Evolution Lightning Blackjack

that already happens regardless with blackjack lightning. theres always that few who will hit on 17 - 20 every hand, without fail regardless of what card the dealer has,

same goes for splitting every pairs.

so far from what I gather, the optimal strategy for this game is essentially to do the opposite (when in possession of high multiplier) of the optimal strategy for normal BJ?

Quote: JDawG888

so far from what I gather, the optimal strategy for this game is essentially to do the opposite (when in possession of high multiplier) of the optimal strategy for normal BJ?
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Isn't that the marketing genius of it? They make a game that looks like BlackJack, plays like blackjack and entices the player to play BlackJack strategy: Thus maximising the Hold. Devious beggars!
Their strategy pages were a very generous gesture, and I do hope we can make them player usable and attack the game, especially if there's a better strategy that might offer an advantage.
Since the game is online, some sort of interactive digital strategy assistant would be handy. Probably against their rules, though.

Here is the Lightning Strategy for all unsplit hands. The formatting is of my own creation. This agrees with the strategy posted by Evolution.

Notes
1) Yes, it is complicated, but this was the simplest way I could find to show it.
2) I want to emphasize, that the strategy for split hands is different. I have an idea how to show it and will present that in a little while.
3. I have tried to accurately to present this, but inevitably I may have made a mistake somewhere.



So, for example, at Hard 14 versus 4, the optimal strategy is:
Hit with No multiplier, (and with multiplier = 2)
With multiplier 3+: Double when possible otherwise Hit
Except, with Multipler 5+: Double when Possible otherwise Stand

Maybe this will be easier to read

Here is the strategy for the First Split Hand for Evolutionary's Lightning BJ game.

In Lightning BJ, you may only HIt or Stand on a Split Hand. Remember that Double After Split and Resplitting are not allowed in Lightning Blackjack. These limitations in the player's options do simplify the analysis and presentation of the optimal strategy for playing split hands. On the first hand after a split, according to Evolutionary's published Strategy, it does not matter whether you have initially split Tens or Nines or Sixes or Twos. - for the first split hand strategy depends only on the active multiplier and whether you have made a total of hard 12 -20 or a soft 13-20 after initially hitting your first split card. (Obviously, the player should hit any hand 11 or below. )

So in the above table, the columns correspond to the dealer's up card in the usual way.. However the rows correspond to the value of the active multiplier, ranging from No Multiplier, to the possible multiplier values in the range of 2x to 25x. And the entries in the table are the stop points for hitting.

Example: For a dealer upcard of 5 and an active multiplier of 4x, the table entry is H13, S19 which means that you should hit until you have made a Hard 13 or a soft 19.



Note that the strategy for the 2nd split hand is very different than this, because it will depend upon the outcome that was achieved in the first split hand. It will also depend upon the multiplier and the dealer's upcard, which makes it challenging to format and present in an intelligible way. I will try to present this strategy as best as I can later today in a subsequent post.

Quote: gordonm888

Here is the strategy for the First Split Hand for Evolutionary's Lightning BJ game.

In Lightning BJ, you may only HIt or Stand on a Split Hand. Remember that Double After Split and Resplitting are not allowed in Lightning Blackjack. These limitations in the player's options do simplify the analysis and presentation of the optimal strategy for playing split hands. On the first hand after a split, according to Evolutionary's published Strategy, it does not matter whether you have initially split Tens or Nines or Sixes or Twos. - for the first split hand strategy depends only on the active multiplier and whether you have made a total of hard 12 -20 or a soft 13-20 after initially hitting your first split card. (Obviously, the player should hit any hand 11 or below. )

So in the above table, the columns correspond to the dealer's up card in the usual way.. However the rows correspond to the value of the active multiplier, ranging from No Multiplier, to the possible multiplier values in the range of 2x to 25x. And the entries in the table are the stop points for hitting.

Example: For a dealer upcard of 5 and an active multiplier of 4x, the table entry is H13, S19 which means that you should hit until you have made a Hard 13 or a soft 19.



