A local casino offers a three card poker game where they reveal one card. All rules remain the same except what if there were no ante bonus? Regardless if you have a straight, trips, or straight flush, you will only receive even money for the ante bet. The play will also receive even money assuming dealer qualifies. What will be the house edge on this game?

Please ask if you need me to clarify anything.

Depends on how the game is dealt and what pay tables are used, whether it's a PA.

Here are rules from Wizard of Odds for 1 version of it.

https://wizardofodds.com/games/face-up-three-card-poker/

Here's a thread from a few years ago about it, including several links to different casino versions.

https://wizardofvegas.com/forum/gambling/tables/23704-ultimate-3-card-poker-face-up/#post485895

More details on the particular game you're seeing, especially a rules card, would be appreciated.

1. Dealer shows 1 up card.

2. Dealer must qualify with a Q.

3. Ante gets paid if dealer doesn't qualify.

4. No Ante Bonus.

I believe that is everything. Let me know if there's a rule i'm missing. It seems like a very decent game.

Quote:ADVplayerIt is not the same as face up three card, it is better. Here are the rules:

1. Dealer shows 1 up card.

2. Dealer must qualify with a Q.

3. Ante gets paid if dealer doesn't qualify.

4. No Ante Bonus.

I believe that is everything. Let me know if there's a rule i'm missing. It seems like a very decent game.

Pairs Plus of course doesn't change. Do they make you play that bet as a 1-3-6 table kills. I don't think point number 3 is a true statement.

Quote:boymimboPairs Plus of course doesn't change. Do they make you play that bet as a 1-3-6 table kills. I don't think point number 3 is a true statement.

No. You can play only the ante and play.

One card is being shown. I am following the wizards basic strategy. If they have a J or lower, I play every hand. Otherwise, i play Q92 vs Q, K92 vs K and A92 vs A.

The only difference is that there is no ante bonus.

It is too good to be true for a casino to offer a beatable game but i thought I'd ask the forum anyways.

Quote:ADVplayerIt is not the same as face up three card, it is better. Here are the rules:

1. Dealer shows 1 up card.

2. Dealer must qualify with a Q.

3. Ante gets paid if dealer doesn't qualify.

4. No Ante Bonus.

I believe that is everything. Let me know if there's a rule i'm missing. It seems like a very decent game.

The big differences between what the wizard has and what you're reporting are:

1. Do you have to beat the dealer even if he doesn't qualify to win the ante?

2. Is there any per-hand ante or surcharge on a win?

Dealer pays my ante if they don’t qualify.

It is free to play every hand.

I know from the Wizard of Odds analysis that in regular casino 3-card poker you have a 3.48% edge on the house if you can see a dealer card, but that includes the Ante Bonus, which this game does not have.

The Pair Plus bet at this game is also better than a typical casino as it includes the mini-Royal payout of 200:1, reducing the house advantage to 4.38% according to Wizard of Odds.

Quote:ThatDonGuyAfter some really quick number crunching, I get a house edge of 3.833% with a visible card and no ante bonus.

Thanks ThatDonGuy, but could the removal of the Ante Bonus swing the edge from player 3.48% to house 3.833% ? Seems a rather huge swing for a bonus that doesn't pay all that often.

Quote:logicGuyThanks ThatDonGuy, but could the removal of the Ante Bonus swing the edge from player 3.48% to house 3.833% ? Seems a rather huge swing for a bonus that doesn't pay all that often.

Well, I did find a problem - I was using the wrong number of hands when determining whether to play or fold a given hand.

I still get a house edge, but it's "only" 1.8022%. When I put the ante bonus back in, I get the numbers the Wizard gets - a player edge of 3.483% with one card shown, and a house edge of 3.373% with no cards shown.

If the dealer shows an Ace: play A9 or better

If the dealer shows a King: play K9 or better

If the dealer shows a Queen: play Q9 or better

If the dealer shows a 2 through Jack: always play - of the 1128 possible pairs of down cards, there are at most 132 ways the dealer can have a qualifying hand (6 pairs of Aces, 6 pairs of Kings, 6 pairs of Queens, 3 pairs of the up card, 3 ways to make a straight flush, 45 ways to make a straight (e.g. with a 6 showing, 16 8-7s, 16 7-5s, 16 5-4s, minus the three straight flushes), and 63 ways to make a flush)

Quote:ThatDonGuyIf the dealer shows a 2 through Jack: always play - of the 1128 possible pairs of down cards, there are at most 132 ways the dealer can have a qualifying hand (6 pairs of Aces, 6 pairs of Kings, 6 pairs of Queens, 3 pairs of the up card, 3 ways to make a straight flush, 45 ways to make a straight (e.g. with a 6 showing, 16 8-7s, 16 7-5s, 16 5-4s, minus the three straight flushes), and 63 ways to make a flush)

I may be misinterpreting your description, but it seems there some additional ways the dealer can qualify. What about a single Ace, King, or Queen - that would be 12 more. And what about any pair of the two down cards, not just K, Q, A?

