Three Card Poker - FAQ

I'm convinced that Q/6/4 represents the most effective strategy for playing three card poker. Interestingly, Stanley Ko reached the same conclusion independently. This recommended approach is informed by a computer program that evaluates all 22,100 possible combinations of the player’s three cards against the 18,424 potential combinations of the dealer's three cards.

If you adhere to the dealer's strategy, there may be instances where you end up folding hands that have a higher expected return than -1 (the return resulting from folding). However, overall, this shouldn’t significantly affect your gameplay.

Let's start by figuring out the probability of a king-high hand and I'll briefly outline how to calculate the probabilities for the other two types. The probability is given by the ratio of king-high hands to the total hands available. Since there are 11 ranks below a king, a king-high hand must include two distinct ranks from this group. The calculation for choosing 2 out of 11 ranks is given by (11,2) = 55. However, one of these combinations is king-queen-jack, which creates a straight, so we must exclude that, leaving us with 54 combinations that do not form a straight. Then, taking into account the four suits available for each rank, we multiply by 4, giving us 64 possible suit combinations. Yet, four of these result in a flush, leaving us with 60 valid combinations. Consequently, the total number of king-high combinations amounts to 54 multiplied by 60, yielding 3,240. Given that there are combin(52,3) = 22,100 ways to select 3 cards from 52, the probability of obtaining a king-high is therefore 3,240 divided by 22,100, which is approximately 0.1466063. For an ace-high hand, the probability equates to: (combin(12,2)-2)*(4, -4)/combin(52,3) = 0.1737557, taking into account an adjustment of -2 to account for both the a-2-3 and q-k-a straights. combin To find the probability of achieving a queen-high hand, we have: (combin(10,2)-1)*(4, ...³How is the house edge calculated in Three Card Poker, specifically concerning ante and play bets? I haven't participated yet, but I suspect the edge stems from the necessity for players to act before dealers. If a player folds while the dealer does not qualify, does that still guarantee a payout on the ante bet? If not, it would seem like a level playing field, which can't be right. I appreciate your help.³You’re correct; the house edge arises from the player acting first. If both the player and the dealer choose to fold, the player suffers a loss.

Firstly, I want to commend you on your impressive website. I inform all my acquaintances that if they plan to gamble, they must first check out your site! I have a query regarding the ante and play aspects of Three Card Poker. If you are aware of one of the dealer's three cards, how should your fundamental strategy shift? Could this knowledge provide an edge over the house, and to what extent?³-4)/combin(52,3)=0.119457.

In the context of Three Card Poker, would it be wise to increase your wager after experiencing 5 or 6 consecutive losses? I understand that the Martingale strategy is typically not advised, but considering the possibility of bonus payouts for superior hands in Three Card Poker, it could be worth considering. Please take a moment to reflect before responding.

Please see my hole carding I was at the Venetian playing three card poker this past weekend when a friend of mine managed to draw three queens of the same suit in two consecutive deals. I'm quite curious about the odds of such an event occurring.

How likely is it to get two identical straight flushes, both in terms of rank and suit, over two hands in Three Card Poker?

That’s an excellent question. In full play of Three Card Poker, the house edge for Pair Plus is 2.32%, while it’s 3.37% for Ante & Play. However, the risk element associated with Pair Plus remains at 2.32%, while for Ante & Play, it falls to 2.01%. In comparing these games, it would be more pertinent to assess the element of risk, effectively comparing the anticipated loss to the overall amount wagered. In this light, the Ante & Play option demonstrates a lower element of risk, marking it as the superior choice. Hence, I would not align with the opinion of the article’s author. By my estimation, the element of risk for Let It Ride stands at 2.85%, which is higher than that of Ante & Play.²Wizard, could you explain whether there is any advantage to playing two hands versus one in Three Card Poker? Some casinos permit you to play two hands, allowing you to evaluate the first hand before making a decision about the second. Conversely, other casinos require you to play the second hand without looking, which seems disadvantageous. Thank you.²/4, or 1 in 122102500.

The probability of getting a straight flush on the first hand is 4*12/combin(52,3) = 48/22100 = 0.0022. The probability that the next hand will be exactly the same is 1/22100. So the answer is (48/22100)*(1/22100) = 48/488410000, on 1 in 10,175,208. This is a 1.37 more likely than hitting a 6/49 lottery, which has a probability of 1 in 13983816.