Note that the strategy for the 2nd split hand is very different than this, because it will depend upon the outcome that was achieved in the first split hand. It will also depend upon the multiplier and the dealer's upcard, which makes it challenging to format and present in an intelligible way. I will try to present this strategy as best as I can later today in a subsequent post.
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What a great strategy, I hope AP can use your strategy to get RTP 99.56(or even more than 100 with certain promotions !)

Quote: ssho88

[
What a great strategy, I hope AP can use your strategy to get RTP 99.56(or even more than 100 with certain promotions !)
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I'm not sure that this strategy (which is a reformatting of Evolutionary's posted strategy) is the theoretically optimum strategy for split hands. I think the person who developed this strategy may have missed something. But even if they did miss something, the extra EV one might gain from better optimization of decisions on split hands is probably incredibly small.

Quote: gordonm888

Quote: ssho88

[
What a great strategy, I hope AP can use your strategy to get RTP 99.56(or even more than 100 with certain promotions !)
link to original post

I'm not sure that this strategy (which is a reformatting of Evolutionary's posted strategy) is the theoretically optimum strategy for split hands. I think the person who developed this strategy may have missed something. But even if they did miss something, the extra EV one might gain from better optimization of decisions on split hands is probably incredibly small.
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I've just been comparing some of the strategy charts and have noticed some subtle differences between the multiplier selections. I'm just wondering if you've accounted for that in the work you've done so far.

There is, for example, five strategy charts for the 2x multiplier, with each one potentially different depending on which "set" of multipliers, are in play.

I'd hate to think that you've done this work and maybe hadn't spotted that. The same is true of all multipliers, each one has 5 different versions - which is perhaps why Evolution presented them in the way they have?

Forgive me I haven't cross-referenced what you've done - my eyes just can't take it lol, just thought I'd flag it up to help.

Quote: NeilLCC

I've just been comparing some of the strategy charts and have noticed some subtle differences between the multiplier selections. I'm just wondering if you've accounted for that in the work you've done so far.

There is, for example, five strategy charts for the 2x multiplier, with each one potentially different depending on which "set" of multipliers, are in play.

I'd hate to think that you've done this work and maybe hadn't spotted that. The same is true of all multipliers, each one has 5 different versions - which is perhaps why Evolution presented them in the way they have?

Forgive me I haven't cross-referenced what you've done - my eyes just can't take it lol, just thought I'd flag it up to help.
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I noticed this too. With no active multiplier, but high potential multiplier, you don't double.

Quote: miplet

I noticed this too. With no active multiplier, but high potential multiplier, you don't double.

Yeah, I think this encapsulates the essence of what makes this game -

a) Potentially attractive to gamblers.
b) Difficult to derive the optimal strategy for.
c) Difficult to present that strategy in a way that can be followed.

- There can be a conflict between the goals of 'banking' what is available to be won on the current hand and shooting for the opportunity of winning more on the next hand.

Quote: miplet

Quote: NeilLCC

I've just been comparing some of the strategy charts and have noticed some subtle differences between the multiplier selections. I'm just wondering if you've accounted for that in the work you've done so far.

There is, for example, five strategy charts for the 2x multiplier, with each one potentially different depending on which "set" of multipliers, are in play.

I'd hate to think that you've done this work and maybe hadn't spotted that. The same is true of all multipliers, each one has 5 different versions - which is perhaps why Evolution presented them in the way they have?

Forgive me I haven't cross-referenced what you've done - my eyes just can't take it lol, just thought I'd flag it up to help.
link to original post

I noticed this too. With no active multiplier, but high potential multiplier, you don't double.
link to original post

The charts I have been supplying in the last two days are not at all connected to any earlier charts that charliepatrick, chesterdog or I have presented, They are a complete restructuring and reformatting of the evolutionary strategy presented here: Evolutionary Strategy and its taken me hours to accomplish this.

