I started tracking consecutive wins and losses in the solitaire player. The results are easily predictable. After playing hundreds of millions of games, my game player wins one game in 5.36 games played. Conversely, it loses one game in about 1.234 games played. Thus the odds of winning two consecutive games is about 1 in 28.729 games played. 28.729 being calculated by taking 5.36 to the power of 2 (5.36^2). The odds of winning three consecutive games is one in 153.99 games played (5.36^3). So on and so forth. If there is a problem with my random number generation, we should see some extreme variance in these odds. That is, my player will have some outrageous number of consecutive wins or losses given the total number of games played.
Let's examine a continuous run of game playing.
Win one in <5.42888> Ave cards remain <10.1497> One color deal one in <103.093> No play one in <52.356> No play/move one in <625> Total played <10000> Won <1842> Max consecutive wins <5> Max consecutive losses <51> seed <-1752695715>
After 10000 games played, the player had won 5 consecutive games and lost 51 in a row.
5.36^5 = 4424.09
1.234^51 = 45401.80
Thus the first 10000 games were quite "unlucky".
Win one in <5.54939> Ave cards remain <10.1738> One color deal one in <102.041> No play one in <51.4139> No play/move one in <526.316> Total played <20000> Won <3604> Max consecutive wins <6> Max consecutive losses <51> seed <-621770119>
After 20000 games played, it had won 6 consecutive games in a row.
5.36^6 = 23713.12
Win one in <5.43833> Ave cards remain <10.1819> One color deal one in <105.932> No play one in <52.1376> No play/move one in <413.223> Total played <50000> Won <9194> Max consecutive wins <7> Max consecutive losses <51> seed <-137475027>
After 50000 games played, it won 7 consecutive games.
5.36^7 = 127102.33
Now a "lucky" run.
Win one in <5.37109> Ave cards remain <10.1601> One color deal one in <105.263> No play one in <53.3204> No play/move one in <413.534> Total played <110000> Won <20480> Max consecutive wins <7> Max consecutive losses <53> seed <-1242274590>
After 110000 games played it had lost 53 consecutive games.
1.234^53 = 69135.87
Win one in <5.38089> Ave cards remain <10.1668> One color deal one in <105.105> No play one in <53.9291> No play/move one in <398.482> Total played <210000> Won <39027> Max consecutive wins <8> Max consecutive losses <53> seed <1626910630>
After 210000 games played, it had won 8 consecutive games.
5.36^8 = 681268.51
Win one in <5.38029> Ave cards remain <10.1704> One color deal one in <105.213> No play one in <53.9877> No play/move one in <402.194> Total played <220000> Won <40890> Max consecutive wins <8> Max consecutive losses <56> seed <-1955633737>
After playing 220000 games, it had lost 56 consecutive games.
1.234^56 = 129911.90
Win one in <5.36085> Ave cards remain <10.1561> One color deal one in <101.571> No play one in <54.1258> No play/move one in <391.144> Total played <530000> Won <98865> Max consecutive wins <9> Max consecutive losses <56> seed <711853774>
After playing 530000 games, it won 9 consecutive games. Lucky!
5.36^9 = 3651599.23
Win one in <5.36107> Ave cards remain <10.1572> One color deal one in <101.317> No play one in <54.1467> No play/move one in <387.597> Total played <600000> Won <111918> Max consecutive wins <9> Max consecutive losses <69> seed <1213694581>
My "luck" ran out after 600000 games played as it lost 69 consecutive games.
1.234^69 = 1998692.66
Win one in <5.36843> Ave cards remain <10.1576> One color deal one in <101.961> No play one in <54.2194> No play/move one in <384.399> Total played <2730000> Won <508529> Max consecutive wins <9> Max consecutive losses <75> seed <2049738009>
After 2.73 million games played, my bad luck continued with 75 consecutive losses.
1.234^75 = 7057273.96
When can we expect 76 consecutive losses and 10 consecutive wins?
1.234^76 = 8708676.07
5.36^10 = 19572571.89
Somewhere around 8 million games played, we should see 76 consecutive losses.
Somewhere around 19 million games played, we should see 10 consecutive wins.
Here's a run of 11 consecutive wins after 67 million games played. I wasn't logging consecutive losses with this version.
Win one in <5.35934> Ave cards remain <10.1514> One color deal one in <101.449> No play one in <54.2281> No play/move one in <381.972> Total played <67229791> Won <12544422> Max consecutive wins <11> seed <-1352972818>
Sometimes they come early, sometimes late, but we won't see extreme variance from these numbers. Casinos bank on this "reality" and this is why they are profitable. When we see extreme variance, we can be fairly certain it's cheating. For those of religious or spiritual persuasion, defying the odds in the extreme can be referred to as a miracle.
What about exceptional people? The world population stands at above 7 billion. The number of people born in the history of humanity is growing quite quickly. As more and more humans are produced, we should see extreme runs of "good" luck and "bad" luck. This would make that person exceptional. Was Adolf Hitler a run of 200 consecutive lost deals? Was Einstein a run of 20 consecutive wins?
I only offer this up as a rebuttal to the history channel alien theory. Einstein was an alien? I can only scoff. Furthermore, what constitutes good and bad luck as opposed to just runs of events that defy long odds? Einstein is viewed as a demigod in our culture but what real good has come from his knowledge? Piling up mounds of radioactive waste. Chernobyl? Fukushima? Hiroshima and Nagasaki? It's unclear what horrors await us. Stephen Hawking is a truly exceptional person but what good has he brought humanity? Visions of "whitey on Mars" does exactly what for the planetary condition?
So what does a "20 consecutive win" person look like?
“For me, I am driven by two main philosophies: know more today about the world than I knew yesterday and lessen the suffering of others. You'd be surprised how far that gets you.”
― Neil deGrasse Tyson
On a planet where one in two people live on $2 a day or less and one billion are starving, I don't see a lot of lessening the suffering of others. In terms of putting aside human exceptionalism, look at all the death and destruction wrought on the planet by humans. That is a lot of suffering life. Where are the "20 consecutive win" people? Instead, I see our most exceptional people on the planet engaged in the wholesale raping and pillaging of the planet. The Bill Gateses, Warren Buffets and Kock brothers held up as demigods. Gordon Gecko, invented as a parody, has become a role model.
Today is Ground Hog Bowl day. It's a ritualistic orgy of consumerist excess that this nation celebrates annually. Victim and predator alike rally to the cause of new commercials and QB success. Oh happy day! As for Mr. Tyson, how exactly do wage and debt slaves lessen the suffering of others? Cura te ipsum (physician heal thyself)?
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