I posed this exact question for one of my assignments in my casino math class at UNLV. Although it’s true that the Ante & Play bet generally carries a higher house edge, it is nonetheless the more advantageous bet. This is largely due to its lower element of risk, meaning the ratio of expected losses to the total amount wagered is better. house edge index When playing Three Card Poker, what would be the most strategic ratio between the Pair Plus bet and the Ante/Play bet? Given that if you hold a Q/6/4 or superior without a pair, but the dealer does not qualify, you would lose the Pair Plus bet while still winning the Ante. In this scenario, having equal bets on both would lead to a push, but increasing the Pair Plus bet relative to the Ante might yield a profit on the Pair Plus.

In your probability chart for Three Card Poker, you indicate that the total number of combinations for Queen to Ace high is 9,720, while the count for Jack high or lower stands at 6,720. I’ve attempted to derive these probabilities independently but have struggled. Could you please share your calculations? I would greatly appreciate it.

Next, let's examine the combinations available for a Jack high or lower hand. With 3 ranks omitted, we have 3 ranks to choose from out of 10. However, 8 combinations can yield a straight (from 2/3/4 through to 9/10/J). Again, with 4, -4 methods available for selecting suits, the total combinations are (combin(10,3)-8)*(4,-4) = 6,720. Consequently, the combinations for Q-A high are simply 16,440-6,720 = 9,720. For clarity on the combin function, please refer to my...

The probability of forming a straight is actually lower than that of achieving a flush with three cards. To form a flush, the combination count is 4*(combin(13,3)-12) = 1096, whereas the number of ways to achieve a straight is only 12*(4, ...

There are combin(52,3) = 22,100 distinct ways to select 3 cards from a standard 52-card deck. Thus, the probability that any given hand will exactly match the previous hand is 1 in 22,100.³-4) = 16,440.

What are the odds of drawing the same hand as the dealer in Three Card Poker, and how did you derive that answer?³The probability of that happening is around 1 in 903.76, but explaining the full solution would be quite complex.³What is the optimal ratio between the Pair Plus and Ante bets in Three Card Poker? probabilities in poker section.

Three Card Poker - Common Questions - Wizard of Odds³-4) = 720.

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You've suggested sticking with the Q/6/4 hand, but a dealer from Tunica indicated Q/J. Can you explain the discrepancy? Is the recommendation to use Q/6/4 rooted in actual statistical analysis? This game appears to be favorable due to its minimal house edge and requires no skill. What are your thoughts?

Choosing to follow the dealer's strategy means you might fold on hands that actually have an expected return higher than -1 (the return you get from folding). However, in the grand scheme of things, this shouldn't significantly impact your overall performance. element of risk What steps should I take to calculate the individual probabilities for achieving: (1) a queen high hand, (2) a king high hand, and (3) an ace high hand while playing three card poker?

(11,2) = 55. However, one of these combinations is king-queen-jack, which creates a straight, so if we subtract that, we have 54 combinations that don't make a straight. Next, for each rank, there are four different suits, or 4, giving us 64 potential suit combinations. Nevertheless, four of these combinations yield a flush, so we end up with 64-4=60 suit combinations that are valid. Thus, the total number of king high hand combinations equals 54*60=3240. The overall total is combin(52,3)=22,100 for arranging 3 cards from a deck of 52. Hence, the likelihood of forming a king high is 3,240/22,100 = 0.1466063. For an ace high, the probability is calculated as: (combin(12,2)-2)*(4',-4)/combin(52,3)=0.1737557. The -2 accounts for both the a-2-3 as well as q-k-a straights.

How is the house advantage calculated in Three Card Poker concerning the ante and play bets? I haven't had the chance to play yet, but I suspect the house advantage arises from the player's obligation to act first. If the player folds and the dealer does not qualify, does that mean the player still receives payment for the ante? Otherwise, it seems like it would play out as an even game, which can't be right. Thank you for the clarification.

Firstly, I want to commend you on your fantastic website. I encourage all my acquaintances to check your site before they make any gambling decisions! My query is regarding the Three Card Poker ante and play. If a player knows one of the dealer's cards, how should they modify their fundamental strategy, and could this give them an edge against the house? If so, to what extent?

In Three Card Poker, do you think it's wise to raise your bets after experiencing, say, 5 or 6 consecutive losses? I'm aware that the Martingale system is often frowned upon, yet given that Three Card Poker includes bonus payouts for superior hands, it might be worth considering. Please take a moment to reflect on this before responding.

