Four card poker question

I'm curious, is there any way to figure out the percentage of the dealer's hands that are "made" by the extra card? Kind of a twofold question: 1. How many times does the dealer make specific hands with the extra card (straight, flush, etc.)? 2. How many times does the dealer beat the player due to the extra card?

You just check the six-card poker table percentages (w/ no joker) against the five-card poker table percentages.
You can use the accurate Durango Bill's five-card tables against the six card table.

Since the dealer always qualfies, getting the advantage of an extra card, all hands are in action, or are "made."

All Math for this has been done eons ago.

Also see Mike Shackelford's page on Four Card poker.

Quote: Paigowdan

You just check the six-card poker table percentages (w/ no joker) against the five-card poker table percentages.
You can use the accurate Durango Bill's five-card tables against the six card table.

Since the dealer always qualfies, getting the advantage of an extra card, all hands are in action, or are "made."

All Math for this has been done eons ago.

Also see Mike Shackelford's page on Four Card poker.

Durango Bill's are for 5 card hands, not 4 card hands.

Yeah, I know.
You're dealt a five-card hand, from which you make a four-card hand. Dealer gets the advantage of a four-card hand from a six-card dealt hand, and always qualifies as a result; all hands are live.

One pair, Two pairs, Trips, quads, straights and flushes do occur more often, but it is a very good start on how it's done algebraicly.
Exact details for Four card hands derived from a five card hand will either require a math report, or asking Roger Snow of Shufflemaster to see his math reports; not likely from an off-the-street ad hoc request, here on an Internet forum. Or asking MathExtremist or the Wizard to provide a free math report on this one - as a forum freebie. Or any other member may do it for free. They might, ahem, as a challenge. I won't, so I gave a lead.

Hey Miplet, you got any better leads, or a math report on this for us all or for this gentleman, on this one?
What have you got that is better for this gentleman?

Perhaps I should have included a link to Free Gaming Math Reports.com.

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Yeah, I know about the dealer always qualifying. I guess I'm just asking about the dealer making specific hands (i.e., any aces-up level hand) with the 6th card when they didn't have that hand with just the initial 5 cards. I'm also wondering about specific player vs. dealer scenarios. EX: I have a pair of 3s and raise 1x. The dealer has a pair of 4s when his 6th card (also the up card) was a 4. Maybe I'm not quite explaining this right.

What you do not seem to understand is there is no published data for you to look at that will answer you questions.

The math behind the answers to your questions is more advanced than just adding 2+2.

If you can do some math yourself, here is a link to a Poker site (from 2000) that shows how to do the math.

6-Card Poker Hands
Now the link shows 6 card poker hands but for 5 cards meaning you will have to redo the math for 4 card hands.
But if can can understand the math there you should be able to take the formulas and the Wizards' table from WoO and answer your own questions.

Then you could post them here for free and let everyone see if you did all the math correctly.
At least give it a try

That's fine; I was just curious if it was possible to figure out. I was fairly good at math in school, but far from a whiz (plus I haven't done much serious math in a few years). I might take a shot at these numbers later on though. I was mainly curious because 4CP is a game I enjoy playing sometimes. Most people I play with shy away from the ante bet because of that extra dealer card. It just got me thinking...

It seems the best approach would be to analyze the game first as if the dealer was dealt only 5 cards, and then analyze it again with the dealer getting 6 cards, then compare the results.

If you were to brute force every possible scenario, you'd have 19.93 trillion scenarios for the 5-card game and 167.44 trillion scenarios for the 6-card game, or 187.37 trillion scenarios in all. This can be reduced to "only" 9.69 trillion scenarios by analyzing each unique 5-card starting hand and weighting the results accordingly.

So, I'm not going to try it either as it would tie up my computer for days or possibly weeks.

If I know miplet, he'll probably have a spreadsheet done by the time I finish posting this. :)

I think what you are asking is "how much does the 6th card help"?

You would have to look at all of the hands and then add the 6th card influence to determine whether it helps or not. For example, if you have 5 cards, unsuited, unmatched, and not near to completing a straight, what are the odds of completing a pair?

If there were were no other cards dealt, you'd deal with the 2.598 million combinations already in the 5 card hand and then multiply that by the 46 other outcomes in the 6th card. You could eliminate a few - 4 of a kinds and straight/royal flushes already dealt, but you would have to consider all other hands as an improvement is possible by the 6th card.

Perhaps a better way to look at it is the 5 card poker probabilities for four card, then to look at the 6 card probabilities for four card and assume the difference is the 6th card.

If I have time tonight, I might take a look at it.