Ultimate X Blackjack?

Introduction

For those of you who are not familiar, Ultimate X Video Poker is a game by which the player will receive multipliers for the following hand in the event that the player wins the previous hand. The value of the multipliers is based on the rank of the prior hand (for instance, on most Jacks or Better based games, a high pair will award a 2x multiplier for the next hand while a two pair will award 3x and so on) and then the multipliers become active for the next hand.

Evolution Lighting Blackjack follows the same principle, sort of. I first heard about the game in this thread, where the original poster, Bustamove, had this to ask:

So online casinos are now offering an interesting variant of Live Blackjack called Lightning Blackjack. The RTP is pretty decent at 99.56%.

I am puzzled as to what optimal strategy to use. For example, if I have a high multiplier going and then I get a 10 against a dealer 8, normally I would double down. However, as a win would achieve the multiplied payout, would it not be safer to just hit, so if I got a 2 (say) making 12, I could then hit again?

I would love to know how to play this game perfectly so as to minimize the house edge, but surely a sophisticated calculator would be required.

Additionally, I wonder if the advertised 99.56% RTP applies to just playing basic strategy or with perfect play.

Any insights would be appreciated.

The answer to his first question is that the RTP seems to be based on the base Blackjack game, but there is also a small chance that the multipliers are worked in such a way as to be EV-neutral....or within a fraction of a percentage of EV-neutral. I also answered the question about doubling down, which I will do later on in this article, though I used an example hand that would normally be a closer decision.

Actually, I think I have seen this game before, but I would have ignored it in favor of normal Blackjack---which I would only play for an online promotion if it was, by far, the best thing available.

Comparison to Ultimate X

The main way that this game compares to Ultimate X is that the player will randomly receive a potential range of multipliers for different hand results ranging from:

4-16, 17, 18, 19, 20, 21, Blackjack

In order to get the multiplier for the next hand, the player must achieve the hand total needed for the multiplier AND have a winning hand. If there was no fee for this privilege, then this game could absolutely be crushed (obviously), but there is a fee and a few other caveats:

1. As mentioned, the player must achieve the hand total for the current hand to unlock a particular multiplier AND win the hand.
2. The player pays a Lightning Fee for this privilege that is equal to the player’s base bet. In other words, if the player bets $5, then he also pays a fee of $5, but does not have to pay anything else if he takes an action such as splitting or doubling.
3. If the player wins a multiplier for the next hand, then on the next hand, the player gets that multiplier multiplied by the Lightning Fee paid on the previous hand. For example:

Player bets $5 and pays a $5 Lightning Fee.

Player hits to a total of eighteen and wins the hand as well as unlocking a 4x multiplier for the following hand.

The player wins the following hand, and in addition to his base game winnings, will receive $5 * 4 = $20 for the Lightning Win.*

*With that, one key difference between this game and Ultimate X is that Ultimate X multipliers apply to the total amount won. If you have a 2x multiplier and hit a four-of-a-kind for 400 credits, then you would get 800 credits on that hand. The amount to be won with the Lightning Multiplier, however, doesn’t care what the base hand does (as long as it wins) and will pay out the amount of the Lightning Fee multiplied by the current multiplier, if applicable.

Would There Be Any Strategy Changes with This Game?

There would be strategy changes that would have to be made if a player wanted to play optimally. In my reply post, I used the example of a Player with a total of ten against a dealer showing a nine. Normally, the player would want to double in this situation, but in this game, that might not always be true.

Why not?

