What if you always knew what the next card will be?

Ok so in regular blackjack the dealer takes one face-up card and one face-down card. One day I started thinking, "what if I knew dealer's hole card" and "what if I always knew the next card that will come."

Clearly, this would be a very beneficial and excellent situation for the player. If you wanted, you would never bust and you'd always know whether to double down or to take insurance or not.

You can try this game by dealing the cards so that you have the deck facing up. Quite soon you'll notice that since you have more information, you win more and lose less. Now I'll show some examples of how seeing the cards will help you:

1. The current hand is finished and you are asked to place your bets. You see there's an ace or a ten coming. Since these cards are good for the player you'll bet more. Say you bet 4x your original bet for an ace and 2x for a ten.

RESULT: YOU'LL HAVE MORE MONEY ON THE TABLE WHEN A POSSIBLE BLACKJACK IS COMING


2.1. You are dealt a nine and dealer is showing a seven and there is an ace (or a ten) coming. Basic strategy says you should hit but since you know you are going to get a good hand you double down. You will total 20 (or 19 if you get a ten). Dealer has a seven so he/she will probably score lower or bust.

2.2. You have a soft 20 and see there's a 10 (or an ace) coming. Dealer is showing a six or something. Normally you would stand and smile happily. But since there's a ten (or that ace) coming, you double down knowing that by betting more you'll retain or even improve your hand.

2.3. You have 11 and the dealer has a six up and a five down (totaling 11), the upcoming card is a three. Normally you would double down hoping for a ten, but in this case you would total 14 and dealer would get a good hand and win your 2x bet. But when you know you are gonna get a bad hand, you just hit (or stand or surrender).

RESULT: YOU'LL KNOW WHETHER TO DOUBLE DOWN OR NOT


3. Dealer is showing an ace and you know he/she has a ten there hidden. Normally, (according to basic strategy, no card counting) you would not take insurance, play your hand and lose. But since you know the dealer has a blackjack you take insurance and win.

RESULT: YOU'LL KNOW WHETHER TO TAKE INSURANCE OR NOT


I played a few games of this so called "open-deck blackjack" with following bets:
- If an ace is coming bet 4x
- If a ten is coming bet 2x
- If something else is coming bet 1x


So the actual question would be, how high would the EV be or how advantageous would this game be?

Sorry for a long post. Please leave a comment of what you think about this. I hope you experts can help me with this problem.

Quote: TheRealBrake

Ok so in regular blackjack the dealer takes one face-up card and one face-down card. One day I started thinking, "what if I knew dealer's hole card" ...

Knowing the hole card is Double Exposure. The Wiz has a page about it: https://wizardofodds.com/games/double-exposure/

Quote: TheRealBrake

I played a few games of this so called "open-deck blackjack"...

When? Where? That seems like it would be a tremendous advantage to the player. What other rule changes were there to bring the odds back to the house's favor?

I don't know if you're going to get an answer on this one because it would require some pretty significant analysis. Furthermore, I enjoy agood theoretical question as much as the next person, but the purpose behind most theoretical questions is that they involve things that could theoetically happen, if not, the answer itself still possesses at least a semblance of possible real-world application.

In this case, unfortunately, nobody could ever hope to apply the answer to this question to anything, unless you're planning on inventing some sort of game by which the cards are all known ahead of time and the House still plays according to House Rules. I fail to see anyway the House doesn't get killed, even if BJ paid 1:1. You could double on 19 knowing a Deuce is next, for example.

If it is your intention to invent a variation that ever could have a slight edge for the casino, I would think, No Splitting, No Doubling, No Surrender, Insurance Pays 1:1, Blackjack Pays 1:1, Dealer Stands on S17, Dealer wins ANY hand that qualifies (17 or better) automatically, UNLESS the player had exactly 21. You'd probably also have to flat bet the player, or just not let the first card out be known ahead of time.