I don't understand what you mean by "5 different strategy charts for each multiplier." The chart are organized by Hard hands, Soft Hands, Pairs, and First split hand, so yes, each chart accounts for the different possible multipliers. Are those the "5 charts" that you are referring to?

Miplet, I agree with your statement but don't understand the issue you are raising. The only No Multiplier doubles I show on my tables are Double 10,11 vs 2-7 and Double S18 vs 5,6. Those are certainly reasonable doubles, aren't they?

Quote: gordonm888

Quote: miplet

Quote: NeilLCC

I've just been comparing some of the strategy charts and have noticed some subtle differences between the multiplier selections. I'm just wondering if you've accounted for that in the work you've done so far.

There is, for example, five strategy charts for the 2x multiplier, with each one potentially different depending on which "set" of multipliers, are in play.

I'd hate to think that you've done this work and maybe hadn't spotted that. The same is true of all multipliers, each one has 5 different versions - which is perhaps why Evolution presented them in the way they have?

Forgive me I haven't cross-referenced what you've done - my eyes just can't take it lol, just thought I'd flag it up to help.
link to original post

I noticed this too. With no active multiplier, but high potential multiplier, you don't double.
link to original post

The charts I have been supplying in the last two days are not at all connected to any earlier charts that charliepatrick, chesterdog or I have presented, They are a complete restructuring and reformatting of the evolutionary strategy presented here: Evolutionary Strategy and its taken me hours to accomplish this.

I don't understand what you mean by "5 different strategy charts for each multiplier." The chart are organized by Hard hands, Soft Hands, Pairs, and First split hand, so yes, each chart accounts for the different possible multipliers. Are those the "5 charts" that you are referring to?

Miplet, I agree with your statement but don't understand the issue you are raising. The only No Multiplier doubles I show on my tables are Double 10,11 vs 2-7 and Double S18 vs 5,6. Those are certainly reasonable doubles, aren't they?
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https://static.egcdn.com/frontend/fec/ring-test/optimalLightningBlackjackStrategy.html?gameType=lightningscalablebj&lang=en#openMenu

There are 5 different next hand multiplier groups each with their own strategy on your current multiplier.

I presumed the 5 groups reference was a typo, and 6 groups is what was meant??

gordonm888, taking your example -

Quote:

So, for example, at Hard 14 versus 4, the optimal strategy is:
Hit with No multiplier, (and with multiplier = 2)
With multiplier 3+: Double when possible otherwise Hit
Except, with Multipler 5+: Double when Possible otherwise Stand

The Evolution strategy tables actually say the following (if I've managed to transcribe it all correctly!) -

If the current set of multipliers on offer is 2x 2x 3x 4x 5x 6x, then
Hit with No multiplier, (STAND with multiplier = 2)
With multiplier 3+: Double when possible otherwise STAND

If the current set of multipliers on offer is 2x 3x 4x 5x 6x 8x, then
Hit with No multiplier, (Hit with multiplier = 2)
With multiplier 3: Double when possible otherwise HIT
With multiplier 4+: Double when possible otherwise Stand

If the current set of multipliers on offer is 2x 3x 4x 5x 8x 12x, then
Hit with No multiplier, (Hit with multiplier = 2)
With multiplier 3,4: Double when possible otherwise HIT
With multiplier 5+: Double when possible otherwise Stand

If the current set of multipliers on offer is 2x 4x 5x 6x 10x 15x, then
Hit with No multiplier, (Hit with multiplier = 2)
With multiplier 3-6: Double when possible otherwise HIT
With multiplier 8+: Double when possible otherwise Stand

If the current set of multipliers on offer is 2x 5x 6x 8x 12x 20x, then
Hit with No multiplier, (Hit with multiplier = 2)
With multiplier 3-8: Double when possible otherwise HIT
With multiplier 10+: Double when possible otherwise Stand

If the current set of multipliers on offer is 2x 5x 8x 12x 15x 25x, then
Hit with No multiplier, (Hit with multiplier = 2)
With multiplier 3-12: Double when possible otherwise HIT
With multiplier 15+: Double when possible otherwise Stand

Quote: gordonm888

Quote: miplet

Quote: NeilLCC

I've just been comparing some of the strategy charts and have noticed some subtle differences between the multiplier selections. I'm just wondering if you've accounted for that in the work you've done so far.