Simply put, there are going to be some situations in which a player will want to simply maximize his probability of winning. There are a few reasons that this might impact double-downs:

1. If the player doubles down, then while it might have the best Expected Value on the Base Game, it might not be the best decision overall. The reason for that is that the multiplier pay doesn’t care whether or not the player wins the double down and only cares that the player wins, for that reason, it might make more sense (EV) just to maximize the probability of winning.
2. If a player doubles down, then the player only gets one card. As you will see in the example below, the player is more likely to win the hand if he leaves himself the opportunity to hit if he doubles and receives a low card to result in a hand total that would normally call for the player to hit again.
3. The player will be offered greater potential multipliers for higher hand totals, so in the case of a player ten v. a dealer showing nine in an eight-deck game, if a player chooses to hit, then he would continue to hit until reaching a total of 17 (or greater) and would therefore get a higher potential multiplier for the following hand more often.***

***It’s important to note that I made no effort whatsoever to calculate this effect in my example hand because it would be ridiculously complicated to even provide one example.

For all of these reasons, the game would require a new Optimal Strategy that would be based on the following components:

1. The player’s multiplier (if any) on the current hand.
2. If there is a multiplier on the current hand, then how much in overall EV is added by focusing on probability of winning as opposed to what the normal Optimal Strategy decision would be for the base game.
3. The difference in EV on the Base Game by making a normally sub-Optimal decision.
4. The difference in EV on the Lightning Fee for the following hand by making a decision that maximizes probability of winning and/or final hand total.

With that, to calculate any decision point, (which I only did based on #2 and #3 as trying to deal with #4 would be ridiculously difficult) you would first have to get the difference in EV on the base game by making the decision that would normally be sub-optimal, figure out the difference in probability of winning by making the normally sub-optimal decision (if the probability of winning is higher) and then separately calculate the EV difference on the Lightning aspect of the hand separately.

After that, based on the current multiplier, you will see if the EV-added of making the best decision to maximize probability of winning is enough to overcome the EV-lost on the base hand by making what would normally be a sub-optimal decision.

Example Hand

For my example hand, I decided to go with a player total of ten v. a dealer showing nine because that is a much closer EV decision (double or hit) as opposed to if the dealer is showing an eight.***

Once again, I want to make it clear that I completely ignored future value from whatever multiplier might be awarded for the hand after this one just because that would have made the analysis of this hand even more convoluted. I should also mention that, for ease, these should be considered estimates as I did not use Effect-of-Removal (after the player hits and receives something) because that would have required calculating every individual possible series of outcomes...of which there would be hundreds.

With that, here is my analysis based just on the current multiplier:

The good news is that the game has a decent RTP and the bad news is that, "Perfect Strategy," is going to be very difficult to come by.

The way that I understand the rules is this:

1. The player will make a bet on an ordinary Blackjack hand (base bet) and then will pay a, "Lightning Fee," equivalent to that bet.
2. The Lightning Fee will enable a player to generate multipliers for reaching certain hand totals which are somewhat randomly assigned before the player takes any action.
3. If the player wins the current hand, then the player will get the multiplier corresponding to the player's hand total for the following hand. If the player wins the following hand, then the player will be paid the Lightning Fee amount from the previous hand multiplied by the multiplier.

With that, I have a question:

Since the Lightning Fee is paid the prior hand, do you have to make the same bet amount (and Lightning Fee) for the following hand? I'm sure if you bet more, then that just means that you would pay a greater Lightning Fee, but any win on the multiplier will be based on the previous hand---so no need to do that. My theory with betting less (if the pay will be based on the amount bet the previous hand) is that it will lessen the impact (base game) of making strategy deviations in an effort to just win the hand.

For now, I will assume the bet amount is the same, so let's look at our variables on this thing:

1. What would normally be the best decision?
2. What are the potential multipliers to be earned for [i]the following hand[/i]?
3. What, if any, is the multiplier active on the current hand?

With that, let's use your example of a 10 against a dealer 8 and compare the two, for this, we will say you already have a multiplier active:

Decks: 8

Dealer Peeks: Yes

Soft 17: Stand

Double Down: Any First Two

Split: Yes

Hit Split Aces: No

Blackjack: 3:2

Okay, so normally with a player ten v. a dealer showing 8 (I made it 6-4 for the player) we would have the following:

Surrender: -.5

Stand: -0.513156

Hit: +0.199206

Double: +0.290356

Personally, I don't think this hand is going to be particularly close in terms of changing the decision to double. For that reason, I'm going to change your example hand to something a little closer, a hand total of ten v. a dealer nine:

Surrender: -.5

Stand: -0.543320

Hit: +0.116689

Double: +0.146896

With that, we are going to go to this calculator.

