Starting capital (credits)

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Reading the draws and working out what chance predicts.

Casanova’s Risky Treasury

A profitable lottery can still run out of money. Explore a fictional treasury inspired by history.

Treasuries unable to pay370 / 100095% sampling interval: 34.06267% – 40.03683%

Expected profit per round166.67

Starting capital (credits)

MedianP10P90Expected capital with unlimited borrowing

Read the data table

Rounds	Median	P10	P90	Expected capital with unlimited borrowing
0	5,000	5,000	5,000	5,000
1	5,505	5,475	5,520	5,166.67
2	5,995	-5	6,025	5,333.33
3	6,500	-5	6,530	5,500
4	6,990	-5	7,035	5,666.67
5	7,480	-5	7,540	5,833.33
6	7,985	-5	8,045	6,000
7	8,475	-20	8,550	6,166.67
8	8,965	-465	9,055	6,333.33
9	9,455	-480	9,545	6,500
10	9,945	-495	10,050	6,666.67
11	10,420	-510	10,555	6,833.33
12	10,895	-510	11,060	7,000
13	5,580	-525	11,550	7,166.67
14	6,070	-525	12,055	7,333.33
15	6,545	-525	12,545	7,500
16	7,035	-525	13,050	7,666.67
17	7,525	-525	13,540	7,833.33
18	8,015	-540	14,045	8,000
19	8,505	-555	14,550	8,166.67
20	8,995	-660	15,040	8,333.33
21	9,485	-955	15,545	8,500
22	9,975	-1,045	16,050	8,666.67
23	10,465	-1,490	16,540	8,833.33
24	10,940	-1,490	17,045	9,000
25	11,430	-1,490	17,535	9,166.67
26	11,920	-1,490	18,025	9,333.33
27	12,410	-1,490	18,530	9,500
28	12,870	-1,490	19,020	9,666.67
29	13,315	-1,490	19,525	9,833.33
30	8,150	-1,505	20,015	10,000
31	8,610	-1,535	20,505	10,166.67
32	9,070	-1,535	21,010	10,333.33
33	9,545	-1,550	21,500	10,500
34	10,020	-1,670	21,975	10,666.67
35	10,510	-1,670	22,465	10,833.33
36	11,000	-1,670	22,940	11,000
37	11,475	-1,670	23,415	11,166.67
38	11,950	-1,670	23,875	11,333.33
39	12,440	-1,670	24,380	11,500
40	12,930	-1,670	24,765	11,666.67
41	13,420	-1,845	19,765	11,833.33
42	13,895	-1,920	20,165	12,000
43	14,370	-1,920	20,655	12,166.67
44	14,845	-1,950	21,130	12,333.33
45	15,290	-1,965	21,620	12,500
46	10,185	-1,965	22,125	12,666.67
47	10,630	-1,965	22,615	12,833.33
48	11,105	-1,965	23,105	13,000
49	11,580	-1,965	23,595	13,166.67
50	12,040	-1,965	24,100	13,333.33
51	12,515	-1,965	24,575	13,500
52	13,005	-1,965	25,065	13,666.67
53	13,480	-1,965	25,555	13,833.33
54	13,955	-1,980	26,045	14,000
55	14,430	-1,995	26,535	14,166.67
56	14,920	-1,995	27,040	14,333.33
57	15,410	-1,995	27,530	14,500
58	15,870	-1,995	28,005	14,666.67
59	16,345	-1,995	28,495	14,833.33
60	16,775	-1,995	28,985	15,000
61	11,715	-1,995	29,475	15,166.67
62	12,130	-1,995	29,980	15,333.33
63	12,590	-1,995	30,440	15,500
64	13,065	-1,995	30,885	15,666.67
65	13,540	-1,995	31,345	15,833.33
66	14,030	-1,995	26,270	16,000
67	14,505	-2,010	26,760	16,166.67
68	14,995	-2,010	27,175	16,333.33
69	15,470	-2,025	27,665	16,500
70	15,930	-2,025	28,140	16,666.67
71	16,405	-2,025	28,615	16,833.33
72	16,880	-2,025	29,105	17,000
73	17,340	-2,025	29,595	17,166.67
74	17,800	-2,025	30,070	17,333.33
75	18,290	-2,025	30,560	17,500
76	18,750	-2,025	31,065	17,666.67
77	13,750	-2,025	31,555	17,833.33
78	14,135	-2,025	32,045	18,000
79	14,610	-2,025	32,550	18,166.67
80	15,070	-2,025	33,025	18,333.33
81	15,560	-2,025	33,530	18,500
82	16,020	-2,040	34,005	18,666.67
83	16,495	-2,040	34,495	18,833.33
84	16,955	-2,040	34,985	19,000
85	17,415	-2,040	35,460	19,166.67
86	17,905	-2,040	35,965	19,333.33
87	18,380	-2,040	36,425	19,500
88	18,870	-2,040	36,885	19,666.67
89	19,375	-2,040	37,285	19,833.33
90	19,850	-2,040	32,315	20,000
91	20,265	-2,040	32,775	20,166.67
92	15,460	-2,040	33,220	20,333.33
93	15,665	-2,040	33,695	20,500
94	16,125	-2,040	34,200	20,666.67
95	16,600	-2,040	34,660	20,833.33
96	17,090	-2,040	35,120	21,000
97	17,565	-2,040	35,595	21,166.67
98	17,995	-2,040	36,085	21,333.33
99	18,470	-2,040	36,560	21,500
100	18,960	-2,040	37,050	21,666.67

