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I have played a long series of games over time. Early on, I won most of my games. Recently, I have lost most of them. The difference is so stark that I wonder whether it can be explained by random variation — a lot of good look early on and bad luck recently — or whether I have actually gotten worse at the game. Is there a statistical test I can run on the data to answer this?

Cap
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  • Yes, this is a classic statistical problem. One thing we need to know is how many games you have played total. If you play 100 games at 50-50 odds, the maximum lose streak is likely to be around 7. (See this related question). Another thing that is very important here is how much randomness is involved in the game. – Caleb Stanford Nov 29 '16 at 20:08
  • Of course there are other possible explanations, e.g. your opponents may have improved. – Robert Israel Nov 29 '16 at 20:09
  • For example, since Chess is a pure strategy game, even a small lose streak is a sure sign you are losing your knack for the game. On the other hand, in a card game like Hearthstone (to use an example I know) it is very common to have long losing and winning streaks even among the best players, because the difference between an excellent player and a mediocre one may only be the difference between a 60 percent win rate and a 50 percent win rate. – Caleb Stanford Nov 29 '16 at 20:10
  • The game does have room for luck. It is poker. Specifically, sit-and-go tournaments. Prizes awarded are 4 entry fees for 1st place (profit of 3 EF), 2 EF for 2nd place (profit of 1 EF), and 1.5 EF for 3rd place (profit of 0.5 EF). I keep track of how much I have won or lost. Early on, my winnings grew steadily for a long time. Then, as if a switch was flipped, I started losing most of them, with an occasional 2nd or 3rd place finish, and my cumulative winnings have fallen below zero. – Cap Nov 29 '16 at 20:26
  • @cap online poker? Sure there is no cheating? Or you're losing useful inhibitions? But typical strategy to determine your theory that you've gotten worse is Hypothesis testing. – Pieter21 Nov 29 '16 at 20:29
  • @Pieter21 Yes, it is online. Cheating is possible but unlikely and wouldn't seem to explain the pattern. Losing useful inhibitions is one way my skill level could plausibly have changed for the worse. – Cap Nov 29 '16 at 21:08
  • Have you collected the data about your wins and losses in a systematic fashion? Or are you basing this on your experience? For if the latter, you may be subject to selective perception and confirmation bias. That is, maybe there is something more cognitive going on than statistical. – Bram28 Nov 29 '16 at 22:59
  • Yes. Not from the very beginning, but a little bit after I started playing I started keeping a log of my results. – Cap Nov 29 '16 at 23:07
  • As a point of clarification for @Pieter21 , it's not real money. – Cap Nov 30 '16 at 02:49

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