by Maolvar
Muemmelmann wrote:
Thanks for writing this :)
An interesting property is that after you draw the first card, and it is yellow, you will probably want to draw the second card because the probability is still larger that it is yellow.
An interesting property is that after you draw the first card, and it is yellow, you will probably want to draw the second card because the probability is still larger that it is yellow.
I disagree. If you did not get penalized for drawing blue or red cards it would be worth the risk, as the probability of drawing yellow cards decreases by roughly 1% on each draw.
The rules do not let you do three independent draws from your deck. Drawing even a single non-yellow card breaks your combo, thus you must calculate the probability of drawing cards in sequence.
I just realized that I made a mistake in my original calculations, by skipping the draw phase in the end of the first round. The calculations are still valid though. I will use the same numbers in the next example for the sake of clarity.
First draw:
27/45 = 0.6
Second draw:
26/44 = 0.59
0.6 * 0.59 = 0.35
Third draw:
25/43 = 0.58
0.6 * 0.59 * 0.58 = 0.21
You must multiply the result of first draw with the second draw to get the probability of drawing two yellow cards in a row. The same applies to the third draw, in which the result of the second draw gets multiplied by the probability of drawing a yellow card from the deck.
Drawing two yellow cards in sequence has 35%, which translates to roughly 1/3 chance. Not bad, but the odds are against you. Drawing three yellow cards in sequence is even less likely with 21% probability. This translates to 1/5 which is not worth it, unless you feel lucky.