There is, for example, five strategy charts for the 2x multiplier, with each one potentially different depending on which "set" of multipliers, are in play.

I'd hate to think that you've done this work and maybe hadn't spotted that. The same is true of all multipliers, each one has 5 different versions - which is perhaps why Evolution presented them in the way they have?

Forgive me I haven't cross-referenced what you've done - my eyes just can't take it lol, just thought I'd flag it up to help.
link to original post

I noticed this too. With no active multiplier, but high potential multiplier, you don't double.
link to original post

The charts I have been supplying in the last two days are not at all connected to any earlier charts that charliepatrick, chesterdog or I have presented, They are a complete restructuring and reformatting of the evolutionary strategy presented here: ml?gameType=lightningscalablebj&lang=en#strategies]Evolutionary Strategy and its taken me hours to accomplish this.

I don't understand what you mean by "5 different strategy charts for each multiplier." The chart are organized by Hard hands, Soft Hands, Pairs, and First split hand, so yes, each chart accounts for the different possible multipliers. Are those the "5 charts" that you are referring to?

Miplet, I agree with your statement but don't understand the issue you are raising. The only No Multiplier doubles I show on my tables are Double 10,11 vs 2-7 and Double S18 vs 5,6. Those are certainly reasonable doubles, aren't they?
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The link you should work from is one level up from the link you posted. Hit the back arrow at the top to see the rest.

This shows the six different multiplier sequences that can be selected for a game round. If you click on one of them it will reveal a strategy chart for that sequence of multipliers. Each Sequence has its own chart and each is different from the other sequence charts. I thought you might only be looking at one of the sequence charts, which I think is what you have done.

Oh, I see.

I have done all of my compilation, restructuring and reformatting for one specific multiplier group, namely:

2,3,4,5,8,12 (12-17 = 2x; 18 = 3x; 19 =4x; 20 = 5x; 21 = 8x, and BJ =12 X)

but I was unaware that there are 5 other multiplier groups:

2,2,3,4,5,6

2,3,4,5,6,8

2,4,5,6,10,15

2,5,6,8,12,20

2,5,8,12,15,25

So, the multiplier group I picked was the 3rd highest of 6, but one would need to repeat what I have done for another 5 multiplier groups to get a rigorously correct strategy that would produce the declared House Edge value.

That is absolutely bat-stool crazy. That is nuts. The strategy for any one multiplier group is already far too complicated, but to multiply that complexity by a factor of 6X? What were the game designers trying to achieve?

Quote: gordonm888

That is absolutely bat-stool crazy. That is nuts. The strategy for any one multiplier group is already far too complicated, but to multiply that complexity by a factor of 6X? What were the game designers trying to achieve?

I think you are being a bit unfair on the game designers. I'm sure they are trying to appeal to typical gamblers, not to the likes of us, and they might well succeed. The complexity of the strategy is only an issue for people trying to follow it, and they will be very few in number! Its publication was probably mostly as a justification for the stated optimal-play house edge, rather than a guide for players.

They've released other 'Lightning' game variations - roulette, baccarat (and maybe some others), each with some kind of random multipliers applied after the betting closes. I guess this is to appeal to slot-player types who like the excitement of random big payouts (or opportunities for a big payout). E.g., in roulette, everyone who has placed a straight-up bet on one of the numbers that then gets a random multiplier has the thrill of then waiting to see if they are about to win unusually big.

This blackjack variant has the additional 'thrill' of the tension between the two conflicting aims of the game - maximise the payout from this round vs maximise the potential payout from the next round. I think the idea is that naive players should be left in a quandary about whether to hit and hope for a big multiplier in the next round or stand for fear of losing the current round's (multiplied) payout.

