charliepatrick
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November 17th, 2021 at 12:02:05 AM permalink
Without taking into the effect of carry over I got similar, if not identical, patterns. It also applies to soft doubling, after a while you always do that.

The reason is that I have now moved on to try and see the effects the carried over multiplier has; obviously this is based on the estimates at this stage.

For instance with no multiplier you probably don't double hard totals vs A, 7, 8, 9, or 10 as you hit until you get to hard 18; the reason for this is probably how valuable it is if you make 21 or 20. vs 2 to 6 you do double 10 and 11 (not 9) and stand on hard 17. Trying to get to 21 or 20 has a large effect on strategy. (I guess similar logic applies to any set of multipliers as the 21 value is the biggest.)

I haven't managed to quantify how useful splitting is, since you get two chances to reach the high totals - my guess is if the first one doesn't then you try hard, otherwise play normally (I haven't taken this into account for the calculations). I suspect simulation is the only way to do this part, except for high multipliers where they take over from the benefit of carry over. (At some multipliers and some up-cards I think you sometimes double 44 rather than split because your chances of winning is better; e.g. at 8x or higher you double 44 vs 6, otherwise split A234 6789X; at 3x you always split A234 6789.)
OnceDear
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November 17th, 2021 at 3:05:39 AM permalink
I see mentions of multipliers of 1x. I don't recall seeing any of those. Does that mean times where there is no multiplier carried forward?
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
DRich
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November 17th, 2021 at 4:55:22 AM permalink
Quote: OnceDear

I see mentions of multipliers of 1x. I don't recall seeing any of those. Does that mean times where there is no multiplier carried forward?

That is my assumption.
At my age, a "Life In Prison" sentence is not much of a deterrent.
gordonm888
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November 17th, 2021 at 5:12:56 AM permalink
Quote: DRich

Quote: OnceDear

I see mentions of multipliers of 1x. I don't recall seeing any of those. Does that mean times where there is no multiplier carried forward?

That is my assumption.

Yes, the minimum multiplier of 1 simply means that you always double; i.e., you double with no multiplier

Here's a phrase from poker theory that may be helpful in having these discussions:

Imputed EV - the ΔEV that you can expect on the next hand from the conditional multipliers that a given decision achieves on the current hand.

Sometimes imputed EV will be negative. Example: for TTv6, when we evaluate splitting the pair of Tens there will almost certainly be a negative imputed EV associated with the next hand - which will be a factor in determining whether to split or not on this hand.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
charliepatrick
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November 17th, 2021 at 5:39:05 AM permalink
I've used multiplier of x0 to mean regular hand (so BJ would pay 6/4). This still has the broad assumptions from my previous update, but it does show the trend. I suspect you hit soft 18 because you're going for the 21's.
Green "0" means under all circumstances, "99" means never, at least not for multipliers up to 25.
(Doubling 4 will never happen as you split 2s instead, Doubling 44 can happen as noted earlier, otherwise I suspect the split takes preference - you never split 5s.)
gordonm888
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November 17th, 2021 at 7:44:10 AM permalink
This feels like what the Manhattan Project must have been, with many of the best people in the world all working on a very hard project. Thanks ChesterDog and charliepatrick!

Ultimately, the figure of merit for deciding between Stand/Hit/Double/Split options on a hand should be

(EV + IEV)

where EV is the EV of the immediate hand, and the IEV is the Imputed EV of the subsequent hand. Imputed EV is a function of the frequency of having winning hands that total 21,20,19,18, and 17 or less)

To calculate the IEV we need the following:

a) As a function of the multiplier for values of 1 to 25, we need the immediate EV and the frequencies of a winning 21,20,19,18, and 17- for this game as integrated across all possible hands, assuming the strategy laid out by charlie above (if people agree with it.). (This will be different than previous numbers posted by Charlie, as those did not include the double down on almost everything strategy for high multipliers.)

b) We continue to need as much information as possible about the frequency of possible multipliers for a winning hand of 17- to 21 that have been designed into the game.

c) We then need to calculate the implied EV of the next hand when you make a winning hand of 17-, 18, 19, 20 and 21. (by combining a and b.)

d) We then need to revisit the determination of optimum strategy for individual hands, as Chester, charlie and I have been doing, but this time by using (EV + IEV) as the figure of merit.

e) we probably need some simulations of shoes to see whether our numbers are actually being realized.

f) we also need people to question this overall approach and help to modify and improve it.

