The "balls in a hat" game --> EV question

[k3nt]

[Pok 7's]

[k3nt]

[starstealer]

[NorthView]

[k3nt]

[starstealer]

[Spank_her_Pair]

if you get white on the first draw, you should then stop and take your dollar. because the EV on your draw gets worse.

Now if you draw a black, you should draw again. Anytime your balls are even... it is positive EV to draw. Because you either win $1 right away (and stop) or you lose the first draw and then can draw the rest of the balls and be guaranteed to win your dollar back or if you get lucky and hit 2 whites in a row you will still win $1. Therefore, the EV of the second draw is a little over $.50.

approx EV of 4 white 5 black = ~$0.17.
44% of the time you win $1 and 56% of the time you lose $1 but then win $.50 of that dollar back on average from continuing to draw
EV = (4/9 * 1) + (5/9 * (.50 - 1)) = +$.166.

(actually your EV will be higher than that because I have not included the times you hit 2 (or 3) blacks then hit 3 (or 4) whites in a row and end up +$1)


In conclusion, if you use the strategy of drawing until you are up +$1 or have drawn all the white balls. Then it is +EV to play this game. Therefore, you will either win $1 or lose $1 (when you draw all the balls). However, by being able to stop when you are ahead you will win more often than you lose.

[Spank_her_Pair]

[starstealer]

[Pok 7's]

[Felonius_Monk]

[Molina]

[Triple B]

[k3nt]