Its a way to quote an attractively low house edge for a game, while having it play as 85-95% return to player.

Quote: gordonm888

Its a way to quote an attractively low house edge for a game, while having it play as 85-95% return to player.
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Indeed. Not trying to say I approve from a moral perspective. Just that I don't think they have in any way blundered in terms of meeting their likely goals.

I'm beginning to have another look at this but have worked out that the chances of each "Set" of multipliers cannot be equal (it makes it too advantageous to the player). Unless there are any better indications I'm going to guess the chances are 40%,25%,15%,10%,5%,5%; this gives an average of 2 2.9 4 5.2 7.05 9.95 which is close to the averages the wizard posted (another idea is 50% 15% 12.5% 10% 7.5% 5% which gives similar results). However without the exact ratios one isn't going to be able to derive a proper House Edge unless it happens to come out at exactly their figure!

The first thing I need to do is work on the splitting strategy, for instance at the lowest level I currently do not have any splitting 4s, so I am guessing it's worth it because of the advantage of having two attempts to get to 21.

Quote: charliepatrick

I'm beginning to have another look at this but have worked out that the chances of each "Set" of multipliers cannot be equal (it makes it too advantageous to the player). Unless there are any better indications I'm going to guess the chances are 40%,25%,15%,10%,5%,5%; this gives an average of 2 2.9 4 5.2 7.05 9.95 which is close to the averages the wizard posted (another idea is 50% 15% 12.5% 10% 7.5% 5% which gives similar results). However without the exact ratios one isn't going to be able to derive a proper House Edge unless it happens to come out at exactly their figure!

The first thing I need to do is work on the splitting strategy, for instance at the lowest level I currently do not have any splitting 4s, so I am guessing it's worth it because of the advantage of having two attempts to get to 21.
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Charlie, no need to work out any strategy, just go to the Evolution Lightning Poker web site and you can find tables of all the strategy for all of the possible situations. The problem is that, given the six sets of multipliers, there are so many thousands of possible situations, that the problem becomes one of mapping the optimal decisions onto whatever structure/framework makes sense for your computational models.

Just for determining how to play the 2nd split 6 of a pair of sixes, you must consider:

12 possible values of active multipliers
6 possible sets of multipliers that you might earn
6 possible categories of outcome for the first split hand (Bust, 12-17, 18, 19, 20, 21)
12 possible totals (12-17, S13-S18) that you might have in your 2nd split hand for which the H/S decision is not fixed.

So that is 12*6*6*12 = 5,184 different possible situations for which one needs to define/know the optimum strategy just to play the second split 6 when dealt a pair of sixes!

Not to mention playing the first split 6 of a pair 66! Or how to draw to a split pair of 10's (TT is a very important hand because this situation occurs frequently). Or playing a S14 vs 14 or a hard 17 vs 8 or any of the >100 "hands" that need to be defined.

Pardon the pun, but I really believe that this game is an evolutionary dead end.

^ As you say there will be so many combinations that have to be looked at (one advantage of DO loops!); looking just at the second hand of split 6s the results I got earlier matches their strategy for Set 2 (2 3 4 5 6 8). I can imagine it could get different for different sets/multipliers. This is probably a game where a computer might know the strategy but no-one in practice would.

Quote: charliepatrick

...Multiplier for this hand is x5

D: 6 Spl: A2346789X H: 13 (13 13 12 12 11 11) h: 7 (7 7 8 7 7 7[u/]) D: D16 D15 D14 D13 D12 D11 D10 D9 D8 D7 D6 D5 D4 D3 D2 D1 d: d10 d9 d8 d7 d6 d5 d4 d3

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After working out the splits (there's actually more to them than in the Evolution strategy) I've had to make a few assumptions, and there's no guarantee that I'm correct, but I played around with the value of passing hands on.
For fun I wondered what would happen if there was no value of passing any hand to the next phase, for a regular game it gave the regular strategy and a house edge of 0.792% (this assumed you didn't pay the "Ante"). Using similar logic you get a range of EVs for various multipliers (0.499 for 2x, up to 16.639 for 25x).