There are so many super-bright people here, I suggest that everyone try to contribute according to what they are good at. Guys like Wizard and Charlie enjoy trying to do everything themselves, and that's good too - but there's a lot of work to do and we're all human and make mistakes, so communicating and questioning is going to be important.
Last edited by: gordonm888 on Nov 17, 2021
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
charliepatrick
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November 17th, 2021 at 8:13:31 AM permalink
If it helps others the approach I used calculated a number of EVs.
(i) PlayerStandsCF = EV for standing where the multiplier (if you win) goes onto the next hand.
(ii) PlayerStandsnoCF = EV for standing where there is no multiplier passed to the next hand - this, given the way I worked, was used on the second hand of a split or when doubling to work out the EV on the doubled part of the bet (it got paid the incoming multiplier but did not benefit from the carry forward value as that had been taken into account on the original wager)
(iii) PlayerHitsorStandsCF = EV for the best choice of standing or hitting where the multiplier (if you win) goes onto the next hand. This applies to an undoubled hand or the first hand of a split.
(iv) PlayerHitsorStandsnoCF = EV for the best choice of standing or hitting on the second split hand (this was an approximation and assumed the first hand's multiplier would be used) - thus there is scope for some HouseEdge improvement here, it also might mean you split slightly more often on close decisions.
(v) PlayersHitsStandsorDoubles = EV for the best option on your first two cards - by definition this will include the multiplier and be based on (i) plus (ii) for all the possible outcomes.
(vi) Split decision uses the above and is remembered as the EV (if better) for hands such as 88 rather than 16.
The net EV is calculated looking at all possible 169 starting hands against each of the dealers' up-cards accounting for BlackJacks and the peeking rules.

I'm not sure of an easy way to work out the benefit given when splitting to the second hand based on what happened to the first hand, this is because one is remembering the best EV decision at each point, rather than keeping the proportion of 20s, 21s etc that one makes. I imagine, given you can't double after a split, knowing the strategy (e.g. hitting until 17) and starting point, you could work out the proportion of times you'd have bust,21, 20... etc on the first hand. With larger multipliers I think you tend to ignore the carry over so make the same decisions, but with lower ones it can be different.
Mission146
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November 17th, 2021 at 8:18:39 AM permalink
Quote: RideTheEdge

At casinobloke.com https://www.casinobloke.com/live-dealer/evolution-lightning-blackjack-live/ it says the payout is capped at 36.5:1. Do you think this is correct, and it is included in your EV calculation and basic strategy for doubles and splits when the multiplier is 20 or 25?

I believe it, but I could be wrong. The way I understood the rules as I read them, the normal Blackjack hand would pay normally and the multiplier pays one Lightning unit * multiplier based on whether or not you win or lose. I still don't think that all winnings are multiplied, but has anyone actually got to play to see whether or not they are?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
ssho88
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November 17th, 2021 at 8:49:40 AM permalink
Quote: charliepatrick

I've used multiplier of x0 to mean regular hand (so BJ would pay 6/4). This still has the broad assumptions from my previous update, but it does show the trend. I suspect you hit soft 18 because you're going for the 21's.
Green "0" means under all circumstances, "99" means never, at least not for multipliers up to 25.
(Doubling 4 will never happen as you split 2s instead, Doubling 44 can happen as noted earlier, otherwise I suspect the split takes preference - you never split 5s.)

17 vs T(Green "0"), meaning that the player always HIT if multiplier < 5 ?
Last edited by: ssho88 on Nov 17, 2021
OnceDear
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November 17th, 2021 at 9:36:43 AM permalink
Quote: Mission146

I still don't think that all winnings are multiplied, but has anyone actually got to play to see whether or not they are?

They are, Though I can't report how Blackjacks are paid. the rules are ambiguous on that. I'll try to look back through game history.
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
gordonm888
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November 17th, 2021 at 10:13:59 AM permalink
Quote: charliepatrick

If it helps others the approach I used calculated a number of EVs.
(i) PlayerStandsCF = EV for standing where the multiplier (if you win) goes onto the next hand.
(ii) PlayerStandsnoCF = EV for standing where there is no multiplier passed to the next hand - this, given the way I worked, was used on the second hand of a split or when doubling to work out the EV on the doubled part of the bet (it got paid the incoming multiplier but did not benefit from the carry forward value as that had been taken into account on the original wager)
(iii) PlayerHitsorStandsCF = EV for the best choice of standing or hitting where the multiplier (if you win) goes onto the next hand. This applies to an undoubled hand or the first hand of a split.
(iv) PlayerHitsorStandsnoCF = EV for the best choice of standing or hitting on the second split hand (this was an approximation and assumed the first hand's multiplier would be used) - thus there is scope for some HouseEdge improvement here, it also might mean you split slightly more often on close decisions.
(v) PlayersHitsStandsorDoubles = EV for the best option on your first two cards - by definition this will include the multiplier and be based on (i) plus (ii) for all the possible outcomes.
(vi) Split decision uses the above and is remembered as the EV (if better) for hands such as 88 rather than 16.
The net EV is calculated looking at all possible 169 starting hands against each of the dealers' up-cards accounting for BlackJacks and the peeking rules.

Yes, definitely if you could share that data I think we could all learn something and may be able to use it. I very much like your approaches, Charlie, because you preserve intermediate data that has the potential to enlighten us as to what is going on. You know I dislike the looping codes that give one the correct answer but often are limited in improving our understanding. And I am always amazed at how quickly you can calculate so much.

