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Ask The Wizard #307

I'm part of a 'dead pool' for the year 2018. Here's how it works:

  1. Participants are required to submit a list of ten living celebrities, all under the age of 100.
  2. If a celebrity from your list passes away, as confirmed by a mention in the Associated Press in 2018, you will earn points based on the formula 100 minus their age at the time of death.
  3. Player with the most points on 1/1/2019 wins.

Considering the averages, what strategy would yield the best results in this competition?

anonymous

As a former professional in actuarial sciences, you’ve turned to the right person. I hope the Society of Actuaries views my assistance as legitimate rather than a misrepresentation of our field. To respond to your query, I referred to a source from my previous employer, the Office of the Chief Actuary at the Social Security Administration. 2014 Period Life Table A life table provides insights such as the likelihood of death for individuals of various ages and genders in 2014. Utilizing this data, I've constructed a table that displays both the mortality probabilities and anticipated points across all ages from 0 to 100, and for every gender.

The findings indicate that the highest expected point total is attributed to a 90-year-old male, with a score of 1.645220.

2014 Period Life Table Death Pool

Age Probability of
Death — Male		 Probability of
Death — Female		 Expected
Points — Male		 Expected
Points — Female
0 0.006320 0.005310 0.632000 0.531000
1 0.000403 0.000352 0.039852 0.034835
2 0.000282 0.000221 0.027626 0.021683
3 0.000211 0.000161 0.020514 0.015612
4 0.000181 0.000131 0.017405 0.012556
5 0.000161 0.000111 0.015313 0.010515
6 0.000141 0.000111 0.013260 0.010405
7 0.000131 0.000101 0.012184 0.009360
8 0.000121 0.000091 0.011127 0.008334
9 0.000091 0.000081 0.008256 0.007328
10 0.000101 0.000091 0.009073 0.008154
11 0.000101 0.000081 0.008973 0.007168
12 0.000131 0.000101 0.011535 0.008861
13 0.000202 0.000131 0.017547 0.011389
14 0.000303 0.000151 0.026023 0.012992
15 0.000404 0.000191 0.034304 0.016267
16 0.000505 0.000232 0.042393 0.019464
17 0.000616 0.000272 0.051129 0.022582
18 0.000748 0.000302 0.061316 0.024796
19 0.000880 0.000343 0.071262 0.027768
20 0.001022 0.000373 0.081780 0.029855
21 0.001145 0.000404 0.090445 0.031884
22 0.001258 0.000444 0.098105 0.034643
23 0.001310 0.000475 0.100880 0.036546
24 0.001332 0.000495 0.101246 0.037625
25 0.001344 0.000526 0.100811 0.039422
26 0.001377 0.000556 0.101864 0.041162
27 0.001389 0.000577 0.101371 0.042106
28 0.001421 0.000608 0.102330 0.043740
29 0.001454 0.000648 0.103234 0.046036
30 0.001507 0.000669 0.105517 0.046837
31 0.001530 0.000710 0.105584 0.048998
32 0.001574 0.000751 0.107011 0.051084
33 0.001617 0.000813 0.108364 0.054454
34 0.001661 0.000864 0.109644 0.057041
35 0.001716 0.000926 0.111521 0.060194
36 0.001781 0.001008 0.113970 0.064538
37 0.001857 0.001081 0.116963 0.068090
38 0.001933 0.001164 0.119830 0.072145
39 0.002020 0.001237 0.123207 0.075427
40 0.002118 0.001340 0.127066 0.080422
41 0.002258 0.001445 0.133232 0.085232
42 0.002410 0.001560 0.139778 0.090455
43 0.002615 0.001696 0.149075 0.096649
44 0.002843 0.001853 0.159228 0.103761
45 0.003105 0.002011 0.170771 0.110606
46 0.003401 0.002191 0.183635 0.118300
47 0.003742 0.002403 0.198314 0.127342
48 0.004108 0.002647 0.213613 0.137656
49 0.004532 0.002894 0.231133 0.147577
50 0.004994 0.003194 0.249696 0.159718
51 0.005473 0.003487 0.268191 0.170880
52 0.005993 0.003794 0.287656 0.182103
53 0.006565 0.004104 0.308561 0.192871
54 0.007159 0.004428 0.329324 0.203676
55 0.007799 0.004767 0.350946 0.214498
56 0.008475 0.005153 0.372902 0.226729
57 0.009179 0.005534 0.394696 0.237972
58 0.009856 0.005889 0.413944 0.247347
59 0.010575 0.006272 0.433558 0.257150
60 0.011350 0.006683 0.453991 0.267338
61 0.012209 0.007180 0.476135 0.280016
62 0.013061 0.007720 0.496330 0.293355
63 0.013921 0.008339 0.515084 0.308537
64 0.014814 0.009029 0.533320 0.325041
65 0.015831 0.009839 0.554094 0.344371
66 0.016981 0.010741 0.577354 0.365197
67 0.018300 0.011752 0.603909 0.387812
68 0.019778 0.012879 0.632894 0.412117
69 0.021443 0.014142 0.664734 0.438397
70 0.023384 0.015613 0.701513 0.468376
71 0.025547 0.017271 0.740873 0.500852
72 0.027877 0.019047 0.780560 0.533320
73 0.030384 0.020918 0.820374 0.564797
74 0.033098 0.022938 0.860535 0.596385
75 0.036256 0.025299 0.906400 0.632465
76 0.039868 0.028043 0.956841 0.673035
77 0.043883 0.031127 1.009299 0.715914
78 0.048257 0.034590 1.061657 0.760984
79 0.053128 0.038456 1.115692 0.807583
80 0.058709 0.043007 1.174177 0.860145
81 0.065070 0.048186 1.236322 0.915536
82 0.072149 0.053762 1.298691 0.967712
83 0.079906 0.059769 1.358409 1.016065
84 0.088524 0.066380 1.416378 1.062085
85 0.098157 0.073823 1.472348 1.107351
86 0.108904 0.082381 1.524651 1.153334
87 0.120889 0.092180 1.571556 1.198344
88 0.134134 0.103305 1.609607 1.239664
89 0.148707 0.115744 1.635778 1.273180
90 0.164522 0.129477 1.645220 1.294772
91 0.181584 0.144435 1.634254 1.299911
92 0.199903 0.160621 1.599225 1.284970
93 0.219362 0.177816 1.535534 1.244713
94 0.239881 0.196194 1.439286 1.177165
95 0.260293 0.214694 1.301463 1.073469
96 0.280129 0.233056 1.120515 0.932225
97 0.299042 0.251152 0.897125 0.753456
98 0.316317 0.268235 0.632634 0.536471
99 0.332667 0.284442 0.332667 0.284442
100 0.348651 0.301417 0.000000 0.000000