What that calculator does is it tells us final hand probabilities for the dealer based on what's left in the shoe and the dealer's upcard. What we see is the following for a dealer starting with 9 and a 6 and 4 also gone from the shoe:

Bust: .229

21: .061

20: .12

19: .354

18: .116

17: .121

SUM: 1.001 (Rounding, I assume)

Okay, so we can break this down into win probability and loss probability conditions with doubling somewhat easily. With your total of ten, there are five ranks (2,3,4,5,6) that would result in a hard total on a double that cannot compete with a made dealer hand. For those, we can just use the probabilities above. We have already removed a 4 and a 6 from the deck, and the dealer's nine is also gone, so there are 413 cards remaining of which 158 are the applicable ranks.

If the dealer busts, you win...if the dealer doesn't bust, then you lose. We are not concerned with overall EV at this time as that has already been calculated for us, so we are only concerned with the probability of winning the hand:

(158/413) * .229 = 0.08760774818---NOTE, Effect-of-Removal would still play a factor, but we can't know what we are removing ahead of time and it's negligible anyway.

With that, you will double and make a hand total of 12-16 8.760774818% of the time and still win due to the dealer busting.

Our next concern is doubling to a hand total of 17 and winning, pushes lose for the purpose of the Lightning Fee, so the only thing we care about for win probability is getting to 17 and the dealer busting:

(32/413) * .229 = 0.0177433414

With that, you will double to 17 and produce a winning hand roughly 1.77433414% of the time.

The next possibility is that you receive an 8, which will beat either a bust or a dealer total of 17 as follows:

(32/413) * (.229 + .121) = 0.02711864406

With that, that result will come to pass 2.711864406% of the time.

The next possibility is that you receive a 9, which will beat Dealer Bust, Dealer 17 and Dealer 18

(31/413) * (.229 + .121 + .116) = 0.03497820823

With that, we will see such a result 3.497820823% of the time.

The next possibility is that you receive a ten, which will beat everything except a dealer twenty or dealer twenty-one:

(128/413) * (.229 + .121 + .116 + .354) = 0.25414043583

With that, we see that this result will happen about 25.414043583% of the time. It's actually slightly less because you have removed a ten from the deck, which makes a dealer total of 19 slightly less likely, but I'm not trying to be perfect here and it's negligible to illustrate the point.

Finally, the player might receive an Ace for a total of 21. That beats all dealer hands and only pushes if the dealer finishes with 21, as well:

(32/413) * (1-.061) = 0.07275544794

With that, we get a win probability of 7.275544794%.

We will now sum up our win probabilities:

8.760774818%+1.77433414%+2.711864406%+3.497820823%+25.414043583%+7.275544794% = 49.434382564%

You might be wondering why we double if that is not at least 50%, but remember, we did not do any math for pushes as they have already been factored into the EV calculations to begin with.

The next thing that we have to do is calculate the probabilities for the player's total on the assumption that the player does not double to get a win probability. While that might sound difficult, it's actually going to be pretty easy because the player will effectively follow the same rules that the dealer does for the remainder of the hand---hit until he reaches a total of 17, or greater. With that, the work is already done for us as we can use the chart that has the probabilities of final hand totals for a dealer starting showing a ten:

Bust: .212

21: .035 + .077

20: .339

19: .112

18: .112

17: .112

(For simplicity, I only removed a ten from the deck for this)

For the 21, the dealer chart has 7.7% for Blackjack, so I had to add that back in as if the player draws an ace to a total of ten.

