For example, the chance of winning a game is 1%. Do I get the same outcome of playing 100 games in the following two ways.

  1. Play one game a day for 100 days.

  2. Play 100 games all at once, one after another until 100 games are played.

Note: The game is not lottery, you can only participate once per game.

From my experiences, it turns out I get better chances of winning the game when I play more games all at once compare to one game at a time spread through a long period of time. Is this correct? whether it's correct or not, any proofs to back it up?

  • $\begingroup$ mathematically it should not make any difference, if the game tries are really independent of each other. when you play in a row, you play differently than over time... $\endgroup$ – gt6989b Jun 19 '17 at 21:22
  • $\begingroup$ When you say play 100 games all at once, are you thinking of buying 100 tickets to the same lottery? Otherwise, what do you mean by playing all at once? $\endgroup$ – Ross Millikan Jun 19 '17 at 21:23
  • $\begingroup$ If we were to assume that the results of the games played are independent from one another (which includes but is not limited to the result of the match and the time of day the game was played, etc...) then there shouldn't be any difference. An example of such a game would be rolling a $100$-sided die and trying to roll a 100. An example where it is not valid is as Ross points out playing the lottery. The result of the first game will influence the result of the second (if you guessed wrong you won't guess the same thing again the second time) but this violates the phrase "chance is 1%" $\endgroup$ – JMoravitz Jun 19 '17 at 21:28
  • $\begingroup$ 100 games at once I meant playing it one after another for 100 games. $\endgroup$ – s-hunter Jun 19 '17 at 21:29

If you look at in in a purely probabilistic way, (i.e., the probability is $0.01$ every time) then the probability should be exactly the same either way. However, it may be true that the situation cannot be modeled so simply. Other variables often affect the gameplay. For example, if you play all $100$ games at the same time, you are more likely to get "in the zone" and play better and better each time, whereas if you wait, you let your experience dissolve in between games.

Basically, my answer is that you can't really model it this way - it is more of a psychological problem than a mathematical one.

  • $\begingroup$ Technically, I agree with you in a purely probabilistic way that there is no difference in these 2 ways. However, my experience is telling me otherwise, and you are probably right, it's just psychologically my brain thinks I get better chances when play all at the same time period. Are there any large scale experiments to prove that it is indeed the same in these 2 ways? $\endgroup$ – s-hunter Jun 19 '17 at 21:55
  • $\begingroup$ Hmm, not that I know of. However, I'm not the one to ask. Is there a "psychology stack exchange" that you could move this question to? $\endgroup$ – Frpzzd Jun 19 '17 at 22:01

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