That might give the House the edge back, but I'm not sure. It would also be an incredibly boring game consisting only of taking any card that doesn't bust you UNLESS it busts the dealer, then you allow the dealer to bust. I suppose if the Dealer had something like 10, and you had 10, and the next card was a six, you'd give the dealer that knowing that the next card should mathematically bust him.

Pretty simple. I would say the cut-off would be either fourteen or fifteen that you would always give the dealer, if you could, unless it made a hand for you.

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Quote: DJTeddyBear

When? Where? That seems like it would be a tremendous advantage to the player. What other rule changes were there to bring the odds back to the house's favor?

Sorry, I forgot to mention that I played alone, by myself, just to try this out. Actually I played 1000 hands of this "game" manually (you know, dealt the cards to myself and so on).

But actually, I didn't know that this kind of game (Double exposure) even existed (well kind of this kind of game). Thanks for that.

Quote: Mission146

Pretty simple. I would say the cut-off would be either fourteen or fifteen that you would always give the dealer, if you could, unless it made a hand for you.

And thanks for your comment too, Mission146. I knew it's almost impossible to calculate edge to this game. As I said, I played those about 1000 hands and used that cut-off of fourteen (or was it 13 or 15, not sure). And I used this "betting system" I told about: ace=4x, 10=2x, anything else=1x. Original bet was 1.

So in those games, I won 675 and lost 333 dollars or whatever they are. The win/loss ratio is 2,03. So the expected return is 2,03 and expected value is 3,03 , right?

Quote: TheRealBrake

And thanks for your comment too, Mission146. I knew it's almost impossible to calculate edge to this game. As I said, I played those about 1000 hands and used that cut-off of fourteen (or was it 13 or 15, not sure). And I used this "betting system" I told about: ace=4x, 10=2x, anything else=1x. Original bet was 1.

So in those games, I won 675 and lost 333 dollars or whatever they are. The win/loss ratio is 2,03. So the expected return is 2,03 and expected value is 3,03 , right?

You're welcome.

1.) I would say that calculating the edge for this is no more or less difficult than calcuating the edge for standard BJ Games, which has obviously been done. In fact, it might be easier given that there are less variables due to knowing all of the cards. For instance, if you are dealt fourteen and the dealer is dealt ten total, and the next card is a ten, there's really no decision to make, except for how you want to lose. Do you want to bust, or do you want to stand on 14 while the dealer gets 20?

2.) 1,000 is a miniscule sample size for determining EV, especially on something that, to my knowledge, has never had anything even close tested.

3.) Your results also surprise me. I am somewhat concerned they are inaccurate, but it also could have been an extremely unusual sample. You're basically talking about 1,008 total dollars won or lost on 1,000 hands, but you are betting two dollars on 10 first card out and four dollars on A first card out. It would take an extremely high Push rate to end up only having $1,008 dollars resolved. Theoretically, you should be betting $2 every 4/13 hands, so 1,000 hands, 4/13 * 1,000 = $307.69 * 2 = $615.38 . You should also be betting $4 every 1/13 hands, so 1,000 hands, 1/13 * 1000 = $76.92 * 4 = $307.69.

It's no surprise that the Ace extra dollars represent the base extra dollars of the Tens (i.e. before multiplying two) you quadruple the bet on the Ace, and there are four Ten-Value cards, so you end up with the same thing.

In any event, you're talking about a theoretical $923.07 in action over-and-above the base bet. You're talking about $1923.07 in bets that could be resolved before we have even factored in Splits/Doubles, I know that you would also be Doubling at times that would otherwise be patently ridiculous, and possibly even splitting at times that would be patently ridiculous. The probabilistic math as to how often this would occur would be extremely complex, so I'm not going to get into that, but when you are talking about a total of twenty (knowing the next card is an Ace) against a known dealer total of twenty, you're going to Double. If you don't know the next card is an Ace, that's a ridiculous play!!! You would probably Split Tens against a Dealer (known total) of sixteen if you know the next card out is an Ace when Splitting Tens against a dealer showing six would be absurd! If you draw the Ace to one hand, whatever card to the other, and the next card out is going to be a Ten, then you would Double on your Soft 21 (if allowed) so you would have 4x base bet right there, but you are also going 2x Base bet on a known first card of Ten, so you're really looking at 8x Base bet, at this point.

