Flip-coin game:
• A chooses a sequence of 3 choices of heads and tails
• B then chooses a different sequences of 3 heads or tails (knowing what A chose)
Flipping coin starts, and the first to hit their sequence of 3 wins.

The table below has 2 rows for each choice pair:
• top of each cell is when giving up after 10 flips if nobody has won
• bottom of each cell is when giving up after 20 flips if nobody has won
The 3 numbers are:
• A win count, B win count, draw count, and an optional ratio of B winning over A winning

So with the table if you play this game, being the second person you know what to chose to statistically win more often.

B=HHHB=HHTB=HTHB=HTTB=THHB=THTB=TTHB=TTT
A=HHH
232 232 754      
28656 28656 92736      
168 272 714 (1.6)
20736 33551 87841 (1.6)
98 169 148 (1.7)
1871 3278 2510 (1.8)
1 463 754 (463.0)
1 57311 92736 (57311.0)
127 186 277 (1.5)
5894 8638 12664 (1.5)
47 220 148 (4.7)
814 4335 2510 (5.3)
232 232 754      
28656 28656 92736      
A=HHT
232 232 754      
28656 28656 92736      
262 87 317      
12639 4022 14536      
161 36 56      
946 121 156      
11 375 611 (34.1)
21 46366 75026 (2207.9)
111 21 26      
421 41 46      
66 66 26      
231 231 46      
220 47 148      
4335 814 2510      
A=HTH
272 168 714      
33551 20736 87841      
87 262 317 (3.0)
4022 12639 14536 (3.1)
66 66 26      
231 231 46      
146 203 317 (1.4)
6766 9895 14536 (1.5)
232 232 754      
28656 28656 92736      
21 111 26 (5.3)
41 421 46 (10.3)
186 127 277      
8638 5894 12664      
A=HTT
169 98 148      
3278 1871 2510      
36 161 56 (4.5)
121 946 156 (7.8)
66 66 26      
231 231 46      
66 66 26      
231 231 46      
203 146 317      
9895 6766 14536      
375 11 611      
46366 21 75026      
463 1 754      
57311 1 92736      
A=THH
463 1 754      
57311 1 92736      
375 11 611      
46366 21 75026      
203 146 317      
9895 6766 14536      
66 66 26      
231 231 46      
66 66 26      
231 231 46      
36 161 56 (4.5)
121 946 156 (7.8)
169 98 148      
3278 1871 2510      
A=THT
186 127 277      
8638 5894 12664      
21 111 26 (5.3)
41 421 46 (10.3)
232 232 754      
28656 28656 92736      
146 203 317 (1.4)
6766 9895 14536 (1.5)
66 66 26      
231 231 46      
87 262 317 (3.0)
4022 12639 14536 (3.1)
272 168 714      
33551 20736 87841      
A=TTH
220 47 148      
4335 814 2510      
66 66 26      
231 231 46      
111 21 26      
421 41 46      
11 375 611 (34.1)
21 46366 75026 (2207.9)
161 36 56      
946 121 156      
262 87 317      
12639 4022 14536      
232 232 754      
28656 28656 92736      
A=TTT
232 232 754      
28656 28656 92736      
47 220 148 (4.7)
814 4335 2510 (5.3)
127 186 277 (1.5)
5894 8638 12664 (1.5)
1 463 754 (463.0)
1 57311 92736 (57311.0)
98 169 148 (1.7)
1871 3278 2510 (1.8)
168 272 714 (1.6)
20736 33551 87841 (1.6)
232 232 754      
28656 28656 92736      

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