Different 3-Card Tables - different optimum raise?
I know the agreed optimum hand to raise from your ante on 3 card poker is Q-6-4 but what about when the qualifying hand for the dealer changes? Is the optimum hand the same?
My local casino dealer qualifies to play with Q-8 so I'm not sure how Q-6-4 can be optimum? Or is that only when it's any Q hand that qualifies the dealer?
Might be something I'm just not getting.
Advice please? Wizard?
This is a strange question. I ran my software with dealer various qualifying hands and recorded the minimal player hand and the house edge.Quote: SmilesAndLegs93My local casino dealer qualifies to play with Q-8 so I'm not sure how Q-6-4 can be optimum? Or is that only when it's any Q hand that qualifies the dealer?
Dealer - Q32, Player Q64, edge = 3.3730%
Dealer - Q42, Player Q64, edge = 3.5563%
Dealer - Q52, Player Q64, edge = 3.9219%
Dealer - Q62, Player Q65, edge = 4.4680%
Dealer - Q72, Player Q72, edge = 5.1939%
Dealer - Q82, Player 984 (3 different suits), edge = 5.9987%
The result for the minimal player hand when the dealer qualifies with Q82 is counter-intuitive. You play 9/8/4 if it consists of three different suits, but if a suit is duplicated, you fold. This logic applies to other borderline hands as well. In other words, it's no longer a linear strategy based on the rank of the hand alone.
For example you play 9/8/4 (three suited) but fold J/T/7 (two suited).
Are you saying the dealer needs at least Q-8 to qualify, not just a Q? IE: Q32 would not qualify? If so, the strategy to raise should be.....ah damn, teliot beat me to it!
Side note question for teliot -- at what point for qualifying gives the highest HE on the game? Clearly it goes up, but it cannot keep going up and should level off somewhere then dip back down.
The answer to this very interesting question is for the dealer to qualify with Q/8/4 or higher, which has a house edge of 6.1327%.Quote: RSSide note question for teliot -- at what point for qualifying gives the highest HE on the game? Clearly it goes up, but it cannot keep going up and should level off somewhere then dip back down.
Q/8/2 -> 5.9987%
Q/8/3 -> 6.1063%
Q/8/4 -> 6.1327%
Q/8/5 -> 6.0729%
Obviously this casino did its homework coming up with the Q/8 qualifier.
Quote: teliotThe answer to this very interesting question is for the dealer to qualify with Q/8/4 or higher, which has a house edge of 6.1327%.
Q/8/2 -> 5.9987%
Q/8/3 -> 6.1063%
Q/8/4 -> 6.1327%
Q/8/5 -> 6.0729%
Obviously this casino did its homework coming up with the Q/8 qualifier.
Interesting, thanks.
I mean.. I could play with Q-6-4 but even if the dealer gets Q-7-2 they won't qualify and I'll win.
How is them needing Q-8 to qualify worse for the player than them needing just a Q?
Thanks
Quote: SmilesAndLegs93How is them needing Q-8 to qualify worse for the player than them needing just a Q?
This is because of being denied more full pay wins when the dealer has a statistically losing hand you can beat. With a dealer's Q32 qualifier level, you get denied full pay about 33% of time; with Q-8-3 you get denied the full pay payouts closer to 40%.
When the qualifier rises above a certain level, this house edge effect reserves, as you're now getting the smaller but guaranteed half-pay win on many more hands you would lost against the dealer higher and stronger non-qualifier, but now win a half pay on. (Look at it this way: if the dealer qualifies or plays with a pair or better, then you get "guaranteed paid" half when he has any high card hand the majority of the time. Now, more of your losing crap hands win half instead of lose.)
Perfect reply, thanks Dan.Quote: PaigowdanThis is because of being denied more full pay wins when the dealer has a statistically losing hand you can beat. with a Q32, you get denied full pay about 33% of time; with Q-8-3 it is closer to 40%.
When the qualifier rises above a certain level, this house edge effect reserves, as you're getting the smaller but guaranteed half-pay on many hands you would have lost but now win.
What's amazing is that Q-8 is the worst possible qualifier from the player side, yet your casino opted for exactly this. Hardly a coincidence, I am sure.Quote: SmilesAndLegs93Thanks guys, I think the penny has dropped. Playing 9-8-4 unsuited seems super strange. But then that's the maths... it's a shame I don't have any other casinos to pick from!
Interesting. Is that a local maximum or a global one?Quote: teliotThe answer to this very interesting question is for the dealer to qualify with Q/8/4 or higher, which has a house edge of 6.1327%.
Q/8/2 -> 5.9987%
Q/8/3 -> 6.1063%
Q/8/4 -> 6.1327%
Q/8/5 -> 6.0729%
Obviously this casino did its homework coming up with the Q/8 qualifier.
Quote: PaigowdanI think the casino is doing a pretty nasty bait & switch here: people know and love Three Card Poker as a relatively fair and reliable staple of the casinos, - so one casino decides to discreetly submit a new and higher-edged version of it, knowing they got a lock on the local gamblers in that neck of the woods. This is messed up, and 100% un-American here, for lack of a better description. I will say so.
