Nine-Nine-Ten

In a dream I had, I saw a video poker machine that, on every initial hand, dealt the player a pair of nines and a ten, along with 2 random cards. The suits of the nines and ten are random.

After waking up, I thought about some of the pros, cons, and odds of the machine.

Pros:
You are always given a medium pair.
You are always given 2 to a straight.
You have a 50/50 shot of being given 2 to a straight flush.

Cons:
No pat straights on initial deal.
No pat flushes on initial deal.

If a machine existed like this, with the gimmick of "always dealt 2 nines and a ten at the start", would it be worth playing? Would you expect to win more or less? Other pros and cons?

What if there was a machine that always dealt a ten as your first card? You'd always have one card to a royal, but it would not guarantee jacks or better on your deal, either. Would you play a machine that always gave you a certain card or cards on the initial deal?

I would not play a machine that dealt me a low pair on every hand. At least on Jacks or Better, the expected value of holding the low pair is $4.11. I would lose pretty quickly.
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On the other hand, I guess I would get some dealt full houses, trips, and quads too so that might make up for it. Maybe somebody can calculate this?
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Off the top of my head, I would not play this machine. Definitely not the one that gave you a ten every time.

Remember, two pair would also be a possibility on the initial deal. 10s and 9s, or anything (if the last two cards match) and 9s. I think this might have a positive EV, since you still get a draw. I also would not play a machine that gave me a low pair on every hand, but I'd probably play one that gave AT LEAST a low pair on every hand.

Wait a sec...

What was the paytable in your dream?


I guarantee that if a machine you're describing was ever introduced, it would have a significantly altered pay table.


But it's a moot point. What you're talking about is, basically, using a stacked deck.

Since machines that simulate cards are required to have the true randomness of a shuffled deck, the machine would never hit the casino floor.

I think it would be legal to introduce this game under the banner of "9-9-Ten Poker". The cards do have to be randomized, but there's nothing wrong with a preset order if it's clearly stated. Not too much different than the "Dream Card" poker.

Quote: DJTeddyBear

What was the paytable in your dream?

Even though I never saw the paytable, I think my brain attempted to justify this question during the dream. I said to myself, "Well obviously, 3 nines or 4 nines would have to pay less than other 3 of a kind or 4 of a kind combinations. I'll bet a 9/10 combo full house would be different pay too."

Quote: DJTeddyBear

Since machines that simulate cards are required to have the true randomness of a shuffled deck, the machine would never hit the casino floor.

So, a game is not allowed to ever deal a predetermined card, or from a subset of the deck, even if it were described in the rules to do so? Off the top of my head, for example:

There are 2 games that were designed using a similar concept: Ace on the Deal and Deuce on the Deal.

While we're on the subject of strange gambling dreams, I had one myself the night before last. In it, there was some casino in Reno (where I have never been) that offered a craps game where each die had 2 of one number (and therefore one missing number), and that the Pass Line bet had no house edge as a result. I don't know what numbers there were two of, or what numbers were replaced because of the duplicates, but an example would be the faces on one die being 1-2-2-3-4-5 and the faces on the other die being 1-2-3-4-4-6. I didn't bother analyzing it to try to figure out if such a scenario were possible, and just chalked it up to the "makes-perfect-sense-in-the-dream-but-is-bizarre-in-reality" quality that dreams tend to have.

Hmmm....

I guess with a disclaimer, it can be done.

But watch that paytable!

Let's think about this:

There are 2,352 combinations to solve for: (49 * 48)/2 x 2. There are two states of the 10: non-matching and matching.

The wizard's JoB optimal strategy tells you to keep hands based on the expected return of keeping that hand.

Hand Dealt	Return	Combinations	Payout
4 of a Kind	25	2	50
Full House	9	18	162
3 of a Kind	4.3025	176	757.24
4 to a SF	2.6734*	9	2.54
2 Pair	2.59574	384	996.76
3 to a Royal	1.2868	6	7.72
4 to a flush	1.2766	43	54.89
Pair of 9s	0.8723	1,714	1411.82
Total		2,352	3,464.50

* the return on the 4 to a SF was adjusted based on the exact cards dealt.

The Player advantage on this Deal is 47.3%. (3,464.50 - 2,352) / 2,352. So I doubt any casino will be offering it anytime soon.