I just don't see how you end up with anything even close to $1,000 bets to be potentially resolved, absent a number of pushes that are waaaaayyyyy outside of that which is probable to occur.

Quote: TheRealBrake

But actually, I didn't know that this kind of game (Double exposure) even existed (well kind of this kind of game). Thanks for that.

You do realize that Double Exposure is ONLY where the dealer shows both cards, right? It's got nothing to do with your other idea. And THAT was what I was asking "where, when" about.

Quote: TheRealBrake

The current hand is finished and you are asked to place your bets. You see there's an ace or a ten coming. Since these cards are good for the player you'll bet more. Say you bet 4x your original bet for an ace and 2x for a ten.

No need to raise your bet. You would bet table max regardless of the card you see. I'm pretty sure a simple strategy like "hit unless you would bust" would be +EV.

Quote: MangoJ

No need to raise your bet. You would bet table max regardless of the card you see. I'm pretty sure a simple strategy like "hit unless you would bust" would be +EV.

Exactly. The only variables would be when to Double/Split as opposed to taking a hit. Under BJ Rules that are otherwise normal, you'd probably double to any guaranteed hard hand, except for when you would split, and also depending on what the dealer has. Double to any hard hand that beats a completed dealer hand, for sure.

First of all I have to apologise for the mistake I made. The wins and losses were correct but I had a mistake with the number of hands I played. I only played about 480 hands. That makes the sample size even smaller so it definately is quite inaccurate.

Quote: Mission146

1.) I would say that calculating the edge for this is no more or less difficult than calcuating the edge for standard BJ Games, which has obviously been done. In fact, it might be easier given that there are less variables due to knowing all of the cards. For instance, if you are dealt fourteen and the dealer is dealt ten total, and the next card is a ten, there's really no decision to make, except for how you want to lose. Do you want to bust, or do you want to stand on 14 while the dealer gets 20?

In that situation, the best option would be to surrender so that you'd get half of your money back. Those situations occured quite often as I played. However, I didn't use surrender when I played these games. Basicly, I took the low cards until I got myself a good hand (like 19 to 21) and I stood if that gave the dealer a bad hand (like 14 to 16). Hit, stand and split (and surrender of course) are quite clear cases, but splitting is a bit harder. For example, you split tens if there's a ten coming (and the dealer has a weak hand) and hope that the other hand will be good too. Some of these decisions definately seem quite stupid but let's leave that out of this problem.

Quote: TheRealBrake

First of all I have to apologise for the mistake I made. The wins and losses were correct but I had a mistake with the number of hands I played. I only played about 480 hands. That makes the sample size even smaller so it definately is quite inaccurate.

That makes more sense. 4/13 * 480 * 2 = $295.38 + (1/13 * 480 * 4) --- $295.38 + $147.69 = $443.07, so about $923.07 in starting card total action. I think that still seems kind of low vs. $1,008 in total action (with Splits/Doubles, especially those coming on a 2x or 4x base bet), but that could be due to a higher-than-expected ratio of pushes, less than optimal play given the Rule set (no offense), or both.

Before I continue, are you considering coming up with some kind of game out of this?

Quote: Mission146

Before I continue, are you considering coming up with some kind of game out of this?

That's what I was wondering too.

Quote: DJTeddyBear

You do realize that Double Exposure is ONLY where the dealer shows both cards, right? It's got nothing to do with your other idea. And THAT was what I was asking "where, when" about.

Yes, I totally understood that Double Exposure doesn't include showing the next card. That wouldn't make any sense. But what I tried to say was that I wasn't aware that this "dealer's both cards showing" game even existed.