Okay, so now we do the same thing. Seventeen only wins if the dealer busts:

(.112) * .229 = 0.025648

Player 18 Beats Dealer 17 and Bust:

(.112) * (.229 + .121) = 0.0392

Player 19 Beats Dealer Bust and 17-18:

(.112) * (.229 + .121 + .116) = 0.052192

Player 20 Beats Dealer Bust and 17-19

(.339) * (.229 + .121 + .116 + .354) = 0.27798

Player 21 Beats All Except Dealer 21:

(.112) * (1-.061) = 0.105168

With that, we sum up our win probabilities:

0.105168+0.27798+0.052192+0.0392+0.025648 = 0.500188

BRINGING IT HOME

Okay, so the example that we ended up using was that of a player total of 10 v. a dealer showing 9 because that is a much closer decision to hit or double on an EV basis.

DISCLAIMER: I know I have already said it, but I want to make very clear that the probabilities above should be taken as a ROUGH ESTIMATION as I did not account for Effect-of-Removal as it would have required me to account for every possible series of player hits (to hand totals) and dealer results individually...and, while I'm capable of doing it, I'm not really inclined to do it for free. Someone could probably write a program to do it much faster, anyway.

The first thing that we will do is go back to our base EV:

Surrender: -.5

Stand: -0.543320

Hit: +0.116689

Double: +0.146896

With that, we will next look at the win rates:

Double: .49434382564

Hit: 0.500188

Even then, it's a bit convoluted for three reasons:

1. We need to win in order to get the value from the current hand multiplier.
2. We need to win in order to get a multiplier for the hand after this one.
3. We have made the Lightning Fee bet again, so we will lose that if we do not win this hand.

For that reason, we must now treat the two bets separately, in terms of EV. We already have our EV for the base game, so now we have to figure out our EV for the Lightning Bet...but we are going to ignore the second point (the multiplier for the following hand) for simplicity---this is mainly because these multipliers offered are not only random, but are also higher based on the higher the hand total is. Going the route of hitting, as opposed to doubling, we are slightly more likely to finish with higher hand totals.

Based on just winning the hand:

Hit: 0.500188

Double: .49434382564

The inverse of these will represent the probability of losing or pushing the hand, which will cause our current Lightning Fee to be lost as well as the Lightning Fee that we paid the previous hand for the current multiplier. That will be a loss of two units, so these must be multiplied accordingly:

((1-.500188) * -2) = -0.999624

((1-.49434382564)*-2) = -1.01131234872

Both of those numbers represent our -EV from Losing the hand as it will cause both the previous Lightning Fee and the current one to be lost as the player would receive zero return on either.

1.01131234872 -0.999624 = 0.01168834872

From that perspective, hitting is better than doubling by .01168834872 units before you even get into possible win. Let's look again at our EV's for each decision based on a normal Blackjack hand:

Surrender: -.5

Stand: -0.543320

Hit: +0.116689 + 0.01168834872 = 0.12837734872

Double: +0.146896

With that, we see the added EV of hitting (for the Lightning Bet) brings the two closer. Let's see how much of a difference there is between the two:

0.146896-.12837734872 = 0.01851865128

Okay, so per multiple, the difference in the winning rates will also be the difference in per unit EV:

Hit: 0.500188 Double: .49434382564 (.500188-.49434382564) = 0.00584417436

In this case, if we had a 4x multiplier, we would see: 0.00584417436 * 4 = 0.02337669744

That, taken together, hitting and maximizing the probability of winning the hand becomes the better decision when you are looking at both bets total expected outcome. The difference in the EV Loss on the base hand of hitting as opposed to doubling has been overcome by the EV gain of maximizing the probability of winning on this particular hand.

I would say that we can also be pretty sure of that because we didn't even factor in the multiplier value for the following hand, which we would also receive if we won the current hand. Depending on the probability of achieving certain results, and what the multipliers for the following hand might be, this could become the correct decision at a multiple for the current hand of 3x, but I have no idea and it would be ridiculous to even try to figure out.

