Three Card Prime

The Palace Station is doing a field trial of the game Three Card Prime. It looks like the same thing as Three Card Poker with a modified Pairplus bet and a new side bet called the Prime.

The Pair Bonus works like the Pairplus in Three Card Poker, except if there is any win, a fourth dummy card is used to possible increase the win. If this dummy card is a deuce, then the wins are increased. Otherwise, they are the pays on the usual Pairplus pay table with a Mini Royal. Please note that this deuce is not part of the hand and not wild. It is just a way to win more automatically if it is a deuce.

The new side bet is the Prime. I think I've seen this on some other Galaxy game because I know I've analyzed it before. It pays 3-1 if all three player cards are the same color, except 4-1 if all six cards, between the player and dealer hands are the same color.

Here is my math:

Pair Bonus

Event	Pays	Combinations	Probability	Return
Mini royal with deuce	75	16	0.000015	0.001108
Mini royal without deuce	50	180	0.000166	0.008311
Straight flush with deuce	50	168	0.000155	0.007757
Straight flush without deuce	40	1,988	0.001836	0.073432
Three of a kind with deuce	40	204	0.000188	0.007535
Three of a kind without deuce	30	2,344	0.002165	0.064937
Straight with deuce	8	2,760	0.002549	0.020390
Straight without deuce	6	32,520	0.030030	0.180183
Flush with deuce	4	4,128	0.003812	0.015248
Flush without deuce	3	49,576	0.045781	0.137342
Pair with deuce	2	14,112	0.013032	0.026063
Pair without deuce	1	169,344	0.156380	0.156380
All other	-1	805,560	0.743891	-0.743891
Total		1,082,900	1.000000	-0.045205

Prime

Event	Pays	Combinations	Probability	Return
Six-card prime	4	9,209,200	0.022618	0.090470
Three-card prime	3	86,595,600	0.212677	0.638030
Loser	-1	311,365,600	0.764706	-0.764706
Total		407,170,400	1.000000	-0.036206

Can anyone confirm or deny?

The question for the poll is would you play Three Card Prime?

What is the Prime bet? All the cards in your hand, or yours and the dealers, have to be prime numbers?

If so, does the three card prime win for all bettors if only the dealers hand is prime? Do they count an ace as a prime of 1? Are all faces non-prime and therefore 10s, or do they assign rank values, which would make the queen prime at 11, but the jack and king even (ace is high-only in 3CP, so I suppose an ace could also be 13).

All of that feels forced. I like the relatively lower HE on both sidebets, but not sure I'd play.

Quote: beachbumbabs

What is the Prime bet?

Sorry, I just added to my post rules of the Prime bet.

I forgot to mention you can play Three Card Prime at the Galaxy web site.

I can deny your pair bonus. Combin(52,3)*49=1,082,900

Quote: miplet

I can deny your pair bonus. Combin(52,3)*49=1,082,900

You're right. Thank you. I forgot to take out the mini royals from the straight flushes.

I didn't notice that the Ante bonus pays more if the player loses. The way they phrase it is there is no more Ante bonus but the Play bet pays according to the following pay table if the player wins:

Mini royal: 10
Straight flush: 6
Three of a kind: 5
Straight: 2
Flush or less: 1

The pays for a straight flush, three of a kind, and a straight are doubled if the player loses. The player must beat or tie the dealer to win the Play bet with a flush or less.

Stay tuned for my analysis.

Okay, my new page on Three Card Prime is ready to preview. As usual, I welcome all questions, comments, and especially corrections.

I can confirm the numbers for the Prime Bet.

Quote: JB

I can confirm the numbers for the Prime Bet.

Thank you.

Rules 8 and 10 include this phrase:

"the Play bet will pay according to the pay table below"

but I am having trouble finding that Play Bet pay table. Is it there somewhere?

Quote: gordonm888

Rules 8 and 10 include this phrase:

"the Play bet will pay according to the pay table below"

but I am having trouble finding that Play Bet pay table. Is it there somewhere?

Good catch. It was there but incorrectly titled as the Pair Bonus pay table.

I'm new to the site and love it, love it, love it! (I love the videos, the strategy guides, the play-for-free emulators, and reading about weird games I've never heard of. Thanks Wiz!) I really haven't played casino games since my early 20's and so even "new" (i.e. 30 year old games) are new to me and I'm trying to catch up.

I confess I'm no mathematician but I do understand the basics of calculating odds. Yet I seem to be baffled by the seemingly simple PRIME wager found in this and other 3-card games. So here are my first site questions...

"Color" means all three cards MUST BE either all red (hearts and/or diamonds) OR all black (clubs and/or spades) correct?
Players DO NOT specify what color (black or red) their cards will be when making a PRIME wager correct?

If the above statements are true I'm confused about where the house edge (which the Wizard and others here calculate at 3.62%) comes from. From what I see the first card dealt determines the color you need the next 2 cards to be. The next 2 cards contain 1 winning combination out of 4 possibilities which would be 3-1 which happens to be what the payoff is for 3 cards in a PRIME wager. So where does the house edge come from? If a 3 card win pays true odds the (terrible) 4-1 pay for a 6 card win would be a freebie lucky bonus.

Obviously I'm missing something. Does a PRIME wager lose if you fold or lose your play bet, or is a PRIME bet independent from the main game like a Pairs Plus wager? I can't find specifics and it's driving me crazy. Please help a guy heading to Vegas soon.

Oh man, I'm a fool. It's CARDS not dice. (I mainly played craps back in the day.) So each (say) red card dealt makes it slightly less likely for the next card to be red. Wow, I really am rusty.

Heh heh, I better postpone that trip to Vegas.

Quote: Gialmere

Oh man, I'm a fool. It's CARDS not dice. (I mainly played craps back in the day.) So each (say) red card dealt makes it slightly less likely for the next card to be red. Wow, I really am rusty.

Heh heh, I better postpone that trip to Vegas.

Welcome to the forum! I like your attitude and your thinking things out for yourself. Also appreciate the compliments on the content - I agree.

Yes, welcome to the forum.
No need to postpone your ravel plans,
you are obviously bright and it will all come back to you.

Note to the Wizard:
When you post these tables showing a 'house edge' for a bet
or for a game, it might be best to remind us math dummies
that for some reason we have to mentally move the decimal
point two spaces to get the real answer.

Quote: FleaStiff

Note to the Wizard:
When you post these tables showing a 'house edge' for a bet
or for a game, it might be best to remind us math dummies
that for some reason we have to mentally move the decimal
point two spaces to get the real answer.

Point taken, but I don't want to dumb down the site too much. Let me poll the audience: Which is larger 25% or 0.25?

25% is vastly larger.

You have to multiply .25 by 4 to get 1 percent and then buy 25 to get 25%.

Quote: Wizard

Which is larger 25% or 0.25?

That can’t really be answered because 25% isn’t a value that can be compared to a real number. It’s 1/4 of an amount that you didn’t specify

.25 is 1/4 of 1

25% could be 1/4 of anything , smaller or larger than 1

By the way I did figure out that .25 is to 1 as 25 percent is to 100 percent, its just that at first looking at the tabular data I forget that we are dealing with a total of 1 rather than a total of 100 percent.

I like pie.

Quote: Wizard

Point taken, but I don't want to dumb down the site too much. Let me poll the audience: Which is larger 25% or 0.25?

7, the answer is 7.

They had Three Card Prime on the Carnival cruise ship I was on in March. I didn't play.

Therefore, I voted "No - better bets available" in the poll.