53.6% swap	k11 −5.5% 53.3% swap	l11 −10.3% 54.2% swap
12, 13	b12 +2.8% 25.5% swap	c12 +6.5% 29.7% swap	d12 +0.2% 51.5% swap	e12 −3.0% 48.4% swap	f12 −4.3% 51.3% swap	g12 −7.8% 54.3% swap	h12 −3.3% 52.1% swap	i12 −7.5% 55.1% swap	j12 −4.6% 56.4% swap	k12 −7.5% 54.3% swap	l12 −7.3% 58.0% swap

75,605 games included (board size 24, pegs > 7 and < 100, excluding forfeits and draws). Elo ratings use K = 32, computed from all size 24 Twixt history. Hover a cell for details.

How to interpret the above table:

Blue areas are bad first moves, for two possible reasons: either the position is inherently weak, or too strong and gets swapped. It seems clear that all of rows 1 and 2 (and 23 and 24) are just too weak. But there is also a large swath of blue in the middle of the board, approximately the entire central octagon and about one link distance around its perimeter. These spots are generally considered too strong, and strong players swap them.

This does not mean white areas are neutral in any absolute sense. This is a zero-sum statistic. It might not seem zero-sum because of all the blue, but the moves are not evenly distributed. For example, d3 has been historically a very popular first move.

The pink areas are likely good first moves, but I must give some disclaimers. Some spots do not have much data on them, such as e9. Also, for the same reason that some blue spots may be as blue as they are because they are too strong and swapped more often than not, some spots are redder than they would be if they were swapped more often. But it's not only about the risk of your opponent swapping; it also depends on players' general sense of opening moves. For example, according to this table, a move like c12 looks like one of the best on the board, but it is also possible that people just don't have a good sense of where to place the second peg. And when you are deciding where to place the first peg, that is a key consideration: do you have an idea where you would place the second peg if your opponent swaps? Or if you are in the position to swap, do you think your opponent knows where to place the second peg?

Ranked by Residual

Click any column header to sort.