The house edge of that pay table is 2.70%.

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What is the chance of being dealt two identical straight flushes (both in rank and suit) in consecutive hands while playing Three Card Poker?

That's a great query. In the case of a full play of Three Card Poker, the house edge for Pair Plus stands at 2.32%, while for Ante & Play it is higher at 3.37%. However, the risk associated with Pair Plus remains at 2.32%, while in Ante & Play it drops to 2.01%. When comparing different games, assessing the element of risk is more relevant—essentially gauging the expected loss against the total amount bet. By this standard, Ante & Play demonstrates a lower risk factor, making it the more advantageous option. Therefore, I would assert my disagreement with the author of the article you've mentioned. According to my calculations, Gambling 102 the risk element in Let It Ride is at 2.85%, which is greater than that of Ante & Play.

That's an interesting question. According to Stanley Ko's publication Mastering Three Card Poker, if you were to utilize an unseen computer that capitalizes on all the information available, having insight into the first hand would reduce the house edge from 3.37% to 3.31% for the second hand. Even with full visibility of all seven hands on the table, the house edge persists at 2.32%. house edge In the context of Three Card Poker, which option is the more advantageous bet: Pair Plus or Ante & Play?

While playing Three Card Poker, what is the ideal proportion of the Pair Plus bet compared to the Ante and Play bet? Given that if you have a Q/6/4 or better but no pairs, and the dealer does not qualify, you lose the Pair Plus bet but win the Ante, in this scenario an equal bet would result in a push. Meanwhile, doubling the Pair Plus bet would grant a win equal to the Pair Plus bet amount on the Ante.

In your probability chart for Three Card Poker, you indicated that the total combinations amount to 9,720 for Queen to Ace high hands, while Jack high or lower consists of 6,720. I'm attempting to replicate these probability calculations myself and have been unsuccessful. Could you please share your working steps? I would greatly appreciate it.

To determine the probability of any hands lower than a pair, one calculates the total combinations available for selecting 3 different ranks from a set of 13, excluding 12 for sequences that lead to a straight, and the number of ways to select suits without repetitions, excluding 4 for instances where the same suit is selected continually. Thus, for ace-high or less, the combinations tally as (combin(13,3)-12)*(4',

What determines the hierarchy of a straight over a flush in the new casino game Three Card Poker?

The total number of ways to arrange 3 cards from 52 is given by combin(52,3) = 22,100. Thus, the probability of drawing the exact same hand as the previous one is 1 in 22,100. Gambling 102 .

The probability of this occurrence is approximately 1 in 903.76, but the explanation involves a more complex process than can be briefly outlined.

The recommendation is to place 100% on the Ante and 0% on the Pair Plus, primarily because the Ante has a lower

Don’t worry, I won’t give your name.

Slot tournaments featuring significant prize pools Texas Hold ’em bonus the element of risk You suggest sticking with Q/6/4, but a dealer from Tunica recommended Q/J. What accounts for this discrepancy? Is your Q/6/4 advice derived from actual computed odds? It seems to be a solid game with relatively low house advantages and minimal required skill. What’s your perspective on this?

By following the dealer's approach, you may end up folding hands that could yield a higher expected return than -1 (the loss incurred by folding). However, in the grand scheme of things, the impact should be minimal.

Let’s begin with calculating the king high hands, and I’ll provide a quick outline of the calculations for the others. The probability is defined as the number of king high hands over the total number of hands. There are 11 ranks lower than a king, and a king high hand must include two different ranks from this selection. The possible arrangements of two ranks from eleven is

-4)/combin(52,3)=0.1737557. Note that we subtract 2 instead of 1 due to the presence of a-2-3 and q-k-a straights.

For queen high, the calculation is: (combin(10,2)-1)*(4

How is the house edge calculated in Three Card Poker (ante/play bet)? I haven’t played yet, but my assumption is that the edge arises because the player must act first on folding decisions. If a player folds and the dealer's hand doesn't qualify, does the player still receive an ante payout? Otherwise, it seems like the game would be balanced, which clearly is not the case. Thank you. flashing Three Card Poker dealers .

First of all, I want to commend you on your excellent website. I recommend it to everyone who’s interested in gambling, urging them to check it out before they play! My question relates to the ante & play in Three Card Poker. If you are aware of one of the dealer's three cards, how should you adjust your basic strategy, and could that provide you an advantage over the house? If so, by how much?