Then I plugged those values into the carry forward and, after a quick play around, found if Set 1 thru Set 6 were picked with 50% 20% 12.5% 7.5% 5% 5% I got a House Edge of 0.36% (i.e. payback of 99.63%).

I've yet to work through the strategy to see if it matches.

About splits - I looked at all the splits as on occasions it mattered which cards you had split (for instance splitting 9s might make it easier to get to 19 than splitting 6s). So the H1: and h1: lines give the hit/stand point for pairs of 2 3 4 5 6 7 8 9 X (Note: some of these values are impossible, e.g. you can't really get a soft total where you might hit from splitting 10s or 9s., also you never split 5s.) I'm not sure why I've got more hitting than they have for the first hand, I only checked one case so might revisit this.

These are for set 1.

Yes, I agree, Evolution's strategy for the first split hand does not account for whether you are splitting Tens or Sixes - and one might wish to be less aggressive hitting stiff hands when splitting Tens than when splitting Sixes because the second hand is more likely to readily get you a high multiplier when the second split hand is a Ten (and less likely when the second split hand is a Six.)

This is what I referred to in a previous post when I said that I think that Evolution missed something when they developed their strategy for Hit/Stand decisions on split hands.

BTW, analyzng the splitting of a 10-10 pair is where the action is - because a 10-10 pair is roughly 16X more likely to occur than any other pair.

Quote: gordonm888

... 10-10 pair is roughly 16X more likely to occur than any other pair.
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In my local casino they have to be identical ranks - so personally I'm currently assuming there are only 4 ways to get a pair of pictures - however this would probably only affect the EV rather than the strategy.

Quote: charliepatrick

For fun I wondered what would happen if there was no value of passing any hand to the next phase, for a regular game it gave the regular strategy and a house edge of 0.792% (this assumed you didn't pay the "Ante"). Using similar logic you get a range of EVs for various multipliers (0.499 for 2x, up to 16.639 for 25x).

Then I plugged those values into the carry forward and, after a quick play around, found if Set 1 thru Set 6 were picked with 50% 20% 12.5% 7.5% 5% 5% I got a House Edge of 0.36% (i.e. payback of 99.63%).

I've yet to work through the strategy to see if it matches.

You're clearly a lot further down the road with this than I am, but I have been giving some thought to how I might go about modifying a CA program to tackle this. In truth, I'm trying to restrain myself from diving in, because -
a) there are other things I am supposed to be doing
b) it looks like a lot of (difficult) work, and
c) there are clearly already some very able people on the case!

What you said in the quoted snippet reminds me of a question I have been pondering - Would an iterative approach work? The idea would be to start by generating a strategy with no value associated with the multiplier being carried forward, use its EVs to generate a modified strategy accounting for the value of the carried forward multiplier, use the EVs of the modified strategy to create yet another modified strategy, and so on until there are no more modifications arising.

Conceptually, the idea is to ask "If I were to apply strategy S0 to the next hand, what is the strategy, S1, I should I apply to the current hand in order to maximise the overall EV?". Then, "If I were to apply S1 on the next hand, what is the strategy S2...." etc.

Does that make sense / sound reasonable?


Also, when it comes to plugging the EVs into the carry forward, I think that it is only the excess EV above what would be won by applying the given strategy under normal BJ rules which should be counted in the carry forward. Otherwise, I think you end up counting this portion of the EV twice, once for each hand. [I have to admit my thoughts on this are all still a little fuzzy, though. I've been going round in circles to some degree.]

