I need some Help

[BruceZ]

The $25 payout for 1 ace alone makes this postive EV. All the payouts together have a positive EV of $2.68.

Since we can only win one prize, I multiplied the probability of making each hand with 1-3 aces by the probability that the next card is not an ace.

The probabilities sum to exactly 1, so we can have confidence that they are correct.


First card A $25:

24/312*(311-23)/311*25 = $1.78


2 unsuited A's $100:

24/312*18/311*(310-22)/310*100 = $0.41


2 suited A's $500:

24/312*5/311*(310-22)/310*500 = $0.57


3 unsuited A's $1000:

[24/312*23/311*22/310*(309-21)/309 - P(3 suited aces)]*1000 = $0.36


3 suited A's $2000:

24/312*5/311*4/310*(309-21)/309*2000 = $0.03


any 4 A's $4500:

[24/312*23/311*22/310*21/309 - P(4 all red or black)]*4500 = $0.11


4 all red or all black A's $131000:

24/312*11/311*10/310*9/309*131000 = $0.33


No prize:

(312-24)/24*(-1) = 92% * (-1) = -0.92


Total EV: $2.68