three card poker

On your site I found the following question and answer regarding three card poker:



Wizard, I have just read an article on another site that was talking about Three Card Poker. The author called the "Pair Plus " bet a sucker bet ,compared to the "ante" bet. Of the two bets , I thought the "ante" bet was more of a sucker bet because of its higher house edge. Also, what is the element of risk in Three Card Poker , compared to Let it Ride , assuming the player is starting with $5 bets in the three betting circles for Let It Ride, and $5 in the Pair plus and ante bet in Three Card Poker?
— Eddie from West Memphis, Arkansas


Good question. In full play Three Card Poker the house edge on Pairplus is 2.32% and on Ante & Play is 3.37%. However the element of risk on Pairplus is still 2.32% while in Ante & Play it is 2.01%. I believe if comparing one game to another the element of risk is more appropriate. In other words comparing the expected loss to the total amount bet. In this case Ante & Play has the lower element of risk and is thus the better bet. So I would disagree with the writer of the article you mention. According to my house edge index the element of risk in Let it Ride is 2.85%, higher than that of Ante & Play.



After I clicked on the link enclosed in the answer it showed a house edge of over 7 per cent. Can you please explain the discrepancy? The number to the far right was the standard deviation.



Poker Pairplus 7.28% 2.85

When the flush pays 3, the edge is 7.28%, when it pays 4, the edge is 2.32%. It pays 3 pretty much everywhere now...

Thank you most earnestly for that clarification, it actually means a great deal to me. I have been attempting to bank CA three card recently. In comparing the game to ultimate Texas Holdem, I have been trying to figure how to quantify player ineptitude. In other words, UTH has a small published house edge based on optimal play, after accounting for element of risk-- around a half percent. But when many of the donkeys don't fourex hands like AK suited, or tend to defend properly with kickers, that house edge must climb significantly. In three card one sees many less egregious misplays, but the base house edge is much higher. I have attempted to contact Stephen How, Grosjean and Shakleford to no avail, thus far, in seeking clarification.

In CA three card I use the following reasoning: If I see a player betting ten across (they usually bet equally on both the pair plus and six card bonus) I figure that the two bonus bets alone approximately offset my two dollar collection to bank. If the pair plus is 7% and the six card bonus is 15% then the two combined should net around a couple of bucks in profit. All the other bets should then be profit gravy. Does this thinking seem sound to you? By accurately clarifying my original question you have eminently qualified yourself to answer whoever you are--not to mention your implied expertise based on your number of posts. Thank you again in advance.

Quote: joethomas135

In CA three card I use the following reasoning: If I see a player betting ten across (they usually bet equally on both the pair plus and six card bonus) I figure that the two bonus bets alone approximately offset my two dollar collection to bank. If the pair plus is 7% and the six card bonus is 15% then the two combined should net around a couple of bucks in profit. All the other bets should then be profit gravy. Does this thinking seem sound to you? By accurately clarifying my original question you have eminently qualified yourself to answer whoever you are--not to mention your implied expertise based on your number of posts. Thank you again in advance.

Usually, the corporation will always bank the bonus bets, and a player-banker will only bank the base game. I'm not even sure if it's possible to elect to bank the side-bets. After all, the corporation has $20k, $30k, $50k (whatever the little button says at that table) in guaranteed funds.

Right now the only thing the third party proposition player (player banker) doesn't bank is the dollar progressive jackpot. You can imagine how strong the rake is on that for them not to give it up. So yes, the banker can and must bank those aforementioned side bets. I usually have at least 15k on the table to do so. If you don't put a substantial sum on the layout they simply refuse to play on your bank. Can't blame them for that. Having said this and returning to my earlier question, is my logic sound that the two ten dollar bets for the pair-plus and six card bonus, an apparent combined average 11% edge, basically off-sets the two dollar collection?

Quote: joethomas135

Having said this and returning to my earlier question, is my logic sound that the two ten dollar bets for the pair-plus and six card bonus, an apparent combined average 11% edge, basically off-sets the two dollar collection?

I don't see why not, but your expected net win would only be $0.20/hand.