Quote: LC1

...What you said in the quoted snippet reminds me of a question I have been pondering - Would an iterative approach work? The idea would be to start by generating a strategy with no value associated with the multiplier being carried forward, use its EVs to generate a modified strategy accounting for the value of the carried forward multiplier, use the EVs of the modified strategy to create yet another modified strategy, and so on until there are no more modifications arising.

Conceptually, the idea is to ask "If I were to apply strategy S0 to the next hand, what is the strategy, S1, I should I apply to the current hand in order to maximise the overall EV?". Then, "If I were to apply S1 on the next hand, what is the strategy S2...." etc.

Does that make sense / sound reasonable?


Also, when it comes to plugging the EVs into the carry forward, I think that it is only the excess EV above what would be won by applying the given strategy under normal BJ rules which should be counted in the carry forward. Otherwise, I think you end up counting this portion of the EV twice, once for each hand...

Yes I have tried the S0, S1 approach (which is how I got the results I did) but also if I carried on I got to a figure to 4 decimal places with 4 iterations. However it was a player advantage under the worst conditions so I suspect I'm missing a (-1) somewhere for paying the "Ante" to play the next hand.

Using S0 S1 can only be an estimate. That method assumes there is no value of a carry forward for the second hand, so you don't pay the "Ante" and also don't benefit from it - however this possibly means the strategy is slightly different - but it will give a rough idea of the correct EV. (It seems to give a strategy for the first hand close to theirs, so I suspect the carry forward EVs are fairly close and if I added in logic for paying for the "Ante", I might get some convergence.)

btw one reason for using coding is each iteration can create the evs[0]=nnnnn evs[1]=mmmm etc to plug into the next!

Thanks for the response.

Quote: charliepatrick

Using S0 S1 can only be an estimate. That method assumes there is no value of a carry forward for the second hand, so you don't pay the "Ante" and also don't benefit from it - however this possibly means the strategy is slightly different - but it will give a rough idea of the correct EV. (It seems to give a strategy for the first hand close to theirs, so I suspect the carry forward EVs are fairly close and if I added in logic for paying for the "Ante", I might get some convergence.)

Yeah, I glossed over some elements. I was sort of aware that there would be a need for an extra term for the EV arising from the average multiplier won by the second hand (I think I saw you mention this in an earlier post.). And, also, I am wondering if what is actually needed is the EV associated with not just the second hand, but with the average-length of winning streak.

How to correctly account for subsequent main + ante bets in relation to the first hand is a bit confusing to me at the moment. It seems like there is scope to inadvertently count them twice (a bit like the issue I mentioned with the carry-forward EV). With a simulation, you could just divide the total amount won or lost by the total of the initial bets of all the hands played, to get the per-hand EV. With an analytical approach the notional hand is simultaneously playing multiple roles (the 1st, 2nd, and maybe 3rd+ hands).

Quote: LC1

-snip-

What you said in the quoted snippet reminds me of a question I have been pondering - Would an iterative approach work? The idea would be to start by generating a strategy with no value associated with the multiplier being carried forward, use its EVs to generate a modified strategy accounting for the value of the carried forward multiplier, use the EVs of the modified strategy to create yet another modified strategy, and so on until there are no more modifications arising.

Conceptually, the idea is to ask "If I were to apply strategy S0 to the next hand, what is the strategy, S1, I should I apply to the current hand in order to maximise the overall EV?". Then, "If I were to apply S1 on the next hand, what is the strategy S2...." etc.

Does that make sense / sound reasonable?
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The approach you are describing has been used for years to develop poker theory - usually with some AI software together with a looping routine that runs the system several million times. See, for example, Modern Poker Theory by Acevedo.

However, poker decisions involve 'opponent behavior' and thus are not strictly optimizable by probability theory. This game does have the complication that how you play your current hand has implied effects on your effective value in the next hand, but I still think that combinatorial probability methods are the best approach here.

Quote: gordonm888

The approach you are describing has been used for years to develop poker theory - usually with some AI software together with a looping routine that runs the system several million times. See, for example, Modern Poker Theory by Acevedo.

