Draw with a dealt full house in video poker?
I'm at a restaurant in Vegas sitting at the video poker bar waiting on dinner. Decided to play some Double Double Bonus video poker while I wait for my food.
I get dealt Q ♣ Q ♦ 3 ♠ 3 ♥ 3 ♣
What's the right play?
For those that don't know the double double bonus payouts, the full house is a guaranteed 45 coin payout (I bet the max at 5 quarters). If I hit four 3's it either pays 400 or 800 depending on whether I also get the kicker (A, 2 or 4 kicker pays 800, any other kicker pays 400). Or if I don't catch quads, then it pays 15.
I gambled by drawing for quads, and hit! But was that the right play statistically?
Love this question! Most video poker strategy "experts" will advise that the ONLY time you should throw away a dealt full house is when it contains 3 aces, then you obviously throw away the other pair and go for the fourth ace. There are some that recommend against even doing this and say you should always hold the dealt full house as the value over time will be in your favor (expected return on DDB 9/6 is 98.98%, assuming you play every hand perfectly).
Everyone has their own preferences with video poker though, I've seen people hold three aces with a kicker card hoping to get 4 aces with kicker. Anyone that knows video poker strategy will say this is a big mistake as the play for the higher expected value is to hold just the three aces and have 2 cards for the draw. Gamblers are superstitious though and if they tried this once and hit, it'll be tough to get them to do anything else.
@Jamie Thanks! My usual strategy in DDB, whether statistically right or wrong, is to draw for 4-of-a-kind if I'm dealt a full house with AAA - 444 since those have the higher payouts for hitting quads (400 - 2,000)....and keeping the guaranteed 45 coin payout if 555 - KKK rather than gunning for the 250 payout. Luckily worked for me last night!
It's not really close.
Chances of hitting are 4.26% (1 - (46/47 * 45/46))
When hitting you make your 'kicker' 26.1% of the time (12/46)
and do not make it 73.9%.
So EV from hitting is (.261 * 800) + (73.9 * 400) = 504.40
EV from drawing is thus (504.4 * .0426) + (15 * .9574) = 35.85
Giving up over 9 units to the EV of taking the 45.
But once again the fish gets rewarded. ;)
So donkey-bad. Even Kessler wouldn't try that.