Quote: charliepatrick

I'm not sure of an easy way to work out the benefit given when splitting to the second hand based on what happened to the first hand, this is because one is remembering the best EV decision at each point, rather than keeping the proportion of 20s, 21s etc that one makes. I imagine, given you can't double after a split, knowing the strategy (e.g. hitting until 17) and starting point, you could work out the proportion of times you'd have bust,21, 20... etc on the first hand. With larger multipliers I think you tend to ignore the carry over so make the same decisions, but with lower ones it can be different.

Regarding the split pair outcomes: let me see, I think you are saying that its hard to calculate a "frequency of winning totals" when you have two split hands and are required to take the best outcome of two. I had not thought of that, First, we could do that with simulation, if necessary. However, if we want to use combination math, I think we just assume that the 2nd split hand performs exactly like the first split hand (the recurrence approximation) and then convolve the frequency distribution of outcomes to generate a frequency distribution for 'Best of two hands."

You have looked at split pairs in Lightning BJ more than me (or anyone else on this thread), so I think you are ahead of all of us in thinking about it. I am happy to kibitz, but I suspect you will be the one to find an approach, if you haven't already.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
charliepatrick
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November 17th, 2021 at 11:25:44 AM permalink
Yes you hit 17 vs 10 on the basic game.
`Dealer upcard = 10 (a) Stand (b) St or Hit (c) StHitorDbl (d) StHit noCF (e) SplitPH: 21 +3.958099002 +3.958099002 S +3.958099002 - +0.811652585 SnoPH: 20 +1.651204291 +1.651204291 S +1.651204291 - +0.434957754 Sno -PH: 19 +0.666833266 +0.666833266 S +0.666833266 - -0.018660154 SnoPH: 18 +0.068759714 +0.068759714 S +0.068759714 - -0.241508831 Sno X 0.856206618PH: 17 -0.380574423 -0.204238748 H -0.204238748 - -0.464357508 SnoPH: 16 -0.491998762 -0.143026344 H -0.143026344 - -0.575224320 Hno X 0.45739613`

When the incoming multiplier gets to 5 then you actually Double Hard 17! Note Double is NOT twice the hit because of the 1x Carry Forward.
`Dealer upcard = 10 (a) Stand (b) St or Hit (c) StHitorDbl (d) StHit noCF (e) SplitPH: 21 +7.512401648 +7.512401648 S +7.512401648 - +4.365955230 SnoPH: 20 +3.836732660 +3.836732660 S +3.836732660 - +2.620486122 Sno X 4.820649916PH: 19 +2.406664280 +2.406664280 S +2.406664280 - +1.721170861 SnoPH: 18 +1.362893374 +1.362893374 S +1.362893374 - +1.052624829 Sno X 3.506180604PH: 17 +0.467861883 +0.470668612 H +0.529148385 D +0.384078798 SnoPH: 16 +0.356437545 +0.583796967 H +0.748528437 D +0.272654460 Sno X 2.804992848`

Explanation of the 3.958 is as follows:-
Basic game chances of winning with 21 is (roughly) 0.889, tie = 0.034, lose = 1/13 = 0.077 (Ten has not yet peeked so you could lose if an Ace).
Value of win is 1 (your base bet) and 3.541 (the estimated value to the next hand based on an average multiplier of x7 for this hand).
Contribution to EV is (1+3.541)*.889 then (-1)*0.077 giving 3.96.

Note: if the first hand in a split was 21 then you would stand on 17 and hit 16 (Sno,Hno) on a multiplier of 0, and on a multiplier of 5 only hit 14. The latter matches Pontoon rules where a tie loses.

As has been said the assumption I've made is the multipliers are 4-17 x2, 18 x3, 19 x4, 20 x5, 21 x7, BJ x10.
gordonm888
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November 17th, 2021 at 12:43:24 PM permalink
Charlie, why does your table indicate that you never hit a 9, and that one should only double on a 9 with a minimum multiplier of 2-4 (depending upon the dealer's card)? What strategy are you supposed to take for a 9 with no multiplier, if you can't hit or double?

Also, Wizard's table of frequency of wins with 17- to 21 cannot be correct for our purposes because he used conventional BJ strategy and wasn't hitting and doubling stiff hands vs 2-6.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
charliepatrick
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November 17th, 2021 at 12:50:04 PM permalink
The "9" and "hit" (as Opposed to "Hit") means you never hit soft 19. (I tend to use lower case for soft totals where possible, similarly "Double" and "double".) I was surprised you hit soft 18 vs 7, but think this is because with the "21" effect it is similar to hitting soft 18 vs 10 or 9 that the added value of getting to 21 is worth the risk.
ssho88
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November 17th, 2021 at 4:14:18 PM permalink
Quote: charliepatrick

Yes you hit 17 vs 10 on the basic game.

Explanation of the 3.958 is as follows:-
Basic game chances of winning with 21 is (roughly) 0.889, tie = 0.034, lose = 1/13 = 0.077 (Ten has not yet peeked so you could lose if an Ace).
Value of win is 1 (your base bet) and 3.541 (the estimated value to the next hand based on an average multiplier of x7 for this hand).
Contribution to EV is (1+3.541)*.889 then (-1)*0.077 giving 3.96.