Quote: rdw4potus

I don't see why not, but your expected net win would only be $0.20/hand.

Does he have to pay out $2 per player hand? Jeez, I am shocked they offer $10 minimums if so.

Quote: tringlomane

Does he have to pay out $2 per player hand? Jeez, I am shocked they offer $10 minimums if so.

Just $2/round. But even at a full table with each player betting $10 across like that, it's only $1.20/round. Factor out what you lose back playing when you aren't banking, and it's not a very big expected gain per hour.

Quote: rdw4potus

Just $2/round. But even at a full table with each player betting $10 across like that, it's only $1.20/round. Factor out what you lose back playing when you aren't banking, and it's not a very big expected gain per hour.

Oh, yeah...he doesn't always get to bank these I suppose. But isn't he gaining 11% x $20 = $2.20 per hand from every player that bets $10 on each when he does bank? And if he only has to pay one $2 fee, doesn't that mean he profits on average $11 - $2 = $9 per bank with 5 other players (if they bet as above)? Pardon my ignorance about California gaming law; I have never played there.

Quote: tringlomane

Oh, yeah...he doesn't always get to bank these I suppose. But isn't he gaining 11% x $20 = $2.20 per hand from every player that bets $10 on each when he does bank? And if he only has to pay one $2 fee, doesn't that mean he profits on average $11 - $2 = $9 per bank with 5 other players (if they bet as above)? Pardon my ignorance about California gaming law; I have never played there.

Yes, yes you're right. careless math error on my part. But then he also spends $1/hand to play the non-banked hands, and loses about $0.32/hand to the house edge assuming that only the ante/play is played. Rules vary about how often the player can bank (like with PGP banking in non-CA casinos), but if the player can bank only 1 in 7 hands, then he loses back 6 $1 fees and about $2 to the house edge on the played hands. So, for each 7 hand cycle, it's $11 in profit from the banked hand minus $8 in total fees minus $2 in house edge exposure=$1 in net profit.

I was in Harrington DE recently and saw that they have the most favorable tables, both bets, for 3 card poker.

I hadn't played any practice games recently. A guy wants to be up to date on what pays when, I think, having heard the dealer can scoop it up and be wrong about it. For these reasons and some time limitations I didnt play, although tempted.

No. Just two dollars per banking round.

When I am confused about math it is usually my A.D.D. brain which has overlooked something simple. However, unless such is the case here, I think you are underestimating the earn substantially. If we disregard the ante-play bets just for the sake of argument, and assume we have four players betting ten across and the remaining two spots not playing, what do we have? According to my calculations, if we just deal with the published and accepted numbers for the ante-plus and the six card bonus, those bets are yielding about two bucks apiece (11% of twenty dollars is more than two bucks). So again, without counting the ante-play, we have eight bucks earn between the four spots. Subtract the collection, a total of two dollars per round, and that leaves a six dollar profit. You only need six banking rounds per hour to reach $72 per hour. I have hundreds of hours in UTH (not three card in which the basic house edge is five or six times greater than UTH ) where I am actually doing much better than that. I believe, and hope, you have miss-placed a decimal in your parsing of the problem. Obviously it cant be only "$1.20" per round when each individual spot is worth more than two dollars.

Somehow I had missed your post acknowledging your "careless" math error before posting my reasoning. I failed to mention that the casinos are not forcing bankers to play, and although I do, many do not. Assuming no banker play and some addition earn on the ante-play, would you now change your pessimistic outlook?

Quote: joethomas135

Somehow I had missed your post acknowledging your "careless" math error before posting my reasoning. I failed to mention that the casinos are not forcing bankers to play, and although I do, many do not. Assuming no banker play and some addition earn on the ante-play, would you now change your pessimistic outlook?

If other players generally aren't banking the game for themselves, I would. Because you have enough to easily cover the 1000:1 payout for a Royal on 6-card, correct? If you were forced to pay out $1M for a 6-card Royal in diamonds (like Vegas), then I would tell you no.

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You are only responsible for what you choose to place on the table.