Fictional rules: 1,000 one-number tickets at 1 credit, five numbers from 90, gross payout includes stake. Concentrated tickets share one number; the rest spread as evenly as possible. Simulate 1,000 treasuries, stopping each below zero. Lines show 10th percentile, median and 90th percentile; these are outcomes, not confidence bands. No taxes, costs or historical payout schedule are modelled.

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Evidence Receipts →

The maths, in plain language

E[profit] = 1000 − 1000 × (5/90) × gross

Stephen M. Stigler · Casanova’s Lottery (2022)

The story behind it

Stephen Stigler’s history connects Casanova with the French lottery of the 1750s. The state faced variable liabilities shaped by players’ choices. Our fictional treasury explores that problem: a positive average return does not supply the cash needed on every night.

Stephen M. Stigler · Casanova’s Lottery (2022)

Casanova’s Risky Treasury

A profitable lottery can still run out of money. Explore a fictional treasury inspired by history.

Treasuries unable to pay370 / 100095% sampling interval: 34.06267% – 40.03683%

Expected profit per round166.67

Starting capital (credits)

MedianP10P90Expected capital with unlimited borrowing

Read the data table

Rounds	Median	P10	P90	Expected capital with unlimited borrowing
0	5,000	5,000	5,000	5,000
1	5,505	5,475	5,520	5,166.67
2	5,995	-5	6,025	5,333.33
3	6,500	-5	6,530	5,500
4	6,990	-5	7,035	5,666.67
5	7,480	-5	7,540	5,833.33
6	7,985	-5	8,045	6,000
7	8,475	-20	8,550	6,166.67
8	8,965	-465	9,055	6,333.33
9	9,455	-480	9,545	6,500
10	9,945	-495	10,050	6,666.67
11	10,420	-510	10,555	6,833.33
12	10,895	-510	11,060	7,000
13	5,580	-525	11,550	7,166.67
14	6,070	-525	12,055	7,333.33
15	6,545	-525	12,545	7,500
16	7,035	-525	13,050	7,666.67
17	7,525	-525	13,540	7,833.33
18	8,015	-540	14,045	8,000
19	8,505	-555	14,550	8,166.67
20	8,995	-660	15,040	8,333.33
21	9,485	-955	15,545	8,500
22	9,975	-1,045	16,050	8,666.67
23	10,465	-1,490	16,540	8,833.33
24	10,940	-1,490	17,045	9,000
25	11,430	-1,490	17,535	9,166.67
26	11,920	-1,490	18,025	9,333.33
27	12,410	-1,490	18,530	9,500
28	12,870	-1,490	19,020	9,666.67
29	13,315	-1,490	19,525	9,833.33
30	8,150	-1,505	20,015	10,000
31	8,610	-1,535	20,505	10,166.67
32	9,070	-1,535	21,010	10,333.33
33	9,545	-1,550	21,500	10,500
34	10,020	-1,670	21,975	10,666.67
35	10,510	-1,670	22,465	10,833.33