Charlie, why value of win is 1 ? Do you assume that the current hand active multiplier is 1x? I thought average multiplier that carry forward from previous hand is more than 1x ?

Suppose the multiplier carry forward from previous hand is 3x, so if current hand is 21 vs T, then total EV = (1*3+3.541)*.889 + (-1)*0.077 = 5.74. Am I missing something ?

I try to find a strategy for a specific hand 17 vs 7,

1) 17 VS 7, current multiplier = 3, STAND, total EV = 0.4105 + 0.1246 = 0.5351
2) 17 VS 7, current multiplier = 4, STAND, total EV = 0.6704 + 0.1246 = 0.795
3) 17 VS 7, current multiplier = 3, DOUBLE, total EV = 0.0219 + 0.4910 = 0.5129
4) 17 VS 7, current multiplier = 4, DOUBLE, total EV = 0.5133 + 0.4910 = 1.0043

So when current multiplier <= 3, should STAND and DOUBLE when current multiplier >=4.

Last edited by: ssho88 on Nov 17, 2021
charliepatrick
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November 18th, 2021 at 1:17:47 AM permalink
I'll have a closer look at your figures later but it's necessary to calculate different strategy for hands at different multipliers to their EVs. In very simple terms the objective is to get the best multiplier and on the next hand tend to double and split to take advantage of that. Thus it is wrong to assume BJ basic strategy applies in this game since the multiplier for getting 21 is so valuable - in practice your chances of winning will be less because sometimes you're better off doubling (e.g. 2x30% is better than 1x40%) but you'll win more in the long run.

As to 21vT - the base game EV is (Win 1 unit plus 3.541) * .889 - 1/13 = 3.96 - the 5x multiplier (Win 5 units plus 3.541) *.889 - 1/13 = 7.51.

Here are my figures for a 2x hand (note this does not show the lower value for doubling as the objective here is to keep the best decision's EV)..
`Dealer upcard = 7 (a) Stand (b) St or Hit (c) StHitorDbl (d) StHit noCF (e) Split (Multiplier in=2)PH: 21 +5.130557606 +5.130557606 S +5.130557606 - +1.851852592 SnoPH: 20 +3.506620029 +3.506620029 S +3.506620029 - +1.620528157 Sno -PH: 19 +2.596084752 +2.596084752 S +2.596084752 - +1.384652061 SnoPH: 18 +1.635445349 +1.635445349 S +1.635445349 - +1.030432769 Sno X 3.293968178PH: 17 +0.259116820 +0.297592903 H +0.297592903 - +0.155503419 SnoPH: 16 -0.109449374 +0.397407741 H +0.397407741 - -0.150540846 Hno X 2.628678798`

and 3x hand
`Dealer upcard = 7 (a) Stand (b) St or Hit (c) StHitorDbl (d) StHit noCF (e) Split (Multiplier in=3)PH: 21 +6.056483902 +6.056483902 S +6.056483902 - +2.777778888 SnoPH: 20 +4.353920959 +4.353920959 S +4.353920959 - +2.467829088 Sno -PH: 19 +3.364760317 +3.364760317 S +3.364760317 - +2.153327626 SnoPH: 18 +2.266323951 +2.266323951 S +2.266323951 - +1.661311372 Sno X 4.359175248PH: 17 +0.521429229 +0.541653010 H +0.546287392 D +0.417815827 SnoPH: 16 +0.152863035 +0.660241703 H +0.772383166 D +0.113697139 Hno X 3.588587172`
charliepatrick
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November 18th, 2021 at 3:13:43 AM permalink
Quote: charliepatrick

...previous picture of strategy...

I may have to revisit this for a few cases, as with some larger multipliers as you don't always hit 17 and where you don't just double everything this might change things. An example is starting with 5 vs 9 at 10x, where you would stand on 17. Similarly you stand (if you can't double) on 17 vs 10 with multiplier of 6x or greater. At very high multipliers you stand even earlier (e.g. 16 vs 10 at x15 stands); this could only apply to a split hand (as most non-split hands double).
I had made a mistake with the Hitting logic (as I had to reverse it from looking to when you do to when you don't!) Also with doubles it assumed if you doubled 17 then you also doubled 7!
ssho88
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November 18th, 2021 at 4:13:38 AM permalink
I think my results for STAND is quite close to yours :-

a) 17 vs 7, 2x multiplier, STAND, your results is 0.2591, my results = 0.1506 + 0.1246 = 0.2752
b) 17 vs 7, 3x multiplier, STAND, your results is 0.5214, my results = 0.4105 + 0.1246 = 0.5351

What is your results for DOUBLE ?

