You have 4 cards, 2 black and 2 red. You play a game where during each round you draw a card. If it's black, you lose a point. If it's red, you gain a point. You can chose to stop at any time. What's the expected value of this game

The expected value of this game is 2/3

Step-by-step explanation:

Give that

If it's black, you lose a point. If it's red, you gain a point. 

And then you can stop at any time. But you should never stop when you are losing because that can guarantee 0 by drawing all the cards.

Assuming you should stop after three cards when you are +2.

The only question is whether to draw if you are +1 on the first draw.

If you draw red first, You have 1/3 chance of drawing red again and this will give you +2 points

1/3 chance of drawing two blacks and earn zero point, chance of drawing black-red and earn +1. This gives +1, so it doesn't matter whether you draw or not.

From the beginning, If you draw red (probability 1/2 you end +1. If you draw black and then draw two reds (probability 1/6 you end +1) Otherwise you break even with probability 1/3. Overall, the value is 2/3

each side has a different length.  

step-by-step explanation:

0.84 dang lotta people are looking for this lol or if you round up its 1 but the overall answer to that is 0.84

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