Riddler Classic

April 21st, 2017

Pick A Card Any Card

From Mont Chris Hubbard, a prediction puzzle inspired by his habit of trying to identify the funniest name as early as possible in a movie's scrolling end credits:

From a shuffled deck of 100 cards that are numbered 1 to 100, you are dealt 10 cards face down. You turn the cards over one by one. After each card, you must decide whether to end the game. If you end the game on the highest card in the hand you were dealt, you win; otherwise, you lose.

What is the strategy that optimizes your chances of winning? How does the strategy change as the sizes of the deck and the hand are changed?

source

Answer:

If your number is greater than 87, then keep it.
If you do, you will win approximately 58% of the time.

Data:

Threshold	Wins	Losses	Percentage
1	101239	898761	0.101239
2	101497	898503	0.101497
3	103525	896475	0.103525
4	104332	895668	0.104332
5	105761	894239	0.105761
6	107613	892387	0.107613
7	107937	892063	0.107937
8	110085	889915	0.110085
9	110999	889001	0.110999
10	112721	887279	0.112721
11	113281	886719	0.113281
12	115391	884609	0.115391
13	117119	882881	0.117119
14	118415	881585	0.118415
15	119678	880322	0.119678
16	121025	878975	0.121025
17	123079	876921	0.123079
18	125278	874722	0.125278
19	126259	873741	0.126259
20	128485	871515	0.128485
21	129346	870654	0.129346
22	131945	868055	0.131945
23	134687	865313	0.134687
24	135832	864168	0.135832
25	138241	861759	0.138241
26	140325	859675	0.140325
27	142767	857233	0.142767
28	144271	855729	0.144271
29	147346	852654	0.147346
30	149174	850826	0.149174
31	152494	847506	0.152494
32	155134	844866	0.155134
33	157999	842001	0.157999
34	160402	839598	0.160402
35	163393	836607	0.163393
36	167013	832987	0.167013
37	169849	830151	0.169849
38	172696	827304	0.172696
39	176378	823622	0.176378
40	180049	819951	0.180049
41	183931	816069	0.183931
42	187763	812237	0.187763
43	191491	808509	0.191491
44	195652	804348	0.195652
45	201354	798646	0.201354
46	204479	795521	0.204479
47	209477	790523	0.209477
48	215810	784190	0.21581
49	220226	779774	0.220226
50	226315	773685	0.226315
51	231389	768611	0.231389
52	238013	761987	0.238013
53	244177	755823	0.244177
54	250801	749199	0.250801
55	257166	742834	0.257166
56	264844	735156	0.264844
57	272537	727463	0.272537
58	280486	719514	0.280486
59	289597	710403	0.289597
60	297732	702268	0.297732
61	306910	693090	0.30691
62	316308	683692	0.316308
63	326522	673478	0.326522
64	335992	664008	0.335992
65	346577	653423	0.346577
66	357683	642317	0.357683
67	369608	630392	0.369608
68	381405	618595	0.381405
69	393297	606703	0.393297
70	405546	594454	0.405546
71	418096	581904	0.418096
72	430892	569108	0.430892
73	444488	555512	0.444488
74	457869	542131	0.457869
75	468890	531110	0.46889
76	482677	517323	0.482677
77	495796	504204	0.495796
78	508259	491741	0.508259
79	520425	479575	0.520425
80	532081	467919	0.532081
81	542764	457236	0.542764
82	552718	447282	0.552718
83	561104	438896	0.561104
84	568501	431499	0.568501
85	572584	427416	0.572584
86	577384	422616	0.577384
87	577921	422079	0.577921
88	575857	424143	0.575857
89	570199	429801	0.570199
90	560882	439118	0.560882
91	547484	452516	0.547484
92	529008	470992	0.529008
93	504268	495732	0.504268
94	473707	526293	0.473707
95	434877	565123	0.434877
96	388726	611274	0.388726
97	332890	667110	0.33289
98	267163	732837	0.267163
99	190151	809849	0.190151
100	100017	899983	0.100017
Threshold	Wins	Losses	Percentage