c) 17 vs 7, 2x multiplier, DOUBLE, your results = ?, my results = -0.4694 + 0.4912 = 0.0218
d) 17 vs 7, 3x multiplier, DOUBLE, your results = ?, my results = 0.0219 + 0.4912 = 0.5131
e) 17 vs 7, 4x multiplier, DOUBLE, your results = ?, my results = 0.5133 + 0.4912 = 1.0045
f) 17 vs 7, 5x multiplier, DOUBLE, your results = ?, my results = 1.0046 + 0.4912 = 1.4958
charliepatrick
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November 18th, 2021 at 7:49:23 AM permalink
If you compare the results to https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/ you'll see that with 17 vs 7.
(i) Win = 26.23%, Tie = 36.86%, Lose = 36.91%. This matches up with the base EVs of -0.1068 for 17 and -0.4754 for 16.
If you're on x2 then you can add 0.2623 to this (as when you win you get an extra \$1), giving 0.1555. Similarly for x3 0.4178.
You'll see these figures in my column 4 (which ignores any Carry Forward).

The value I'm using for the Carry Forward on a x2 would be (say, as it's an estimate at this stage) 0.395, and this has to be multiplied by the Pr(win) = 0.2623*0.395=0.1036. This is how I get 0.2591 for standing on x2.

I'm happy to be corrected on the value of the Carry Forward, but at this stage I don't think we really know the exact value. All I know is my value is lower than reality due to the way I'm handling splitting decisions; so if you're saying it's 0.4750 I wouldn't disagree.
charliepatrick
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November 18th, 2021 at 1:30:42 PM permalink
I'm going away tomorrow so here's where I'm at. I looked at "second" hands where the first hand had (i) Bust (ii) 4-17 (iii) 18 (iv) 19 (v) 20 (vi) 21. This meant there were different incentives (i.e. the difference between what's already got and the possible benefit of a better multiplier). In most cases you hit less but, occasionally, you hit soft 9 (or 8) where a low multiplier had already been obtained.
For the base hand
`D: 1 Spl: A89     H: 17 (17 17 17 17 17 16) h: 8 (8 8 8 8 8 8) D: d:D: 2 Spl: A23789  H: 16 (16 17 16 15 14 12) h: 8 (8 8 8 8 8 7) D: D11 D10 d:D: 3 Spl: A23789  H: 16 (16 16 16 15 13 12) h: 8 (8 8 8 8 8 7) D: D11 D10 d:D: 4 Spl: A236789 H: 16 (16 16 16 14 13 11) h: 8 (8 8 8 8 8 7) D: D11 D10 d: d8D: 5 Spl: A236789 H: 16 (16 16 16 14 13 11) h: 8 (8 8 8 8 8 7) D: D11 D10 d: d8D: 6 Spl: A236789 H: 16 (16 16 16 14 13 11) h: 8 (8 8 8 8 8 7) D: D11 D10 d: d8 d7D: 7 Spl: A23789  H: 17 (17 17 16 16 16 16) h: 8 (8 8 8 8 7 7) D: d:D: 8 Spl: A23789  H: 17 (17 17 17 17 16 16) h: 8 (8 8 8 8 8 7) D: d:D: 9 Spl: A89     H: 17 (17 17 17 17 16 16) h: 8 (8 8 8 8 8 8) D: d:D: X Spl: A89     H: 17 (17 17 17 17 16 16) h: 8 (8 8 9 9 8 8) D: d:`
Multiplier for this hand is x2
`D: 1 Spl: A2346789 H: 17 (17 17 17 17 17 16) h: 8 (8 8 8 8 8 8) D: D11 D10 d:D: 2 Spl: A2346789 H: 16 (16 16 15 14 13 12) h: 8 (8 8 8 8 8 7) D: D12 D11 D10 D9 d: d9 d8 d7 d6 d5 d4D: 3 Spl: A2346789 H: 16 (16 16 15 14 13 12) h: 8 (8 8 8 8 8 7) D: D13 D12 D11 D10 D9 D8 d: d9 d8 d7 d6 d5 d4 d3D: 4 Spl: A2346789 H: 15 (15 16 14 13 12 11) h: 8 (8 8 8 8 8 7) D: D13 D12 D11 D10 D9 D8 d: d9 d8 d7 d6 d5 d4 d3D: 5 Spl: A2346789 H: 15 (15 15 14 13 12 11) h: 8 (8 8 8 8 8 7) D: D13 D12 D11 D10 D9 D8 d: d9 d8 d7 d6 d5 d4 d3D: 6 Spl: A2346789 H: 15 (15 15 14 13 12 11) h: 8 (8 8 8 8 7 7) D: D14 D13 D12 D11 D10 D9 D8 d: d9 d8 d7 d6 d5 d4 d3D: 7 Spl: A2346789 H: 17 (17 17 16 16 16 16) h: 7 (7 8 8 7 7 7) D: D11 D10 D9 d: d8 d7D: 8 Spl: A2346789 H: 17 (17 17 17 17 16 16) h: 8 (8 8 8 8 8 7) D: D11 D10 d: d8D: 9 Spl: A2346789 H: 17 (17 17 17 17 16 16) h: 8 (8 8 8 8 8 8) D: D11 D10 d:D: X Spl: A234789  H: 17 (17 17 17 16 16 15) h: 8 (8 8 8 9 8 8) D: D11 D10 d:`
Multiplier for this hand is x5
`D: 1 Spl: A2346789  H: 17 (17 17 17 17 17 17) h: 8 (8 8 8 8 8 8) D: D17 D16 D15 D14 D13 D12 D11 D10 D9 d: d9 d8 d7 d6 d5D: 2 Spl: A2346789X H: 14 (14 14 13 13 12 12) h: 8 (8 8 8 8 8 7) D: D16 D15 D14 D13 D12 D11 D10 D9 D8 D7 D6 D5 D4 D3 D2 d: d10 d9 d8 d7 d6 d5 d4 d3D: 3 Spl: A2346789X H: 13 (13 14 13 12 12 11) h: 8 (8 8 8 8 8 7) D: D16 D15 D14 D13 D12 D11 D10 D9 D8 D7 D6 D5 D4 D3 D2 d: d10 d9 d8 d7 d6 d5 d4 d3D: 4 Spl: A2346789X H: 13 (13 13 13 12 11 11) h: 8 (8 8 8 8 8 7) D: D16 D15 D14 D13 D12 D11 D10 D9 D8 D7 D6 D5 D4 D3 D2 d: d10 d9 d8 d7 d6 d5 d4 d3D: 5 Spl: A2346789X H: 13 (13 13 12 12 11 11) h: 8 (8 8 8 8 8 7) D: D15 D14 D13 D12 D11 D10 D9 D8 D7 D6 D5 D4 D3 D2 D1 d: d10 d9 d8 d7 d6 d5 d4 d3D: 6 Spl: A2346789X H: 13 (13 13 12 12 11 11) h: 7 (7 7 8 7 7 7) 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 d3D: 7 Spl: A2346789X H: 16 (16 16 16 16 16 16) h: 7 (7 7 7 7 7 7) D: D17 D16 D15 D14 D13 D12 D11 D10 D9 D8 d: d9 d8 d7 d6 d5 d4 d3D: 8 Spl: A2346789  H: 17 (17 17 17 16 16 16) h: 8 (8 8 8 8 8 8) D: D17 D16 D15 D14 D13 D12 D11 D10 D9 D8 d: d9 d8 d7 d6 d5 d4 d3D: 9 Spl: A2346789  H: 17 (17 17 17 16 16 15) h: 8 (8 8 8 8 8 8) D: D17 D16 D15 D14 D13 D12 D11 D10 D9 D8 d: d9 d8 d7 d6 d5 d4 d3D: X Spl: A2346789X H: 17 (17 17 16 16 15 14) h: 8 (8 8 8 8 8 8) D: D17 D16 D15 D14 D13 D12 D11 D10 D9 D8 d: d9 d8 d7 d6 d5 d4 d3`
Last edited by: charliepatrick on Nov 18, 2021
NeilLCC
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November 19th, 2021 at 3:23:29 AM permalink
Quote: Wizard