Quote: Mission146

Before I continue, are you considering coming up with some kind of game out of this?

What do you mean by "coming up with some kind of game out of this?" I don't quite understand your question, so please clarify.

I am basically asking if you are looking to develop a casino variant of Blackjack in which all cards are known ahead of time.

Aaa, ok. Well I haven't thought of that. I just started thinking if you could somehow see the next card or if you had an inside person as the dealer, who flashed the corner of each card.

Why are you asking this, if I may ask?

You mean this ?

Quote: TheRealBrake

Aaa, ok. Well I haven't thought of that. I just started thinking if you could somehow see the next card or if you had an inside person as the dealer, who flashed the corner of each card.

Why are you asking this, if I may ask?

This reminds me of when I'm dealing and someone flops down in the chair, wants to play, yet doesn't even know what game it is.

So, let's take this step by step...

This is a gambling website with a forum. We're in the "Math" section. People come to the Math section for various reasons. Sometimes they've been beat real bad and want a logical explanation of why their fool proof system didn't work. Sometimes they've come up with a game idea and want some help figuring out if it's viable. And sometimes they just wander in and say whatever happens to be on their mind. I'm sure there are other reasons, or at least variations on them, but that should cover the basics.

So, what we're all wondering is what's the deal?

Because if there isn't some purpose behind this then there is no purpose and I for one will just be moving along.

Quote: MonkeyMonkey

Because if there isn't some purpose behind this then there is no purpose and I for one will just be moving along.

Why not make it your own purpose? Consider the game posed: the dealer always deals a single card to a "next-card" box on the layout prior to delivering it to either the player or the dealer (as appropriate), so the next card is always known in advance. You can know perfectly whether to double or insure, and if you're at third base, you know what card you'll be giving to the dealer when you stand.

Given all that:
1) What is the player's advantage (pick your favorite common rule set), and
2) Propose one or more modifications to the game to restore the house's edge.

FWIW, I wouldn't expect this to be patentable. Bilski issues aside, Tetris and bubble-shooter games have had a "what's coming next" feature for a very long time.

Quote: MangoJ

You mean this ?

Hahahha, laughed my ass off. Great video. Well played, Austin. That's kind of what I meant.

MonkeyMonkey, I'm sorry if I hurt your feelings, but I just thought that this would be a good place to discuss this thing with like-minded people. After all, the original question was: how advantageous would your game be if you knew the next card (just like in the video)?

MathExtremist, the best modification to restore house edge would most probably be to make players lose all ties. The last place is actually so much better than the rest of the places (because you can determine dealer's fate) that no one would like to play on those places.

Quote: TheRealBrake

MonkeyMonkey, I'm sorry if I hurt your feelings,

Not at all.

Quote: TheRealBrake

but I just thought that this would be a good place to discuss this thing with like-minded people.

I suppose so, I just won't be one of them. Without purpose this seems little more than mental masturbation, and I have no interest in pursuing it.

Quote: TheRealBrake

After all, the original question was: how advantageous would your game be if you knew the next card?

Was the original question ever in doubt? I can't for the life of me find the necessity on your part to provide this supporting statement.

Quote: TheRealBrake

After all, the original question was: how advantageous would your game be if you knew the next card (just like in the video)?

Obviously large enough to play hands at 10k and funding a multi-billion company with it.

Monkey² is right, there is no reason to discuss such a game in a more serious manner. It won't make you understand any aspect of the original game. If you wan't to devote your time for it - go figure it out for yourself. It's certainly not impossible, just an ordinary basic strategy for your hand against dealers upcard and next card.
Infinite analysis can easily be done in a spreadsheet..... but honestly I couldn't care less about the result of some ill-designed game.

MangoJ and MonkeyMonkey, I understand and respect your view that this is complete bullshit. But only the fact that this issue maybe doesn't have any relevance to the actual game, doesn't mean that it would be totally pointless and stupid.

