# Is there a better way for calculating the odds for the horserace card game?

horserace card game in progress

Game:

1. The 4 aces ("horses") are laid face-up at one end of the table.
2. 6 cards face-up are laid ("race track") in a straight line perpendicular to the aces.
3. The race proceeds by flipping the remaining deck, & the ace matching that suit advances one step until a winner reaches the finish line (card 6).

Question: How do you compute the odds for the horses after observing the cards on the racetrack?

I believe I have come up with one solution that computes the probabilities of all possible winning hands, and sums them before converting them to odd which you can find described here, although this (brute force) solution probably wouldn't scale well if we increase the number of cards, and makes me think they could be a simpler, more beautiful solution...

• To be clear, what exactly is your question? Are you trying to calculate the odds for the horses after the 6 cards are laid face up? – Théophile Dec 23 '15 at 2:36
• @Théophile Yes, I hope to establish the odds after observing the cards on the racetrack. – andyandy Dec 25 '15 at 12:51