36	11,000	-1,670	22,940	11,000
37	11,475	-1,670	23,415	11,166.67
38	11,950	-1,670	23,875	11,333.33
39	12,440	-1,670	24,380	11,500
40	12,930	-1,670	24,765	11,666.67
41	13,420	-1,845	19,765	11,833.33
42	13,895	-1,920	20,165	12,000
43	14,370	-1,920	20,655	12,166.67
44	14,845	-1,950	21,130	12,333.33
45	15,290	-1,965	21,620	12,500
46	10,185	-1,965	22,125	12,666.67
47	10,630	-1,965	22,615	12,833.33
48	11,105	-1,965	23,105	13,000
49	11,580	-1,965	23,595	13,166.67
50	12,040	-1,965	24,100	13,333.33
51	12,515	-1,965	24,575	13,500
52	13,005	-1,965	25,065	13,666.67
53	13,480	-1,965	25,555	13,833.33
54	13,955	-1,980	26,045	14,000
55	14,430	-1,995	26,535	14,166.67
56	14,920	-1,995	27,040	14,333.33
57	15,410	-1,995	27,530	14,500
58	15,870	-1,995	28,005	14,666.67
59	16,345	-1,995	28,495	14,833.33
60	16,775	-1,995	28,985	15,000
61	11,715	-1,995	29,475	15,166.67
62	12,130	-1,995	29,980	15,333.33
63	12,590	-1,995	30,440	15,500
64	13,065	-1,995	30,885	15,666.67
65	13,540	-1,995	31,345	15,833.33
66	14,030	-1,995	26,270	16,000
67	14,505	-2,010	26,760	16,166.67
68	14,995	-2,010	27,175	16,333.33
69	15,470	-2,025	27,665	16,500
70	15,930	-2,025	28,140	16,666.67
71	16,405	-2,025	28,615	16,833.33
72	16,880	-2,025	29,105	17,000
73	17,340	-2,025	29,595	17,166.67
74	17,800	-2,025	30,070	17,333.33
75	18,290	-2,025	30,560	17,500
76	18,750	-2,025	31,065	17,666.67
77	13,750	-2,025	31,555	17,833.33
78	14,135	-2,025	32,045	18,000
79	14,610	-2,025	32,550	18,166.67
80	15,070	-2,025	33,025	18,333.33
81	15,560	-2,025	33,530	18,500
82	16,020	-2,040	34,005	18,666.67
83	16,495	-2,040	34,495	18,833.33
84	16,955	-2,040	34,985	19,000
85	17,415	-2,040	35,460	19,166.67
86	17,905	-2,040	35,965	19,333.33
87	18,380	-2,040	36,425	19,500
88	18,870	-2,040	36,885	19,666.67
89	19,375	-2,040	37,285	19,833.33
90	19,850	-2,040	32,315	20,000
91	20,265	-2,040	32,775	20,166.67
92	15,460	-2,040	33,220	20,333.33
93	15,665	-2,040	33,695	20,500
94	16,125	-2,040	34,200	20,666.67
95	16,600	-2,040	34,660	20,833.33
96	17,090	-2,040	35,120	21,000
97	17,565	-2,040	35,595	21,166.67
98	17,995	-2,040	36,085	21,333.33
99	18,470	-2,040	36,560	21,500
100	18,960	-2,040	37,050	21,666.67

Share this finding

Evidence Receipts →

The maths, in plain language

E[profit] = 1000 − 1000 × (5/90) × gross

Stephen M. Stigler · Casanova’s Lottery (2022)

The story behind it

Stephen M. Stigler · Casanova’s Lottery (2022)