Evolution Lightning Blackjack

Quote: Wizard

Thank you.

I was wondering what was to prevent a player from betting small with no multiplier and big with a large one. According to Live Casino Comparer, the multiplier applies only up to the amount bet in the hand it was earned. Anything bet above that is paid at standard odds.
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That's correct. It's basically a two-step process by which the multiplier for the next hand is awarded based on winning the prior hand, so it is based on the amount bet the prior hand. That makes sense, otherwise, people could crush this game.

The way I understood it from Live Casino Compare is that, if you bet less on the following hand than the hand that earned the multiplier, once again, the multiplier will pay based on the lesser of the two bets.

That's actually kind of unfortunate because otherwise people could earn a multiplier with the big bet and then play a much smaller bet so that any deviations from Optimal Strategy (to maximize the probability of winning) wouldn't take so much away from making the right decision on the base game.

Quote: ChumpChange

This game is like getting a push for two pairs in video poker.
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I still think Ultimate X is the closest comparison. The only difference is the payout is based on the Lightning Fee paid and not total amount won.

I can see a possible way to approach this but only based on infinite decks and a general assumption of what the next hand might look like.

For the first hand we need to know the value of this round's BJ bet, the value of winning this hand and passing on a specific multiplier to the next hand.

For the next hand we need to know the value of that round's BJ bet (same as above), the value of the bonus pay-out based on the multiplier coming in, the value of the next hand's fee bet (we can only guess at the next hand's multipliers).
Combine the EVs at each decision point to generate a revised strategy and the value of coming into the next hand with a specific multiplier.

Use the next hand values to establish the value of the various totals on the first hand and work out the strategy.

For each of the above generate a spreadsheet which gives the basic EVs of various player decisions vs all possible dealer up-cards (Hit, Stand, Double, Split) (assuming you never surrender or take even money). Add together the EVs and create a combined strategy.

NB I haven't done any calculations except the probabilities of the dealer's hands (infinite) this but let's say getting 21 has an EV of 2.5 for the effect of handing over a multiplier to the next hand, then interestingly you might hit 17 vs 7, and you wouldn't double 11 and 10; the reason is getting 21 and 20 have such high values worth shooting for.
(Personally I think carrying over a multiplier from a winning 21 is higher than this, but it shows that sometimes you may need to go for those to get the big payoffs.)

Note: I have not worked out the value of handling over various multipliers, also the actual values will vary from hand to hand. This just assumed the multipliers were 7x 5x 4x 3x 2x, the worth was proportional to the multiplier, and factoring in the chance of winning the hand on your total. The object is to show, using a conservative estimate, how it might be worth considering not doubling and hitting more aggressively.

Player Total	EV St Base	EV St Ante	Combined St EV	Combined Hit EV
21	.925 926	2.500 000	3.425 926	.000 000
20	.773 227	1.634 080	2.407 307	.263 533
19	.615 976	1.185 956	1.801 933	.448 710
18	.399 554	.730 016	1.129 571	.587 320
17	-.106 809	.202 355	.095 546	.674 210
16	-.475 375	.202 355	-.273 020	.723 378
15	-.475 375	.202 355	-.273 020	.782 216
14	-.475 375	.202 355	-.273 020	.841 990
13	-.475 375	.202 355	-.273 020	.906 833
12	-.475 375	.202 355	-.273 020	.976 622
11	-.475 375	.202 355	-.273 020	1.842 385
Double 11				1.541 027
10	-.475 375	.202 355	-.273 020	1.343 537
Double 10				1.328 291

That's some pretty incredible work already, CharliePatrick. I figured I'd try to give this game a little more attention so that better minds than mine (such as yours, Wizard's and perhaps Teliot's and others) could take a stab at figuring this bad boy out.

In theory, I could figure this out, but the only way that I know how would take forever because it would be to analyze every possible decision point and possible series of results of one decision v. another by hand. Even the 10 v. Dealer 9 that I did (Double v. Hit) took a lot of shortcuts, though I'm pretty confident (Hit if 4x multiplier, or greater, for the current hand) is correct. It might even be a multiplier of 3x, depending on what the multipliers that are available for the next hand (if this hand is won) are.

Let's consider 9,8 v 6
Active Multiplier = 20
Upcoming mulitpliers = lowest paytable (2,2,3,4,5,6)
This makes some crude calculations as to the additional value on the upcoming hand if you get a specific multiplier.
As you can see, the values are very close, and only slightly favor standing. However, if you are playing for a higher set of future multipliers, this will flip so that you will double.

Given a high enough active multiplier and future multipliers, you will double hard 17 v 6.