My advice is not to play this if there is a standard Blackjack game with the same House Edge, or lower. At some point, you'll be put into situations where you must sacrifice the EV of one aspect of the hand in order to satisfy the other aspect for the best overall EV. It would also be crazy difficult to calculate all of them because of all the different situations that can come up with hand results, current multipliers and potential future multipliers...which would all be a factor every time.

In fact, the potential for future multipliers (if they are really high) might even be enough to try to maximize the probability of winning (or even just trying to achieve a particular multiplier) for hands that don't even currently have a multiplier.

For example, if you skip to 17:27 of this video:

Imagine if the player ended up with a hand total of hard 13 against a dealer two. Base hand EV favors standing, so by necessity, so do the win probabilities...but the difference isn't astronomical and you have potential multipliers for the following hand that could become a consideration.

My conclusion is that this game is a total mess that nobody should play and optimal strategies for the game would require the following charts:

1. An optimal strategy for hands with no current multiplier available that is based not only on the base EV, but also, on all of the potential multipliers that are available for the following hand. You obviously couldn't really have a chart like that because of how many possible combinations there might be, so you'd probably have to create a calculator that does this.
2. An optimal strategy based on hands that currently do have a multiplier that either does, or does not, also include the potential multipliers that are available for the next hand.

It doesn't appear that Surrender is available, but if it was, you would never do it. You would be forfeiting 1.5 units as you would lose the Lightning Bet and could not receive a multiplier for the next hand.

With that, I concluded that the player would favor hitting to maximize his probability of winning the hand (as opposed to doubling) if the multiplier for the current hand is 4x, or greater.

I also think it’s possible that 3x would be a sufficient enough multiplier when you factor in the fact that the multipliers for hand totals 17+ will be greater than hand totals of 16, or below. As I stated in the Double part of the analysis:

With that, you will double and make a hand total of 12-16 8.760774818% of the time and still win due to the dealer busting.

However, when the player hits, the player never wins with such a hand total because the player will always hit until he has 17, or greater. Because of that, the player’s average multiplier for the NEXT HAND is going to be greater than if the player Doubles, which is in addition to the fact that the player is more likely to win to begin with.

Other Strategy Changes?

As I mentioned in my response:

1. An optimal strategy for hands with no current multiplier available that is based not only on the base EV, but also, on all of the potential multipliers that are available for the following hand. You obviously couldn't really have a chart like that because of how many possible combinations there might be, so you'd probably have to create a calculator that does this.
2. An optimal strategy based on hands that currently do have a multiplier that either does, or does not, also include the potential multipliers that are available for the next hand.

So, it’s really difficult to guess how many potential strategy changes that there could be to maximize EV, but in short, the answer is, “A lot.”

For one thing, the player could have a multiplier for the current hand of 25x, so given the potential difference in win probability, such a multiplier might mean that a player would do well to hit a Hard Total of Ten against a Dealer showing an eight, and I suspect that the player would want to hit to maximize his probability of winning the hand.

Once again, if the player did hit the Hard Ten v. Dealer Eight, then there is no circumstance in which the player would stand on a total of less than 17, so as a result, the average multiplier will also be higher for the next hand when the player does win. Intuitively, we also know that the player’s probability of simply winning the hand at all would go up by hitting.

With that, here are some other potential strategy changes, though someone would have to do the math on all of these except for #1.

1.) If Surrender is offered, the player would definitely NEVER surrender. In the only video of this game that I saw in action, Surrender was not available, but you’d never do it anyway.

The reason why you would never Surrender is that your probability of winning the hand would be 0%, and as a result, you would forfeit not only half of your base bet, but you would also lose all of your Lightning Fee. For that reason, I can pretty comfortably say that Hitting is always superior than Surrendering just by doing an eyeball check.

2.) It’s possible that a player might be slightly more aggressive about Splitting on hands that would otherwise be very close calls. The reason why is because, when a player splits, the multiplier for the next hand (assuming the player wins either hand) will be based on the highest hand total, and therefore, the best multiplier available.

That said, I imagine that this would come into play only rarely and possibly never.