However, poker decisions involve 'opponent behavior' and thus are not strictly optimizable by probability theory. This game does have the complication that how you play your current hand has implied effects on your effective value in the next hand, but I still think that combinatorial probability methods are the best approach here.
link to original post

I think you have misunderstood what I was trying to say. See Charlie's reply to me - the approach I was describing does chiefly consist of combinatorial probability methods, and is essentially the same approach that he is taking.

That being said, I've been thinking some more, and have some new concerns/ideas which I will put in another post...

The double counting issue I've mentioned a couple of times is leading me to think I'm on completely the wrong track, and, by extension so might others be (since I thought we were on the same track!). [It is of course possible, likely even, that I have misunderstood some crucial detail of what's been described. Apologies if that's the case.]

What I hadn't previously considered is this -

Suppose we play two hands, A then B. We play B with a multiplier which we won in A.
If we assign an EV to B's blackjack bet, based on the multiplier, having also incorporated that EV into hand A ,then surely we have accounted for it twice! (The EV we assign to each hand includes both the winning of the multiplier and the playing of the multiplier.)

So I think we may need to do the following -

Use the sum of the hand EV and the carry-forward EV to rank the strategy decisions, but do not actually update the hand EV to include the carry-forward EV. (That way, the value of a multiplier is only counted when it is actually applied, but we make the right strategy decisions to exploit the multipliers.)

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And, in general, the fundamental idea would be that only the amounts available to be directly won/lost on the current hand factor into the calculated EV for the hand. The additional EV that stems from carrying forward a multiplier to the next hand (and maybe beyond) only directly impacts the strategy decisions.


Does that make sense?

[Edit: On reflection, I'm not sure it does entirely. Seems like what is missing from the above is the need to determine the frequency with which each multiplier gets won, and use these to weight the contribution of the corresponding strategies to the total EV. Not sure if that can be done.

If I'm right that there is an issue regarding the double counting, maybe there are other, better ways to solve it??]

NB: I have not checked very much, especially whether the correct strategy is being followed. So please only look at the trends not the actual House Edges. Also note these do not take the "Ante" into account, so subtract 1 from all the values.
I'm not sure whether my strategy is being followed (i.e. whether I have transferred all my decisions correctly) but one can see the trend for various hands (the count shows the Multiplier coming in, then the Set of multipliers being carried forward). Typically if the multipliers are higher (i.e. higher set number) you tend to try harder to get towards 21, so the pay-outs for this hand drop a bit.
As I said I don't know the ratio of the set numbers so the bottom line cannot be a realistic indication - as I said earlier I may be hitting the first split hand too much.
The EV of 0.9195... does not take account of having to Pay the "Ante" each round, so the simulation's House Edge is about 8%. So please ignore this value as there's just not enough information!

Edit: Changing the ratios to 40% 20% 16% 12% 8% 4%, but keeping the same strategy (which might still be close but could be slightly wrong) gives a House Edge of 1%!

Quote: OnceDear

Quote: LC1

Hi,
Evolution has published their full strategy for the game, accessible via a link in the in-game help text.

[I've been trying to post the link here, but the forum interface keeps removing the bulk of the text when I paste it in, for some reason! In the game help, you can find it in the 'payouts' section - 'Open Strategy in New Window'.]

link to original post

BRILLIANTLY WELL SPOTTED
https://static.egcdn.com/frontend/fec/ring-test/optimalLightningBlackjackStrategy.html?gameType=lightningscalablebj&lang=en#openMenu

It's a little complex and each icon is a link to a busy page.
Something for our maths guys to get their teeth into
link to original post

Seems like that link doesn't work any more. Has anyone captured all the raw information in all those strategy tables, or even a copy of the pages?

Thanks so much for everyone who has done work on this game and has been willing to share.

This link seems to work: https://static.egcdn.com/frontend/evo/r2/optimalLightningBlackjackStrategy.html?gameType=lightningscalablebj&lang=en#openMenu