It's very misleading! I wish I had a contact at Live Casino Comparer, because that is a good site, but they are misleading their followers with that basic strategy.

Hi,

What a great thread this is turning out to be, I've learnt so much reading through it - you guys certainly know your stuff, way above anything I could come up with.

I'm certainly not in the game of wanting to mislead anyone, certainly not visitors to my site. If you've read any of my content I like to say how it is, not make promises and never suggest you can win big or even win. My advice is generally around maintaining your bankroll for as long as you can and you may pick up the odd in profit session.

That being said if any parts of the Lighting Blackjack page are incorrect or misleading I'm happy to change the content to reflect current thinking.

At the time I played the game, in its first few days, I just couldn't see how'd you win in the long term, and could only recommend playing basic strategy, in lieu of anything else.

Is the thread at the point where there are some succinct recommendations we should make to players who want to try and play this game?

Best Regards
Neil
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billryan
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November 19th, 2021 at 5:01:22 AM permalink
Thanks for coming by. I hope you enjoy your time here.
The difference between fiction and reality is that fiction is supposed to make sense.
Mission146
• Posts: 16832
Joined: May 15, 2012
November 19th, 2021 at 6:15:47 AM permalink
Quote: NeilLCC

Quote: Wizard

It's very misleading! I wish I had a contact at Live Casino Comparer, because that is a good site, but they are misleading their followers with that basic strategy.

Hi,

What a great thread this is turning out to be, I've learnt so much reading through it - you guys certainly know your stuff, way above anything I could come up with.

I'm certainly not in the game of wanting to mislead anyone, certainly not visitors to my site. If you've read any of my content I like to say how it is, not make promises and never suggest you can win big or even win. My advice is generally around maintaining your bankroll for as long as you can and you may pick up the odd in profit session.

That being said if any parts of the Lighting Blackjack page are incorrect or misleading I'm happy to change the content to reflect current thinking.