#	Move	Games	Win Rate	Expected	Swap %	Residual ▼
1	e9	71	54.9%	47.0%	47.9%	+7.9%
2	c12	1,119	61.7%	55.2%	29.7%	+6.5%
3	c6	707	58.3%	53.9%	29.1%	+4.4%
4	c11	179	55.9%	51.7%	29.6%	+4.2%
5	g4	1,592	60.4%	56.4%	47.0%	+4.0%
6	c7	364	62.9%	59.3%	23.9%	+3.6%
7	c8	611	54.7%	51.3%	26.4%	+3.4%
8	b6	152	46.7%	43.6%	38.2%	+3.1%
9	h6	344	55.8%	52.8%	54.1%	+3.0%
10	b12	141	51.8%	48.9%	25.5%	+2.8%
11	c5	1,546	53.3%	50.7%	26.9%	+2.6%
12	c4	3,019	55.8%	53.4%	29.0%	+2.5%
13	d5	1,109	48.2%	46.0%	39.6%	+2.1%
14	d4	3,704	53.3%	51.5%	38.8%	+1.9%
15	e4	3,453	50.8%	49.0%	42.8%	+1.8%
16	d7	415	55.2%	53.4%	48.0%	+1.8%
17	b3	66	48.5%	46.7%	3.0%	+1.8%
18	c10	162	61.1%	59.4%	24.7%	+1.7%
19	d8	224	52.2%	50.8%	45.1%	+1.5%
20	d3	14,298	57.1%	55.7%	24.9%	+1.4%
21	d6	1,060	49.3%	48.0%	44.5%	+1.4%
22	i5	316	50.9%	49.9%	44.9%	+1.0%
23	e5	1,949	47.6%	46.7%	46.3%	+0.9%
24	f4	2,711	47.5%	46.7%	44.6%	+0.8%
25	e3	5,306	55.7%	54.9%	24.9%	+0.8%
26	h5	1,214	44.3%	43.8%	44.2%	+0.5%
27	i4	379	60.2%	59.7%	34.8%	+0.5%
28	g3	452	51.5%	51.1%	26.3%	+0.4%
29	b4	146	54.8%	54.6%	4.8%	+0.2%
30	e7	223	48.9%	48.7%	52.0%	+0.2%
31	d12	239	48.5%	48.4%	51.5%	+0.2%
32	e10	82	48.8%	48.9%	40.2%	−0.2%
33	k7	180	40.6%	40.8%	53.3%	−0.2%
34	l8	311	45.7%	45.9%	46.9%	−0.3%
35	g5	664	46.1%	46.7%	45.0%	−0.6%
36	j4	181	53.0%	53.7%	28.7%	−0.6%
37	c3	1,151	47.0%	47.7%	18.8%	−0.7%
38	l3	244	42.6%	43.4%	20.1%	−0.8%
39	b9	55	25.5%	26.3%	38.2%	−0.9%
40	b8	54	55.6%	56.5%	16.7%	−0.9%
41	k5	222	41.0%	42.0%	35.6%	−1.0%
42	i10	305	36.1%	37.1%	52.1%	−1.0%
43	d9	118	50.0%	51.2%	47.5%	−1.2%
44	h4	679	57.1%	58.4%	37.3%	−1.2%
45	j10	638	41.7%	43.1%	48.0%	−1.4%
46	j5	307	49.2%	50.7%	49.5%	−1.5%
47	g11	114	40.4%	41.9%	46.5%	−1.5%
48	f3	2,418	54.7%	56.3%	23.3%	−1.6%
49	h3	224	49.6%	51.2%	23.7%	−1.6%
50	k6	186	50.0%	51.6%	40.9%	−1.6%
51	h7	232	39.2%	41.0%	52.2%	−1.7%
52	l9	254	41.7%	43.5%	53.1%	−1.8%
53	c9	119	53.8%	55.8%	28.6%	−2.0%
54	i6	269	48.3%	50.4%	49.1%	−2.0%
55	f9	87	41.4%	43.5%	52.9%	−2.1%
56	b10	15	26.7%	28.8%	13.3%	−2.1%
57	g6	429	45.5%	47.6%	49.4%	−2.2%
58	e6	414	44.7%	46.9%	48.3%	−2.2%
59	f8	145	43.4%	45.7%	53.8%	−2.3%
60	f2	42	38.1%	40.4%	9.5%	−2.3%
61	b7	94	52.1%	54.4%	43.6%	−2.3%
62	f5	930	46.6%	48.9%	47.8%	−2.3%
63	i11	216	34.3%	36.7%	53.2%	−2.5%
64	j8	194	50.5%	53.0%	56.7%	−2.5%
65	k9	229	41.0%	43.6%	43.2%	−2.6%
66	l4	179	38.5%	41.4%	20.1%	−2.8%
67	k10	278	35.3%	38.1%	45.0%	−2.9%
68	e12	95	45.3%	48.3%	48.4%	−3.0%
69	f6	834	41.4%	44.4%	49.9%	−3.0%
70	f7	269	40.1%	43.4%	58.7%	−3.3%
71	h12	261	35.2%	38.6%	52.1%	−3.3%
72	b5	122	47.5%	50.9%	9.0%	−3.4%
73	i7	172	39.5%	43.0%	47.1%	−3.5%
74	i9	1,864	37.1%	40.9%	56.5%	−3.8%
75	h10	156	34.0%	37.9%	57.1%	−3.9%
76	i1	31	25.8%	29.9%	3.2%	−4.1%
77	d2	62	38.7%	42.8%	3.2%	−4.1%
78	j1	44	31.8%	36.0%	4.5%	−4.2%
79	f12	115	46.1%	50.4%	51.3%	−4.3%
80	g7	407	37.8%	42.2%	57.0%	−4.3%
81	j12	335	34.3%	38.9%	56.4%	−4.6%
82	l6	319	39.5%	44.1%	46.1%	−4.6%
83	j9	346	38.4%	43.2%	56.1%	−4.7%
84	h8	353	44.2%	48.9%	53.8%	−4.7%
85	h9	183	35.0%	40.0%	53.6%	−5.0%
86	l7	378	36.2%	41.5%	42.6%	−5.3%
87	k11	460	34.3%	39.8%	53.3%	−5.5%
88	j11	319	36.7%	42.2%	53.6%	−5.5%
89	e8	258	41.5%	47.0%	51.6%	−5.5%
90	e11	66	42.4%	48.2%	45.5%	−5.7%
91	j6	323	41.8%	47.6%	49.5%	−5.8%
92	k4	137	40.1%	46.0%	27.7%	−5.8%
93	g10	123	33.3%	39.2%	58.5%	−5.8%
94	k8	209	40.2%	46.2%	60.3%	−6.0%
95	d11	87	39.1%	45.1%	46.0%	−6.0%
96	h11	262	34.4%	40.6%	52.7%	−6.3%
97	f10	225	27.1%	33.7%	54.2%	−6.6%
98	i3	172	40.7%	47.5%	20.9%	−6.8%
99	f11	60	41.7%	48.6%	45.0%	−6.9%
100	i8	255	45.1%	52.2%	52.5%	−7.1%
101	g9	134	33.6%	40.8%	61.2%	−7.2%
102	l12	2,585	31.1%	38.4%	58.0%	−7.3%
103	d10	106	45.3%	52.7%	42.5%	−7.4%
104	i12	236	31.4%	38.9%	55.1%	−7.5%
105	k12	693	31.0%	38.6%	54.3%	−7.5%
106	g12	293	31.4%	39.2%	54.3%	−7.8%
107	j3	86	36.0%	43.9%	22.1%	−7.9%
108	j7	246	33.3%	41.4%	54.9%	−8.1%
109	c1	20	20.0%	28.1%	0.0%	−8.1%
110	g8	180	38.3%	46.5%	57.2%	−8.1%
111	e2	69	36.2%	44.4%	7.2%	−8.2%
112	c2	55	36.4%	45.2%	3.6%	−8.8%
113	b1	47	31.9%	40.7%	2.1%	−8.8%
114	l10	286	27.6%	36.7%	50.0%	−9.1%
115	k3	95	36.8%	45.9%	25.3%	−9.1%
116	b2	108	26.9%	36.2%	0.9%	−9.3%
117	b11	14	21.4%	31.3%	7.1%	−9.9%
118	l11	677	28.1%	38.3%	54.2%	−10.3%
119	l5	340	30.9%	41.2%	35.0%	−10.4%
120	e1	31	19.4%	31.8%	0.0%	−12.4%
121	j2	17	23.5%	36.7%	0.0%	−13.2%
122	l1	114	20.2%	33.6%	1.8%	−13.4%
123	h1	29	24.1%	37.8%	3.4%	−13.6%
124	k1	74	20.3%	33.9%	0.0%	−13.6%
125	d1	23	21.7%	36.4%	0.0%	−14.7%
126	i2	16	31.3%	47.4%	6.3%	−16.1%
127	f1	28	21.4%	38.2%	0.0%	−16.7%
128	l2	75	22.7%	39.5%	4.0%	−16.8%
129	k2	20	15.0%	37.0%	0.0%	−22.0%
130	g2	17	17.6%	40.9%	5.9%	−23.3%
131	g1	37	8.1%	31.6%	0.0%	−23.5%
132	h2	22	13.6%	39.3%	4.5%	−25.6%