In basic Blackjack etiquette, you can do this by softly scratching your cards against the Blackjack table to indicate to the dealer that you want another card – when it’s your turn, of course. If you start out with a King and a 5. Today, however, virtually all Blackjack games feature the players' cards dealt face up on the condition that no player may touch any cards.) Naturals If a player's first two cards are an ace and a 'ten-card' (a picture card or 10), giving a count of 21 in two cards, this is a natural or 'blackjack.' The automatic win upon receiving five cards in blackjack is called “5 Card Charlie”. However, the rule doesn’t apply to most blackjack games online or in land-based casinos. You’ve probably heard this from someone who plays blackjack at home. That’s where the five card rule is the most prominent. Blackjack 5 card trick, also known as ‘5 card Charlie rule’, is a point in the game in which a player who has been dealt 5 cards, automatically wins the game. This move has been criticised heavily and layers today are uncertain if casino sites or venues allow this move to be accepted in their gameplay.
I'm less interested in a final answer and more interested in a process to answer the following question.
Moreover, is my math estimate of probability a * probability b * probability c * probability d = final probability a valid way to solve this problem or not? Thanks for reading?
I'm interested in the following situational question - In a standard Double Deck game, What is the probability of being dealt a two card 20 as a starting hand, the dealer having an Ace up, and the player not taking insurance, and the dealer not having a blackjack, and the dealer drawing to a 5 card 21? What is the probability the same occuring, but being dealt a two card combination without including A,9 combos? For some reason when I do the math of the 52,2 20 combos by hand for % P = x/y, My brain freezes up :x. I lost my math skills 10 years ago :D. Any help/contribution/jumble of formulas/estimates welcome.
The number I got was roughly around .016% of the time. This seems awful low, and doesn't account for the dealer not having it, as well as only counting 3+ card 21 draws. Solve for whatever you like, however you like. More interested in the process. :]
There are 32 of these in a double deck, so there are (32)C(2) = 496 different pairs you can get.
There are (104)C(2) = 5356 total pairs of cards in two decks.
The probability is 496 / 5356 = 0.0926, or about 1 / 10.8.
Meanwhile... And I quote another resource with the correct answer..
Probability of obtaining 20 points from the first two cards is P = 68/663 = 10.25641% in the case of a 1-deck game and P = 140/1339 = 10.45556% in the case of a 2-deck game.
[[P = 140/1339]] is the same as
[[P = 560/5356]]
We've got 496 different unique combos of face cards to make our 20, now what type of math do we use to get our apparent 64 combos of A,9?
Blackjack 5 Cards Rule
When I try to choose 2 of 16 = 120 , and eliminate A,A combos and 9,9 combos, I come up with the wrong answer, still :/
Odds of drawing any two card 20 is 10.46%.
Odds of a Face 20 is 9.26%.
Odds of dealer having an Ace Up, disregarding our hand, is 8/104, or 7.70% of the time.
If we have an A,9 combo, the odds of one dealer Ace reduces to 7/102 or 6.86% o the time?
Moreover, the odds of the dealer having Ace Up, No blackjack in DD, disregarding our hand, should be..
A combo hand of one of [8] aces, plus any card A(7) thru 9, or [71] cards out of 5356 2 card combos for the deelah?!?!
8 x 71 / 5356
or 10.6% of the time
Does anyone know any way of calculating that probability other than essentially listing all the 4 card draws to an Ace that total 21 without making a soft 18-20 or a hard 17-20?
Assuming dealer hits a soft 17, basically there are two pathways for dealer to make a 5 card 21 starting from an Ace:
1. Two small cards totally 2-6 to make a hand between S13-S17, followed by a card larger than a 4 to make a hard 12-16, followed by a final card to make 21.
2. One small card, A-6, followed, by a card (larger than a 4) to make a hard 12-15, followed by a small card to keep the total under 16, followed by a final card to make 21.
But, as you look at the details, I don't think that is easy to write as an analytic algorithm.
That’s assuming infinite deck which will be very close.
You could also list out all 5 card permutations, there are only 100,000.
You can easily do it with a Markov chain. You should only need 65 cells - 5 rows and 13 columns.
I'm an excellent Excel programmer but I'm weak on Markov chains. Still trying to figure out how to do that.
You could also list out all 5 card permutations, there are only 100,000.
No, the first card is always an Ace, which reduces it from 100,000 to 10,000. And then, you can eliminate whenever the 2nd card is a 7-T, which reduces it to 6,000. Then, also eliminate whenever the last card is a Ten or A-4, which reduces it to 3,000. Then, also eliminate these combinations:
- whenever the 2nd and 3rd card add to 7,8,9 or 10.
- whenever the 2nd and 3rd cards add up to 15 or more
- whenever the 2nd, 3rd and 4th cards add to 7,8,9 or 10.
- whenever the 2nd, 3rd and 4th cards add up to 16 or more.
In reality, the number of permutations to write out is reasonable.
Assuming, the H17 rule and infinite decks, I got that the probability of dealer starting with an Ace and making a 5 card 21 to be 183/13^4 = 0.006407.