3.) As the example said, there are some situations in which a player would prefer to hit than double to maximize probability of winning and probability of higher hand totals.

Advantage Play & Card Counting

One clear potential for Advantage Play would be if you could earn a multiplier with a small bet and have it applied to a hand where you make a much larger bet, but they’ve already thought of that. If you have an active multiplier for the current hand and win, then your payout will be based on whatever Lightning Fee that you paid on the previous hand.

I don’t know if it would bring it to the level of potentially being an Advantage Play, but another possibility would be to get a multiplier for the next hand and bet far less on the next hand. Unfortunately, it seems that if you pay a lower Lightning Fee for your current hand, then even if you paid more on the previous hand, you would be awarded based on the lower of the two.***

***Also, I don’t think that would be an actual advantage. The only benefit that this would have is that you could make a lower base bet (with the multiplier based on the bet from the previous hand) and any deviations that a player would make to favor higher probability of winning compared to what would normally be Optimal Strategy wouldn’t hurt the EV of the base game.

Whether or not this could be card counted is a really interesting question. In this game, it seems that the game starts with an eight-deck shoe and the deck penetration is only 50%, which is terrible, but then you have to remember that NATURALS actually have more value to the player than just the 3:2 payout on the base game.

Going back to the Youtube video I linked, Natural Blackjacks always give the best of the available multipliers, so while it is a limited sample size, let’s look at the multipliers from that video v. the number of hands:

8x, 15x, 8x, 15x, 8x, 6x, 8x, 12x, 6x, 6x, 20x, 15x, 15x, 8x, 6x, 12x, 6x, 12x, 6x

The average for that sample is 10.105x multiplier if the hand is won.

I have no idea whether or not that offsets the poor penetration enough to matter, but it seems that the value of naturals is increased by way of rewarding the multiplier for the following hand and that multiplier being greater than the other ones. It would take someone much better than I am to develop:

1.) A comprehensive strategy for this game in the first place.

AND:

2.) To be able to figure out what kind of count could be used and at what point the game becomes positive. What I can say is that the base RTP is pretty decent in the first place and, given the nature of this game, the True Count needed for the game to be positive would almost certainly go down a little bit. If not, then someone will have to tell me why not because I can’t think of a reason why it wouldn’t.

Opinion and Conclusion

Personally, I would not recommend that anyone play this game, unless they can figure out some sort of angle on it or can determine an Optimal Strategy.

The reason that I would not recommend this game is that there are standard Blackjack games out there with RTP’s that are just as good online, and as we determined above, there are some decisions where a player would have to sacrifice base game EV (deviating from normal optimal strategy) in order to be making the best EV decision overall. If the player does nothing but follows Optimal Strategy for the base game all the time, then the player will sometimes NOT make the best EV decision overall largely due to sacrificing probability of winning and probability of hitting higher hand totals which would result in greater multipliers for the following hand.

It will be interesting to see if someone can come up with an Optimal Strategy for this game, but I can pretty safely say that is going to require an excellent programmer and several hours of computing time just because of all of the variables involved. There is also some information that would need to be known that I couldn’t find, such as the average multiplier for each hand total.

Even if you knew the average multiplier for each hand total, strategy decisions would still also depend on the ACTUAL multipliers for the different hand totals as well as the multiplier available for the current hand.

I don’t know if there is a way that this can be played at an advantage, but for recreational Blackjack players, I think they will be giving up some EV as opposed to just playing a standard Blackjack game. In addition to that, the Lightning Fee is 100% of whatever amount the player bets, so that adds variance and effectively the best the player can do is win 24x (profit) the Lightning Fee amount (Blackjack + Highest Possible Multiplier + Win the Following Hand) for the Lightning Fee being paid for the current hand.

I suspect that there is a much lower House Edge with this game than there are when a player plays Blackjack side bets, but in my opinion, unless there is some sort of an advantage play angle---recreational players would do best just to stick to traditional Blackjack if the RTP’s are similar.