But hey, if you find this thread so irritating and frustrating, why do you keep coming back here, again and again? If you don't like it, ignore it.

Quote: MonkeyMonkey

I for one will just be moving along.

Quote: TheRealBrake

MangoJ and MonkeyMonkey, I understand and respect your view that this is complete bullshit. But only the fact that this issue maybe doesn't have any relevance to the actual game, doesn't mean that it would be totally pointless and stupid.

But hey, if you find this thread so irritating and frustrating, why do you keep coming back here, again and again? If you don't like it, ignore it.

Perhaps you're having difficulty distinguishing between my non-participation in the masturbation fest, and posting in the thread. True to my word I haven't given a second thought to calculating the odds you seek, but that doesn't mean I have anything better to do than to wander these forums when I get off work.

Plus I find your somewhat unique take on language syntax entertaining. Take for example: "But only the fact that this issue maybe doesn't have any relevance to the actual game, doesn't mean that it would be totally pointless and stupid." What does that even mean?

Look, no one is interested in your masturbation preferences. Maybe you should go check your own threads about "table size." Now how interesting is that!

Secondly, English is not my mother tongue. So excuse me if I make some mistakes. What I meant was:
1. This "game" I'm talking about has very little to do with the actual game of blackjack
2. That doesn't mean this thread would be pointless and stupid

I don't have anything against you, seriously.

Quote: TheRealBrake

Look, no one is interested in your masturbation preferences.

Or yours, yet you persist.

Quote: TheRealBrake

Maybe you should go check your own threads about "table size." Now how interesting is that!

I have checked it, I found the responses left me in good spirits.

How interesting? To me? Very. To anyone else? I have no idea. It's important to me for a number of reasons, the main one you'll need to sign an NDA before I'll disclose to you.

Quote: TheRealBrake

Secondly, English is not my mother tongue. So excuse me if I make some mistakes. What I meant was:
1. This "game" I'm talking about has very little to do with the actual game of blackjack
2. That doesn't mean this thread would be pointless and stupid

All that's been asked of you is (a) if this game is very little like blackjack and you have no plan to attempt some variant, then (b) why isn't this a pointless discussion? You've yet to answer a pretty simple question, instead reiterating the 2 points you made above as if we're too dense to follow along. Your first point is self-evident, what you're describing is not like blackjack as it's currently played. I don't think anyone disputes that. Your second point, that this is a worth while subject to discuss, especially in light of the first point is a little more suspect. Several have asked why you're bothering to ponder this question and you're answer seems to be the rather circular logic of "it's worth discussing because it's worth discussing."

So then, if it's a matter of such importance then perhaps you should get on with it instead of responding to me.

I started this thread to discuss about strategy modifications (other than those clear cases) and the advantage of this "game." That's why I don't find this pointless.

What do you say we leave this conversation here and "get on with it," as you said? Okay?

Quote: TheRealBrake

Aaa, ok. Well I haven't thought of that. I just started thinking if you could somehow see the next card or if you had an inside person as the dealer, who flashed the corner of each card.

Why are you asking this, if I may ask?

Basically, you are describing hole-carding above, which is a totally different question than seeing the next card out. That would simply be a Blackjack game in which you knew the dealer's starting hand ahead of time, but not what is going to come out, so that's a totally different question.

I was just wondering if you were planning to premise a game on this because I thought that could be an interesting game. You'd essentially want to turn it into as much of a coin-flip as possible and then still find some way to give the House an edge. I would say:

1.) No Splits
2.) No Doubles
3.) Surrender is a good question. If you end up in a position where the next card out either busts you and the dealer, or busts you but causes the dealer to win, should you be allowed to surrender?
4.) I would say that you would have the dealer stand on any 17, unless the player had a total of 18 or higher, in which event the dealer would continue to take cards until he either busted, pushed or beat the player. He would play each player seperately to the extent that if you had a player with 18, the Dealer had Soft-19 and another player had 20, the dealer would collect from the player who had 18 and then proceed to hit in an effort to push or beat 21.

