Odds of Completing Four Aces and a Kicker in Video Poker

3 May 2014

By Jerry Stickman

Dear Stickman,

I have a video poker question for you.

What are the odds of hitting 4 aces plus a kicker while holding only one ace? I did just that a couple of weeks ago at Mohegan Sun while playing double-double bonus poker.

Regards,
Ludi


Hi Ludi,

First of all, congratulations on your great win. It is always nice to hit one of the highest hands in video poker. Now let’s take a look at your situation.

The odds of getting quad aces with a kicker when holding just one ace vary depending on the number of kickers you threw away. There are 178,365 possible hands that can be made when saving one ace. If you threw away no kickers, there would be 12 quad-aces-with-a-kicker hands out of 178,365 so the odds against getting your final hand in this case is 178,365 divided by 12 or about 14,864 to 1.

If you threw away one kicker you would have one less chance of completing the desired hand and the odds against would be 178,365 divided by 11 or 16,215 to 1. Throw away three kickers and the odds against completing your hand increase to 178,365 divided by 10 or about 17,837 to 1.

If you are playing proper strategy you would never throw away four kickers as they would include a low pair and you would save the low pair.

With all that said, and averaging all the possibilities, the overall odds against drawing four aces and a kicker when saving one ace are about 16,215 to one. This is not quite the long shot a royal would be but still quite a feat.

Congratulations again and may many more of them be in your future.

All the best in your casino and life endeavors,

Jerry “Stickman”