This topic surfaced and was deliberated in my non-gambling discussion forum,

I documented 7,456 spins on a roulette wheel, and the outcomes are as follows. I have a hunch that the wheel may be biased; however, the evidence isn't strong enough to justify placing bets on it. Diversity Tomorrow .

The following chart depicts your results in the order they occurred on the wheel. The blue line represents your outcomes, while the red line indicates the target number, 207.11, which is needed to overcome the house advantage of 5.26%.

Roulette Data

Winning
Number		 Occurrences
0 204
28 214
9 175
26 177
30 203
11 181
7 223
20 205
32 184
17 222
5 224
22 241
34 194
15 210
3 209
24 176
36 203
13 217
1 217
00 197
27 173
10 195
25 198
29 217
12 197
8 207
19 163
31 180
18 201
6 186
21 203
33 171
16 164
4 200
23 191
35 163
14 177
2 194
Total 7456

Bnitty

A chi-squared test applied to this data yields a statistic of 68.1 with 37 degrees of freedom. The odds of obtaining such a skewed result or more extreme is about 1 in 725.

While I don't believe the chi-squared test is ideal for this situation—since it overlooks the sequence of results—I’m not sure which alternative would be more suitable. Some have proposed using the alternative tests, but in my view, they may not be fitting. If there are any better tests available, I would appreciate suggestions.

If you had placed a bet on the three-number range surrounding the number 5, you would have realized a profit of 10.57% based on your recorded spins. However, if you expanded your bets to a seven-number range, your advantage diminishes to just 2.84%. Kolmogorov–Smirnov test In simple and straightforward terms, I would suggest that there are indications of bias in the wheel, but not enough evidence to claim it beyond a reasonable doubt. However, this bias might not be significant enough to reliably counteract the house edge. Assuming the casino doesn't rotate the wheels among tables, it's advisable to gather more data before wagering substantial amounts. I apologize for the indecisiveness in this response.

This matter has been broached and is currently under discussion in my forum at

There are two competitors, Sam and Dan, each holding five coins. They must simultaneously decide how many coins, from one to five, to place in their hands. Once they've made their choices, they reveal the amounts. If they select the same number of coins, Sam wins all the coins in play. Conversely, if their selections differ, Dan claims everything. Assuming both players are perfect logicians, what strategy should Dan adopt?

Dan is recommended to randomize his decisions according to the following pattern: Wizard of Vegas .

By adopting this approach, Dan can expect to secure an average of 3.640510949 coins with every round, regardless of Sam's chosen amount.

ThatDonGuy

This question arose from a previous discussion, which can be found in my forum at

  • Probability of picking one coin = 77/548.
  • Probability of picking one coin = 107/548.
  • Probability of picking one coin = 117/548.
  • Probability of picking one coin = 122/548.
  • Probability of picking one coin = 125/548.

In a blackjack variant known as Hot Action Blackjack being played at the California Grand Casino in San Francisco, the rules are outlined as follows:

A solution can be found in my Math Problems site, problem 230.

This game utilizes six decks in a continuous shuffling machine, supplemented with 18 jokers that are valued at 2. Wizard of Vegas .

If a player is dealt two jokers as their opening cards, they are awarded a bonus of 4 to 1.

  • Should a player receive two suited aces as their initial cards, a bonus of 5 to 1 is granted.
  • Dealer hits soft 17.
  • Double on any first 2 cards.
  • Re-split up to four hands.
  • No drawing to or re-splitting aces.
  • No surrender.
  • Blackjack pays 6 to 5.
  • What strategies can be employed, and what is the house edge for this game?
  • To begin, here is my fundamental strategy given these specific rules:
  • Player must pay a 5% commission to play.

Taking everything into account, my calculations reveal a house advantage of 6.01% (which is rather high) based on the initial bet. In practical terms, if a player bets $100—excluding the $5 commission—they can anticipate a loss of $6.01. This illustrates why I tend to avoid player-banked games in California, unless I am acting as the banker.

JPClav

Mathematically sound strategies and insights for various casino games such as blackjack, craps, and roulette, among many others.

Please check your mailbox and click the link we provided to finalize your registration.

Dan is recommended to randomize his decisions according to the following pattern: Wizard of Vegas .