Odds Difference

[FAA]

Why is there a quoted odds differential between a four Aces and four deuces hand?

[FloridaPhil]

Why is there a quoted odds differential between a four Aces and four deuces hand?

If you are playing deuces wild, I think it's because the deuces are wild and can make more paying combinations. If you are playing a game where four aces gives you a bonus, it's because four aces pays more than four deuces. I'm not an odds expert, so I could be wrong.

[onemoretry]

Why is there a quoted odds differential between a four Aces and four deuces hand?

I have no idea what you mean by the term "odds differential". Could you elaborate? And, could you also identity the game and pay table involved?

[New2vp]

OMT, I am going to guess that FAA is talking about the Statistics subtab under the Learn tab on this cite.

FAA, Is that true? I've posted them below. So, it seems here that Four Aces is less frequent than Four Deuces. But you have to look at the sentence below, which on the website is above the odds. It is a disclaimer that OMT's instincts are telling him you need to consider. The odds are different for every game depending upon your holding strategy. If all you cared about were hitting 4 aces, the odds would be 1/3384.0625, but you won't for example toss a dealt royal flush to go for four aces. Similarly, is all you cared about was hitting four deuces, the odds would be the same, 1/3384.0625.

Jackpot Frequencies Odds
Royal Flush dealt 1 / 650,000
Royal Flush ending hand 1 / 40,000
Four of a kind 1 / 423
Four Aces 1 / 5,761
Four Aces with a kicker 1 / 16,236
Four Deuces 1 / 4,909
2’s – 4’s 1 / 2,601
2’s – 4’s with a kicker 1 / 6,984
Full House 1/90
Flush 1/85
Straight 1/80
Straight Flush 1 / 9,150

These numbers are ON AVERAGE and vary based on the game you play, but are good benchmarks with which to set your expectations as you play:

[Vman96]

The four Aces category is for DDB and are the odds of getting 4 Aces WITHOUT the kicker.

The four Deuces category (1 in 4909) is for Deuces wild and has a different strategy than DDB.

Overall in DDB 4 Aces with or without a kicker from the statistics above would be:

1/5761 + 1/16,236 = 1 in 4252 which is more than Deuces.

[billryan]

In a non wild game, one holds a single Ace, but not a single Deuce.
In a wild game, it's the opposite.
What you hold effects what you end up with.

[FAA]

Yeah, I meant those numbers. Without attaching a category or kicker, one would assume that the odds would be identical given that each deck contains four of each. I'm sure that the furnished replies have merit, but it remains vague for me.

[billryan]

Which card are you most likely to discard in JOB? An Ace or a Deuce? As you generally hold an Ace, you end up with more 4OAK than low cards. Should be true for the KQJ as well.

[FAA]

I think I see. It's a YMMV odds table constructed based on game and premium hand emphasis?

[BobDancer]

I agree with BR's analysis --- but would phrase it differently

You, FAA, seem to be thinking of being DEALT four aces versus four deuces. And those numbers would indeed be the same --- which is what your intuition is telling you.

The hand distribution you are looking at is AFTER THE BEST PLAY IS MADE. And that's going to vary by strategy.

It's not so much about premium hands, but whatever the correct strategy is. You'll get four jacks more frequently than four sevens (neither of which would normally be called premium hands) in a game like DDB because you hold a pair of jacks more and you also hold a single jack which can be converted into quads on occasion.

This kind of thing matters in a "card of the day" promotion, where you get an extra xxx coins for the right quad. Getting that bonus on jacks would be worth more than getting it on sevens. That is important in your calculation on whether the game is worth playing in the first place --- or which game offers the better odds.

Such a promotion can easily make what is called a "negative game" by some on this site into a profitable opportunity.