As a matter of revenge against such a morally reprehensible casino like this one, would you be supportive of someone partaking in the equally horrific and disgusting act of counting cards at their blackjack tables?
Analytically, to prove it's global I would need to run the program for 22100 different dealer qualifiers. I'm going to pass on the analytical solution to your question.Quote: MathExtremistInteresting. Is that a local maximum or a global one?
Maybe someone here can come up with a heuristic argument.
My "argument by mathematical instinct" says it's global.
Thanks JB! Excellent. BTW, I realized just after I typed my last that you could reduce to equivalence classes.Quote: JBQ-8-4 is indeed the global maximum, as determined by running a full analysis of the game using each possible hand rank (there are 741) as the dealer's minimum qualifying hand.
It seems like this fact should be recorded somewhere in the official record of trivia about 3CP.
Quote: michael99000As a matter of revenge against such a morally reprehensible casino like this one, would you be supportive of someone partaking in the equally horrific and disgusting act of counting cards at their blackjack tables?
No.
Read Romans 12:17, ("Return evil for evil to no one...."/Do not seek revenge.)
If a game offers a bad value, just don't play it, or support a better/fairer casino.
It's rare enough I condemn a casino, don't push yer luck.
Quote: teliotIt seems like this fact should be recorded somewhere in the official record of trivia about 3CP.
Of the 741 unique hand ranks, only 72 have a house edge, and here they are:
(the house edge figures assume an ante bonus paytable of 0-0-0-1-4-5)
| Qualifier | House Edge |
|---|---|
| J85 | 0.1506% |
| J86 | 0.3423% |
| J87 | 0.5334% |
| J92 | 0.7243% |
| J93 | 0.9160% |
| J94 | 1.1067% |
| J95 | 1.2972% |
| J96 | 1.4873% |
| J97 | 1.6766% |
| J98 | 1.8657% |
| JT2 | 2.0548% |
| JT3 | 2.2444% |
| JT4 | 2.4337% |
| JT5 | 2.6227% |
| JT6 | 2.8109% |
| JT7 | 2.9986% |
| JT8 | 3.1862% |
| Q32 | 3.3730% (standard) |
| Q42 | 3.5563% |
| Q43 | 3.7392% |
| Q52 | 3.9219% |
| Q53 | 4.1041% |
| Q54 | 4.2862% |
| Q62 | 4.4680% |
| Q63 | 4.6497% |
| Q64 | 4.8312% |
| Q65 | 5.0125% |
| Q72 | 5.1939% |
| Q73 | 5.3703% |
| Q74 | 5.5340% |
| Q75 | 5.6920% |
| Q76 | 5.8481% |
| Q82 | 5.9987% |
| Q83 | 6.1063% |
| Q84 | 6.1327% (highest) |
| Q85 | 6.0729% |
| Q86 | 5.9688% |
| Q87 | 5.8557% |
| Q92 | 5.7409% |
| Q93 | 5.6222% |
| Q94 | 5.5005% |
| Q95 | 5.3760% |
| Q96 | 5.2495% |
| Q97 | 5.1210% |
| Q98 | 4.9907% |
| QT2 | 4.8587% |
| QT3 | 4.7229% |
| QT4 | 4.5842% |
| QT5 | 4.4427% |
| QT6 | 4.2992% |
| QT7 | 4.1536% |
| QT8 | 4.0061% |
| QT9 | 3.8568% |
| QJ2 | 3.7058% |
| QJ3 | 3.5503% |
| QJ4 | 3.3920% |
| QJ5 | 3.2308% |
| QJ6 | 3.0676% |
| QJ7 | 2.9024% |
| QJ8 | 2.7352% |
| QJ9 | 2.5660% |
| K32 | 2.3950% |
| K42 | 2.1892% |
| K43 | 1.9805% |
| K52 | 1.7691% |
| K53 | 1.5555% |
| K54 | 1.3393% |
| K62 | 1.1204% |
| K63 | 0.8995% |
| K64 | 0.6758% |
| K65 | 0.4494% |
| K72 | 0.2212% |
Quote: JBOf the 741 unique hand ranks, only 72 have a house edge, and here they are:
(the house edge figures assume an ante bonus paytable of 0-0-0-1-4-5)
Qualifier House Edge J85 0.1506% J86 0.3423%
Just wait, now Phil Ivey is going to try to get a casino to play high stakes Three Card Poker with purple Gemaco cards and a Jack-or-better qualifier.
Quote: MathExtremistJust wait, now Phil Ivey is going to try to get a casino to play high stakes Three Card Poker with purple Gemaco cards and a Jack-or-better qualifier.
Meanwhile, several casinos will switch to the Q-8 qualifier.
Quote: JBMeanwhile, several casinos will switch to the Q-8 qualifier.
They will shoot themselves in the foot with this one.
Perhaps Mike will update his WOO page to alert all to this threat, in a "no Good Housekeeping seal of approval" for this maneuver.