The first table is for standing

Total	p(win this total)	Win	Added EV for Multiplier Next Hand	Contribution
17	0.421500182		0.4	0.168600073
18	0		0.4	0
19	0		1	0
20	0		1.5	0
21	0		2.2	0
BJ	0		3	0
p(win)	0.421500182	20		8.430003642
p(lose)	0.41233857	-1		-0.41233857
p(push)	0.166161248	0		0
				8.186265144

The second table is for Doubling

Winning Total	Probability	Win	Added EV for Multiplier Next Hand	Contribution
17	0		0.4	0
18	0.045442856		0.4	0.018177143
19	0.053750286		1	0.053750286
20	0.062023491		1.5	0.093035236
21	0.069925159		2.2	0.153835351
BJ	0		3	0
p(win)	0.231141793	40		9.245671708
p(lose)	0.736843198	-2		-1.473686396
p(push)	0.032015009	0		0
				8.090783328

Good stuff, Crystal and Charlie.

I've spent much of the day on a simulator for this game, based on blackjack basic strategy. I already suspect proper strategy is very dependent on the multiplier earned the previous hand.

If either of you or any other qualified person feels they are comfortable with a full analysis of this, I would be interested in publishing it on WoO. Not only would I give full credit and a link to any business interest you may have, but might pay a little something too. Not enough to make it worth your time, but hopefully enough for a nice dinner.

Let me know by PM if you're interested.

Quote: CrystalMath

Let's consider 9,8 v 6
Active Multiplier = 20
Upcoming mulitpliers = lowest paytable (2,2,3,4,5,6)
This makes some crude calculations as to the additional value on the upcoming hand if you get a specific multiplier.
As you can see, the values are very close, and only slightly favor standing. However, if you are playing for a higher set of future multipliers, this will flip so that you will double.

Given a high enough active multiplier and future multipliers, you will double hard 17 v 6.

The first table is for standing

Total	p(win this total)	Win	Added EV for Multiplier Next Hand	Contribution
17	0.421500182		0.4	0.168600073
18	0		0.4	0
19	0		1	0
20	0		1.5	0
21	0		2.2	0
BJ	0		3	0
p(win)	0.421500182	20		8.430003642
p(lose)	0.41233857	-1		-0.41233857
p(push)	0.166161248	0		0
				8.186265144

The second table is for Doubling

Winning Total	Probability	Win	Added EV for Multiplier Next Hand	Contribution
17	0		0.4	0
18	0.045442856		0.4	0.018177143
19	0.053750286		1	0.053750286
20	0.062023491		1.5	0.093035236
21	0.069925159		2.2	0.153835351
BJ	0		3	0
p(win)	0.231141793	40		9.245671708
p(lose)	0.736843198	-2		-1.473686396
p(push)	0.032015009	0		0
				8.090783328

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The game rules is 8D, S17, NoDAS, SPL1, PEEK, DOA2, NoSurr.

How do you get the Added EV for Multiplier Next Hand, 0.4, 0.4, 1.0, 1.5, 2.2, 3.0 ?

When multiplier is 2X, my estimated additional EV is 0.51571 as shown below. Where did I go wrong? How do you get 0.4 ?

I had assumed when you doubled, with no incoming multiplier, the value of the bet for the carry over would remain at the original bet. As I haven't played the game I don't know whether if you have an incoming multiplier and then double, whether the doubled wager is paid x1 or the multiplier (perhaps the rule if you increase your bet only the original bet is multiplied could apply). If the doubled value is paid the multiplier then you will be doubling more often, e.g. some stiff hands; I haven't looked but under some circumstances you might just double almost anything.

Similarly if you split there was a comment that it only paid out on the best hand, or was this for the multiplier that carried forward. Again you might just split everything (except 5s and 10s) and if you already had 20 on the first hand might be less aggressive on the second (since only getting 21 is of any benefit).

Quote: charliepatrick

I had assumed when you doubled, with no incoming multiplier, the value of the bet for the carry over would remain at the original bet. As I haven't played the game I don't know whether if you have an incoming multiplier and then double, whether the doubled wager is paid x1 or the multiplier (perhaps the rule if you increase your bet only the original bet is multiplied could apply). If the doubled value is paid the multiplier then you will be doubling more often, e.g. some stiff hands; I haven't looked but under some circumstances you might just double almost anything.

Similarly if you split there was a comment that it only paid out on the best hand, or was this for the multiplier that carried forward. Again you might just split everything (except 5s and 10s) and if you already had 20 on the first hand might be less aggressive on the second (since only getting 21 is of any benefit).
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-deleted-

Quote: charliepatrick

I had assumed when you doubled, with no incoming multiplier, the value of the bet for the carry over would remain at the original bet. As I haven't played the game I don't know whether if you have an incoming multiplier and then double, whether the doubled wager is paid x1 or the multiplier (perhaps the rule if you increase your bet only the original bet is multiplied could apply). If the doubled value is paid the multiplier then you will be doubling more often, e.g. some stiff hands; I haven't looked but under some circumstances you might just double almost anything.

Similarly if you split there was a comment that it only paid out on the best hand, or was this for the multiplier that carried forward. Again you might just split everything (except 5s and 10s) and if you already had 20 on the first hand might be less aggressive on the second (since only getting 21 is of any benefit).
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I think this video can answer most of your questions.

https://www.youtube.com/watch?v=16ok5a-Aoq8