Why random yellow cards provide an easier ride

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Offline JustMike

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Why random yellow cards provide an easier ride
« on: December 13, 2018, 12:45:14 AM »
I'm going to need someone to confirm my calculations here, but I think I've worked out that adding random yellow cards to a lock actually helps the person playing the game.

Here's how I worked it out:

There are five types of yellow card -
  • +1 red cards
  • +2 red cards
  • +3 red cards
  • -1 red cards
  • -2 red cards

On the face of it, it looks like random yellows aren't good news because there's more chance of encountering ones that add red cards, than ones that remove them. If you take an average of the five possibilities, you get +0.6 cards added to the deck.

However, the key element to this theory is that if you pick a yellow card, then once it has adjusted the number of red cards accordingly, you get to pick again immediately. This means that 1 extra card is removed from your deck, and so the actual effect of a random yellow card is to reduce the number of cards in your deck by an average of 0.4.

If this theory is accurate, there are a few countermeasures that could be added to the app to resolve it:

  • Adding a "+4 red cards" and/or "+5 red cards" yellow card
  • Not allowing another card to be picked immediately after a yellow card
  • Adding yellow cards that increase the number of freeze, reset, or double up cards (this would potentially have more drastic consequences and would need to be looked at more carefully)

Of course, this theory is only applicable to random yellow cards, if specific yellow cards are selected for a particular run, then these numbers can easily be manipulated accordingly.

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Offline Colonus

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Re: Why random yellow cards provide an easier ride
« Reply #1 on: December 14, 2018, 06:35:36 PM »
I like your second option JustMike but that would also make the -1 yellow card meaningless.

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Offline JustMike

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Re: Why random yellow cards provide an easier ride
« Reply #2 on: December 15, 2018, 08:51:35 PM »
I like your second option JustMike but that would also make the -1 yellow card meaningless.

Perhaps not, if you view it from the angle that it gives you the opportunity to suffer the same consequences as picking a red card, or you have the other potential options of adding or removing further red cards.

Think of it as a happy medium, a neutral option, and escape from adding red cards, but without the benefit of removing enough that it feels worthwhile.

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Offline peterbln

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Re: Why random yellow cards provide an easier ride
« Reply #3 on: January 12, 2019, 12:02:20 PM »
Let's say the current deck contains G green cards, Y yellow cards, and R red cards. Then your chances of picking a green card next are:

           G
    -------------- .
     G + Y + R

Now, let's assume you've drawn a yellow +1 card. Then your chances of picking a greed card next are:

                G                           G
    -----------------------  =  -------------- .
     G + (Y-1) + (R+1)        G + Y + R

In other words, your chances of finding green after having found a yellow +1 are exactly the same as before.

I guess it's fair to say that yellow +1 cards shouldn't be considered a disaster, but they certainly don't make things easier for the person who's playing. Drawing a yellow +1 card is essentially the same thing as drawing a red card.

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Offline ShortHairs

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Re: Why random yellow cards provide an easier ride
« Reply #4 on: May 02, 2021, 08:34:25 PM »
The conclusion above seems to be that having a yellow+1 in a deck is essentially the same as having a red in a deck.
I agree that a yellow +1 is not a disaster, but one thing that I don't think has been considered in the above analysis is as follows:
If the deck contained a yellow +1 versus a red, then the user will have two draws to find a green when a yellow+1 is drawn versus the only one chance when a red is drawn, so the chances of making progress are twice as high with a yellow+1 as with a red.  As a result, I would say that yellow+1 cards do, in fact, make it easier for the person who's playing.  A lockee will typically find all the green cards twice as fast in a deck that contains 5 green and 20 yellow+1 cards instead of 5 green and 20 red cards.

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Offline Lizzy

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Re: Why random yellow cards provide an easier ride
« Reply #5 on: May 14, 2021, 06:37:57 PM »
apples are fairer than oranges, discuss.