In the long run, your approach won’t have any significant impact. I’ve mentioned before that long-term outcomes show every betting system to be equally ineffective. Strategies that involve chasing losses with larger bets can lead to short-term gains, yet they come at the price of even greater losses during bad luck streaks.

That’s a thoughtful query. In terms of full play, the house edge for Pair Plus in Three Card Poker is 2.32%, while for Ante & Play, it stands at 3.37%. Nevertheless, the risk factor associated with Pair Plus remains at 2.32%, whereas for Ante & Play, it's lower at 2.01%. When comparing the two games, evaluating risk is key, specifically the expected loss against the total bet amount. In this instance, Ante & Play presents a lower risk level, making it the more favorable choice. Therefore, I would disagree with the perspective shared by the author of the article you mentioned. Based on my analysis

Wizard, could you explain the benefits of playing two hands in Three Card Poker instead of just one? Some casinos permit playing two hands, where the first one is made before looking at the second, while others only allow the second hand to be played blind — which doesn't seem advantageous for the player. Thank you.

That’s a solid question. In Stanley Ko’s guide Mastering Three Card Poker, he notes that if you had a concealed computer to maximize the information you gather, examining the first hand could reduce the house edge from 3.37% to 3.31% on the second hand. Even if you had visibility into all seven hands at the table, the house edge would still rest at 2.32%.

When engaging in Three Card Poker, which bet is more advantageous: Pair Plus or Ante & Play?

I addressed this same question in one of my assignments for my casino mathematics course at UNLV. Even though the house edge tends to be greater on Ante & Play, it remains the more advantageous bet overall. This is primarily because it has a diminished risk factor — essentially, a more favorable ratio of anticipated losses to the total wagered amount. Wizard of Vegas .

The ideal ratio is to place 100% on the ante and 0% on Pair Plus. Given optimal payout circumstances, the risk factor is 2.01% for Ante and 3.37% for Pair Plus. It’s crucial to reduce the element of risk as much as feasible. Be cautious, as fellow players often place bets on Pair Plus and may mock those who don’t conform. One time, I wagered $50 solely on the Ante and ended up with a straight flush, which would have paid out $2000 on the Pair Plus—other players found it amusing, but I held no regrets.

6 decks
Dealer hits soft 17
Player has A,6
Dealer shows 2

According to my blackjack appendix 9 In your probability table for Three Card Poker, you indicate 9720 combinations for Queen to Ace high, with Jack high or less totaling 6720. I’ve attempted to calculate these probabilities but haven’t succeeded. I would greatly appreciate it if you could share your calculations.

Stand -0.152739
Hit -0.000274
Double -0.004882

The likelihood of any hand below a pair can be determined as the product of the number of ways to select 3 different ranks from 13, subtracting 12 for consecutive ranks that result in a straight, and determining the number of ways to select 3 suits, minus 4 for instances where the suit is the same for all. Hence, the overall combinations for ace high or less is (combin(13,3)-12)*(4 blackjack house edge calculator Now let’s analyze combinations for Jack high or less. Since we've ruled out 3 ranks, we have 3 ranks available to choose from among 10. However, eight of these combinations result in a straight (spanning from 2/3/4 up to 9/10/J). Once again, there are 4

-4 different suit selections. Therefore, the total combinations yield (combin(10,3)-8)*(4 Three Card Poker page -4) = 6,720. Consequently, the total number of combinations for Q-A high is simply 16,440-6,720=9,720. For more details regarding the combin function, please refer to my

What makes a straight a superior hand compared to a flush in the newly introduced game of Three Card Poker?

I addressed this same question in one of my assignments for my casino mathematics course at UNLV. Even though the house edge tends to be greater on Ante & Play, it remains the more advantageous bet overall. This is primarily because it has a diminished risk factor — essentially, a more favorable ratio of anticipated losses to the total wagered amount. Wizard of Vegas .

The answer is 384 times the bet amount.

While playing Three Card Poker with a Shufflemaster, I ended up with two consecutive hands comprising the same cards and suits (dealt from the same deck). I was positioned at first base, thus these were the initial cards for both instances. What are the odds of this happening consecutively?

There are combin(52,3) = 22,100 possible combinations to arrange 3 cards from a full deck of 52. Therefore, the likelihood of any specific hand mirroring the previous one exactly is 1 in 22,100. Wizard of Vegas .