1.) Another alternative would be one in which you could have Splits, but no Doubles, and the player would, "Pay," a certain percentage of the bet for every new card that he wanted. The player would only be able to win on the base bet, but would lose all bets if he were to bust or get beaten by the dealer. The money on each, "Paid card," would Push in the event that the player wins/pushes.

However, that could actually give the House too much of an edge, so it could be possible that the player would pay for the first hit card (and that bet could only Push/Lose) but he would not have to pay extra for additional cards.

Quote: Mission146

I would say that you would have the dealer stand on any 17, unless the player had a total of 18 or higher.

That would not work well with multiple players or split hands.

If the game features the next card (i.e. by putting the cards upside down into the shoe), why not let the dealer draw to 21 unless he would bust ?
Keep the doubles and splits, the house edge could come from losing ties, reduced payout on blackjack etc.

Quote: MangoJ

That would not work well with multiple players or split hands.

If the game features the next card (i.e. by putting the cards upside down into the shoe), why not let the dealer draw to 21 unless he would bust ?
Keep the doubles and splits, the house edge could come from losing ties, reduced payout on blackjack etc.

You would resolve multiple players and split hands by way of the dealer clearing a bet as soon as he beats a player's total. When the dealer has the Soft 19, one player has 18 and another has 20, the dealer wins against the 18 and takes the bet, then proceeds to hit against the 20.

I don't think that the HE gained from losing ties and reducing the payout on Blackjack to 1:1 could possibly mitigate the advantage the player has in absolutely knowing whether or not to hit.

Good ideas from both of you. In my opinion, the main ingredient is to keep this game as simple as possible. That means that the dealer should have a specific stand-value. Then again it would be great if some original blackjack rules would remain, such as 3:2 blackjack payout. Making the game too different from the original might not be a good idea. Also keeping the doubles and splits would certainly make the game more interesting than without them.

But as said, player losing all ties and making dealer's stand-value higher (18, 19 or something else) would bring back some of the house edge. There should also be some other "bad rules" to lower player's edge. Any ideas?

Good grief, the back and forth in this thread is ridiculous. Monkey, consider a scenario where the dealer tries to deal a hit card to the player to your right but the player insists that he didn't want a hit. The pit boss is called over and—surprisingly—tells the table that the card will remain in play. As the next player to act, you know what the next card to be dealt is. Not exactly "mental masturbation." To answer the OP, yes—the edge in this "game" is strong. Without going into detail, it's in the low double digits. Unfortunately, most players will never find a situation that warrants a knowledge of the appropriate strategy to employ. If this doesn't tell you everything you need to know, you're welcome to PM me.

Quote: LonesomeGambler

Monkey, consider a scenario where the dealer tries to deal a hit card to the player to your right but the player insists that he didn't want a hit. The pit boss is called over and—surprisingly—tells the table that the card will remain in play. As the next player to act, you know what the next card to be dealt is. Not exactly "mental masturbation."

Ok, I considered the scenario, as shot takers try it quite often. They usually get 1 freebie. Now, consider the thread title: What if ALWAYS knew what the next card will be? (emphasis mine in case you missed it, which you apparently did when you decided to jump in). Of course the value is high in knowing the next card, but unless you're designing a bj variant where this is the case and you've come here looking for a free mathematical analysis or are some kind of psychic this discussion is about as valuable as "What if you always knew what the next powerball numbers were going to be". Um... yeah, pretty valuable, duh.

Exactly, so if it was a game idea, then I'd be interested in throwing a few preliminary things out there, and maybe doing a little (but not much) math on it. If it is not for a variant idea, I really have no interest in the hypothetical as it is (no offense) pragmatically meaningless.

Edit: fair enough!