Thanks for the analysis!

Quote:logicGuyI may be misinterpreting your description, but it seems there some additional ways the dealer can qualify. What about a single Ace, King, or Queen - that would be 12 more. And what about any pair of the two down cards, not just K, Q, A?

Good question.

Here's what I get for having a Jack face up:

Of the 1275 possible pairs of down cards ("didn't you say 1128?" Yes, but that assumes you are looking at a specific 3-card player hand)

3 are pairs of Jacks

72 are other pairs (12 ranks; for each, there are 6 different pairs)

144 are Jack and something else (for each of the 3 remaining Jacks, there are 4 Aces, 4 Kings, ..., 4 2s)

176 are Ace and something besides Ace and Jack (which have already been counted - for each of the 4 Aces, there are 4 Kings, 4 Queens, 4 10s, ..., 4 2s)

160 are King and something besides Ace, King, and Jack

144 are Queen and something besides Ace, King, Queen, and Jack

16 are 10/9 (which makes a Jack-high straight)

35 are the same suit as the face-up Jack that have not already been counted (there are 66 total, but the 11 with an Ace, the 10 others with a King, the 9 others with a Queen, and 10/9 have already been counted)

This is 750 qualifying hands; the other 525 do not.

Quote:ThatDonGuyThis is 750 qualifying hands; the other 525 do not.

So why would I always make the Play wager in this case? If I have a non-qualifying hand, and dealer shows a Jack, the strategy says to make the Play wager, hoping the dealer won't qualify. But based on your numbers it looks like the dealer will qualify 750/1275 times and I would lose more often than not.

Quote:logicGuySo why would I always make the Play wager in this case? If I have a non-qualifying hand, and dealer shows a Jack, the strategy says to make the Play wager, hoping the dealer won't qualify. But based on your numbers it looks like the dealer will qualify 750/1275 times and I would lose more often than not.

If you fold, you lose 1.

If you play with a non-qualifying hand, then you lose 2 750/1275 of the time and you win 1 525/1275 of the time, which is an expected loss of 975/1275, which is a better result than a loss of 1.

Quote:ThatDonGuyIf you fold, you lose 1.

If you play with a non-qualifying hand, then you lose 2 750/1275 of the time and you win 1 525/1275 of the time, which is an expected loss of 975/1275, which is a better result than a loss of 1.

It certainly is! Thanks!

Quote:ThatDonGuyHere is what I get for the strategy if the dealer shows a card:

If the dealer shows an Ace: play A9 or better

If the dealer shows a King: play K9 or better

If the dealer shows a Queen: play Q9 or better

If the dealer shows a 2 through Jack: always play - of the 1128 possible pairs of down cards, there are at most 132 ways the dealer can have a qualifying hand (6 pairs of Aces, 6 pairs of Kings, 6 pairs of Queens, 3 pairs of the up card, 3 ways to make a straight flush, 45 ways to make a straight (e.g. with a 6 showing, 16 8-7s, 16 7-5s, 16 5-4s, minus the three straight flushes), and 63 ways to make a flush)

I did this three years ago, Combination Analysis results for 3CP, delear show 1 card, WITHOUT ante bonus, raise if equal or better than X92( X is dealer's upcard, Q, K or ACE).

I proposed the X92 strategy as well but it may NOT the optimum strategy. Anyone can verify it ? gordonm888 ?

See image : https://ibb.co/52DjWwy

Quote:ssho88I did this three years ago, Combination Analysis results for 3CP, delear show 1 card, WITHOUT ante bonus, raise if equal or better than X92( X is dealer's upcard, Q, K or ACE).

I proposed the X92 strategy as well but it may NOT the optimum strategy.

What is your strategy if X is not Queen or higher? If it's "always raise," then I can confirm your strategy.

Yes I can confirm the strategy and house edge of 1.802206%.Quote:ssho88I did this three years ago, Combination Analysis results for 3CP, delear show 1 card, WITHOUT ante bonus, raise if equal or better than X92( X is dealer's upcard, Q, K or ACE).

I proposed the X92 strategy as well but it may NOT the optimum strategy. Anyone can verify it ? gordonm888 ?

See image : https://ibb.co/52DjWwy

The worst hands you can have versus a low card is one with no matching suits nor any straight penalty cards. The ranks of your hand (assuming you don't have A,K or Q) are irrelevant as it's only how many outs the dealer has that matters.

Perms: 1128 Win: 0 Lose: 726 Tie: 0 DNQ: 402 Ch1: 0 Ch4: 0 Ch5: 0 TEV: -0.9308510638297872 Cards: 2s 3h 5d/9c

As an example here are the close hands versus a Queen...