At the time I played the game, in its first few days, I just couldn't see how'd you win in the long term, and could only recommend playing basic strategy, in lieu of anything else.

Is the thread at the point where there are some succinct recommendations we should make to players who want to try and play this game?

Best Regards
Neil

NeilLCC,

Welcome to WoV, hopefully you'll stop in from time to time even after these guys get this game figured out! As far as this question goes:

Quote:

Is the thread at the point where there are some succinct recommendations we should make to players who want to try and play this game?

The recommendation in my article was flatly don't play this game.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Wizard
• Posts: 26842
Joined: Oct 14, 2009
November 19th, 2021 at 6:20:12 AM permalink
Quote: NeilLCC

What a great thread this is turning out to be, I've learnt so much reading through it - you guys certainly know your stuff, way above anything I could come up with.

I'm certainly not in the game of wanting to mislead anyone, certainly not visitors to my site. If you've read any of my content I like to say how it is, not make promises and never suggest you can win big or even win. My advice is generally around maintaining your bankroll for as long as you can and you may pick up the odd in profit session.

That being said if any parts of the Lighting Blackjack page are incorrect or misleading I'm happy to change the content to reflect current thinking.

At the time I played the game, in its first few days, I just couldn't see how'd you win in the long term, and could only recommend playing basic strategy, in lieu of anything else.

Is the thread at the point where there are some succinct recommendations we should make to players who want to try and play this game?

Best Regards
Neil

Hi Neil. Thank you for coming by. Let me start by saying that I'm a big fan of your videos and they have helped with my work many times. If you're ever in Vegas, it would be my honor to buy you lunch or dinner.

As to Lightning, here is what it says at Live Casino Comparer (LCC):

This strategy is not appropriate for this game. Players using it will face a house edge of 17.6%. The actual strategy needs to consider the multiplier for the current hand. We're actively discussing such strategy here and have some great minds on it.

I would recommend you remove that table from the site. I do not have one one at Wizard of Odds yet.

While I have you, do you have more data on the multipliers, other than the 19 hands in your video?

Again, thanks for coming by. I hope you'll stick around. Finally, sorry if my words you quoted were a bit harsh.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
NeilLCC
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November 19th, 2021 at 6:28:14 AM permalink
Quote: Wizard

Hi Neil. Thank you for coming by. Let me start by saying that I'm a big fan of your videos and they have helped with my work many times. If you're ever in Vegas, it would be my honor to buy you lunch or dinner.

While I have you, do you have more data on the multipliers, other than the 19 hands in your video?

Again, thanks for coming by. I hope you'll stick around. Finally, sorry if my words you quoted were a bit harsh.

What a shame, I was in Las Vegas all last week - I'll be back at the beginning of October next year for G2E.

What data do you need? I don't have any at hand, but can certainly collect some for you or even try and get answers from my contacts at Evolution.

I really don't mind feedback, as long as it's constructive, which in this instance it is. I'll drop the table for now and update the content with the revised RTP, and add a similar recommendation until we know more about how to play the game.
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Wizard
• Posts: 26842
Joined: Oct 14, 2009
November 19th, 2021 at 3:17:29 PM permalink
Quote: NeilLCC

What a shame, I was in Las Vegas all last week - I'll be back at the beginning of October next year for G2E.

Let's plan on meeting for G2E 2022 then.

Quote:

What data do you need? I don't have any at hand, but can certainly collect some for you or even try and get answers from my contacts at Evolution.

I am trying to get more data to determine the average multiplier for any given win. Maybe Evolution will just tell you, but I've find them to be very secretive about such things.

Quote:

I really don't mind feedback, as long as it's constructive, which in this instance it is. I'll drop the table for now and update the content with the revised RTP, and add a similar recommendation until we know more about how to play the game.

Thank you for making those changes. If you ever feel anything is in error on the Wizard sites, please let me know. I'll PM you my best Email address.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
gordonm888
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November 19th, 2021 at 6:02:30 PM permalink
Quote: Wizard

-snip-
I am trying to get more data to determine the average multiplier for any given win. Maybe Evolution will just tell you, but I've find them to be very secretive about such things.

I imagine any information about the multipliers will be helpful, but we really should be looking for the frequency distribution of multipliers for each win with a total of 18-21 and not the average multiplier for a win with 18-21.

The reason is that as the mutlipliers increase so too does the frequency of doubling and splitting, with the result that the benefit of a multiplier does not scale linearly with the size of a multiplier.

So, if the game provides a multiplier of 2 fifty percent of the time and a multiplier of 3 the other 50% of the time, one does not calculate the correct benefit, or implied EV of the following hand, by assuming an average value of 2.5. I'm not claiming its a terrible approximation to do the calculation that way, but its not correct.
Last edited by: gordonm888 on Nov 20, 2021
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
Wizard
• Posts: 26842
Joined: Oct 14, 2009
November 19th, 2021 at 6:55:09 PM permalink
Quote: gordonm888

I imagine any information about the multipliers will be helpful, but we really should be looking for the frequency distribution of multipliers for each win with a total of 18-21 and not the average multiplier for a win with 18-21.