If you assume the S17 rule, I calculate the probability for a 5 card 21 to be 138/13^4 =0.004832
Edit: corrected numbers (whoops!)
The automatic win upon receiving five cards in blackjack is called “5 Card Charlie”. However, the rule doesn’t apply to most blackjack games online or in land-based casinos.
You’ve probably heard this from someone who plays blackjack at home. That’s where the five card rule is the most prominent.
When it comes to real casinos, though, it’s simply not there. So, to answer your question:
“No, 5 cards do not automatically win in blackjack.”
There are practically no land-based casinos that would allow this blackjack rule in Europe or America. You’re much more likely to find it in online blackjack software. However, it’s a rare occasion even at virtual casinos.
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What is 5 Card Charlie Rule?
5 Card Charlie is a blackjack rule that gives an edge to the player. It simply states that if you collect five cards without busting, you automatically win.
The exception is the dealer’s blackjack, which usually wins even if the player has a blackjack too. The payout of this kind of a win can differ as well, ranging from 1:1 to 2:1.
“The odds of collecting five cards without busting are roughly 50:1 (other rules can affect this probability).”
This isn’t a likely scenario in blackjack. However, it’s much more likely than getting six or seven cards without busting. Such rules exist as well, yet you won’t find them easily in real or licensed online casinos anyway.
5 Card Charlie + Other Rules
If you do find a blackjack game with this variation, it most certainly has some additional rules. All kinds of other rules may apply in conjunction with the automatic win rule, namely:
- Split
- Double Down
- Insurance
- Side Bets
Obviously, if you split your cards, you’ll have to collect five cards in each hand separately. Also, this auto-win rule doesn’t work as side bets do.
In other words, if you get five cards and win, you immediately end the round. This means that you can’t win both by getting a Charlie and beating the dealer on the same round. Only one kind of a win is possible per round.
Why Don’t Five Cards Win?
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The answer to that is simple. The rule isn’t in popular use because it wouldn’t be a lucrative strategy for the house. Depending on other rules of the game, it could tip the scale in the player’s favour. So, casinos simply can’t have that.
“Automatic five card win rule adds 1.46% RTP to the game.”
With many blackjack software and real casino rules, these games already have house edges below 1%. That’s why adding this rule simply wouldn’t be feasible.
Of course, some games have lower payouts, so this rule could be added to them. Yet, casinos don’t like to implement it anyway as it isn’t part of the classic blackjack.
Blackjack Games with 5 Card Win Rule
Nevertheless, it isn’t impossible to find games with the automatic win rule. Here are a few titles that we know of:
- Blackjack 5-Card Charlie
- Blackjack Six Card Charlie
- Blackjack Charlie 7
The number indicates how many cards you need to collect to win without checking their value. Unfortunately, not all of these titles are legally available to the UK players.
Regardless, should you stumble upon such a variant and wish to play it, you should know how to do it well.
Blackjack 5 Card Charlie Strategy
Every single rule in blackjack affects the gameplay. So, the best strategy differs accordingly too. The Charlie rules are not an exception in this case.
There are certain tips and tricks that you can use to increase your odds in this variant. They don’t guarantee success in every round. However, you’re more likely to end up with a positive balance if you stick to these strategies:
- Don’t count on it
- Know when to hit or stand
- Know when to double down
Here’s the explanation of each of these points:
1. Don’t Count on It
Don’t count on getting five cards from the start. Remember, this will only happen once in 50 rounds or so. So, it makes no sense to change your gameplay in any significant way if you’re playing Charlie blackjack.
That is unless you’re getting close to actually collecting five cards and are still under 21. If not, just play it as you would any other standard blackjack game and pay attention to other rules.
Depending on the variant, other rules might be much more important in most cases. For example, things like card decks used, dealer’s rules and splitting and doubling will affect the game in every round. The Charlie rules won’t.
So, take the automatic win rule into consideration only if you already have at least 3 cards in your hand.
2. When to Hit or Stand
Depending on the number of decks used in the game and your current hand, you have several choices. You can either:
- Hit
- Stand
- Double down (if allowed)
The lower the number of decks used, the more important are the cards already in the game. If you can’t make out anything from them though, we suggest to:
- Hit if your hand is soft 17 or lower
- Hit if you have four cards worth up to soft 21
- Stand if you have a hard 17 or higher
- Hit if you have a 7 or higher card, no aces and your hand is worth between 12 and 16
- Stand if all your cards have a value of 2 to 6 and your hand is worth at least 13 unless you already have four of them
3. When to Double Down
Generally, doubling down is an overused strategy in blackjack. However, there are some cases where it’s lucrative to use it.
Doubling can be used to capitalize on the automatic win to double your winnings. All you’d have to do is collect four cards and then double down on a fifth one without busting.
If you have less than four cards, you’ll want to consider which path is better. Should you aim for five cards or lose this opportunity by doubling down? In most cases, we’d suggest you to:
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- Double down on hard 10 or hard 11
- Double down on soft 15 to 18 if all your cards have low value
You shouldn’t blindly follow these guidelines though, due to numerous possible rule variations for which we can’t account for.
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Remember that automatic win rule is always in your favour. So, it can’t make your matters worse than they’d be in classic blackjack games.