Perms: 1128 Win: 291 Lose: 829 Tie: 8 DNQ: 0 Ch1: 0 Ch4: 0 Ch5: 0 TEV: -0.9539007092198581 Cards: 2s 9h Qd/Qc

Perms: 1128 Win: 270 Lose: 849 Tie: 9 DNQ: 0 Ch1: 0 Ch4: 0 Ch5: 0 TEV: -1.0265957446808511 Cards: 7s 8s Qh/Qs

Quote:Runlikegod777I asked this same question to wizard or another top guy on here few years ago,they showed the math as 1.8% house edge. California 3 card poker right?

I was under the impression that CA 3-card poker has a commission and this game did not. Otherwise I believe it is essentially CA 3-card poker.

Quote:charliepatrickYes I can confirm the strategy and house edge of 1.802206%.

The worst hands you can have versus a low card is one with no matching suits nor any straight penalty cards. The ranks of your hand (assuming you don't have A,K or Q) are irrelevant as it's only how many outs the dealer has that matters.

Perms: 1128 Win: 0 Lose: 726 Tie: 0 DNQ: 402 Ch1: 0 Ch4: 0 Ch5: 0 TEV: -0.9308510638297872 Cards: 2s 3h 5d/9c

As an example here are the close hands versus a Queen...

Perms: 1128 Win: 291 Lose: 829 Tie: 8 DNQ: 0 Ch1: 0 Ch4: 0 Ch5: 0 TEV: -0.9539007092198581 Cards: 2s 9h Qd/Qc

Perms: 1128 Win: 270 Lose: 849 Tie: 9 DNQ: 0 Ch1: 0 Ch4: 0 Ch5: 0 TEV: -1.0265957446808511 Cards: 7s 8s Qh/Qs

Ssho88, this looks right to me.

The decision to not fold your hands that are Jack-hi and lower vs a dealer 2-J is not close. And the dealer's upcard will be 2-J with a frequency of 10/13 and you will have a J-high or lower about 30% of the time -so this is a big deal.

On a hand like 2s 9h Qd vs Qc you will lose whenever the dealer has at least one T, J,Q,K or A as one of his two other cards. Notice that simplifies the analysis, because you don't need to worry about the dealer making a straight or pairing the Q -those would involve cards that are in the range T-A, which I have just said is an automatic loser. You also lose when the dealer has 9 and a third card higher than a 2. There are basically 27 cards left in the deck from 2-8 and you win only when the dealer has 2 of those 27 cards without those two being a pair, and without those two cards being the same suit as the queen.

If you peek at a neighbor's hand you can sometimes make different decisions vs a Q,K or Ace depending upon how many of those 27 low cards you see -but, as I remember it that is worth less than 0.1% in house edge. My PC's hard disk is still in the the clean room at the data recovery shop so I can't quote anything specific.

The only info I have is for regular 3CP.Quote:gordonm888...If you peek at a neighbor's hand....

I ran a quick simulation where you're able to see all cards in the other five players and then make the decision whether to play or fold. As the numbers were small it's only a rough estimate. The basic House Edge (5 4 1) for 3CP is 3.373% (EoR 2.015%) and the House Edge went to 2.621% (EoR 1.523%).

The sim always played K-high and gradually folded various Q-highs. Note it often (about 18%) played zip hands.

The fold rates were about

10% at QT2

25% at Q87

50% at Q64

67% at Q32

82% at zip

Quote:charliepatrickThe only info I have is for regular 3CP.

I ran a quick simulation where you're able to see all cards in the other five players and then make the decision whether to play or fold. As the numbers were small it's only a rough estimate. The basic House Edge (5 4 1) for 3CP is 3.373% (EoR 2.015%) and the House Edge went to 2.621% (EoR 1.523%).

The sim always played K-high and gradually folded various Q-highs. Note it often (about 18%) played zip hands.

The fold rates were about

10% at QT2

25% at Q87

50% at Q64

67% at Q32

82% at zip

The reason that Q32 is folded so much less (67%) than "zip" (*2%) is because the player has a Q in his hand, depriving teh dealer of that card.

As I remember (I've done this same calc, lol) most of the advantage comes from times when you bet with zip -because you have zip so frequently.

Quote:gordonm888The reason that Q32 is folded so much less (67%) than "zip" (*2%) is because the player has a Q in his hand, depriving teh dealer of that card.

As I remember (I've done this same calc, lol) most of the advantage comes from times when you bet with zip -because you have zip so frequently.

I have a regular 3CP EV calculator for any specific 3CP hand, you can input your cards and up to other six players cards(rank and suit), you can even input dealer's hole card if you can see it(LOL!).There are three types of EVs, RAISE ALL THE TIME, RAISE ACCORDING TO BASIC STRATEGY(Q64) and RAISE ACCORDING TO HOLE CARD STRATEGY.

I can help to calculate the ev if you wish.

3CP is actually one of the easiest casino games to model, don't we all agree?