Good point. I agree.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
JDawG888
• Posts: 3
Joined: Nov 20, 2021
November 20th, 2021 at 3:31:32 PM permalink
Hi guys,

New here, came across this forum and the Wizard's websites.. words cannot describe how useful it has been for me.

Having read this thread, I noticed that there seems to be uncertainty as to how multipliers are paid out on BJs. I hope the attached image helps clarify this:

imgur.com/a/p6tvWvl

Thanks!

J
Last edited by: unnamed administrator on Nov 20, 2021
Dieter
• Posts: 5788
Joined: Jul 23, 2014
November 20th, 2021 at 4:17:21 PM permalink
Jdawg, Welcome.

Tried to approve your image link, but it doesn't seem to be compatible for inclusion in the forum.

https://imgur.com/a/p6tvWvl

It does appear to have some information about Lightning Blackjack, if someone else cares to investigate.
May the cards fall in your favor.
JDawG888
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November 20th, 2021 at 5:19:19 PM permalink
Thanks Dieter.

Yep its the game history for one of the hands where I got blackjack and outlines the payout structure with x2 multiplier from previous hand.

Basically from what I can see, only the original bet of \$1 qualified for the multiplier (which is how much I wagered in the previous hand), and the main bet of \$2 qualified for the 3:2 blackjack payout (as I increased current bet to \$3 from previous hand of \$1)
LC1
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November 21st, 2021 at 8:52:12 AM permalink
Hi,

I discovered this game a couple of days ago, and, not for the first time, a thought process of "I wonder if the Wizard has anything on this?" took me to a helpful page, with a link to a thread here.

I've been motivated to sign up on this occasion because it looks as though no one has noticed that 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'.]

Presumably, this strategy is the one that equates to their quoted house edge. They break the multipliers down into six possible groupings. The only information that is missing is whether those six groupings occur with equal frequency, (It seems like that might be the case.)

Apologies if this has in fact been mentioned already. The thread is growing faster than I can keep up with it! :-)
Mission146
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November 21st, 2021 at 9:03:21 AM permalink
That's beautiful---thank you!!!

Anyone who is capable of it (not me) can just order a simulation to follow that strategy and see what happens.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
LC1
• Posts: 14
Joined: Nov 21, 2021
November 21st, 2021 at 9:17:37 AM permalink
Quote: Mission146

That's beautiful---thank you!!!

You're welcome

Quote: Mission146

Anyone who is capable of it (not me) can just order a simulation to follow that strategy and see what happens.

Assuming the six multiplier groups are equally likely, yes. If not, it will be slightly more complicated.
Mission146
• Posts: 16832
Joined: May 15, 2012
November 21st, 2021 at 9:25:27 AM permalink
Quote: LC1

Quote: Mission146

That's beautiful---thank you!!!

You're welcome

Quote: Mission146

Anyone who is capable of it (not me) can just order a simulation to follow that strategy and see what happens.

Assuming the six multiplier groups are equally likely, yes. If not, it will be slightly more complicated.

Right, but I just meant to get the House Edge assuming their published strategy is followed.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
LC1
• Posts: 14
Joined: Nov 21, 2021
November 21st, 2021 at 9:32:26 AM permalink
Quote: Mission146

Right, but I just meant to get the House Edge assuming their published strategy is followed.

You cannot get the house edge unless you know the frequencies of the multipliers. The higher the average multiplier, the lower the house edge.

We can start by assuming each group has a 1/6 chance, and see if that gives the quoted house edge. If not, it might be necessary to sample a large number of rounds to determine the actual frequencies.
Mission146
• Posts: 16832
Joined: May 15, 2012
November 21st, 2021 at 9:34:50 AM permalink
Quote: LC1

Quote: Mission146

Quote: LC1

Quote: Mission146

That's beautiful---thank you!!!

You're welcome

Quote: Mission146

Anyone who is capable of it (not me) can just order a simulation to follow that strategy and see what happens.

Assuming the six multiplier groups are equally likely, yes. If not, it will be slightly more complicated.

Right, but I just meant to get the House Edge assuming their published strategy is followed.

You cannot get the house edge unless you know the frequencies of the multipliers. The higher the average multiplier, the lower the house edge.

We can start by assuming each group has a 1/6 chance, and see if that gives the quoted house edge. If not, it might be necessary to sample a large number of rounds to determine the actual frequencies.

I think I was talking past you---and I apologize for that. To be more clear, I meant that we could see what return is yielded by their strategy that they provide...not what the HE would be with perfect strategy.

EDIT: Never mind, I see what you mean. I'm sorry. I'm trying to do too many things at once and long ago gave up on this game as being a terrible game for recreational players. I'd be curious as to the counting aspect, but am not spending any time on that as I don't have access to this game anyway.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
LC1
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November 21st, 2021 at 9:38:16 AM permalink
We can't, unless we know the frequencies.

The frequencies to use are a part of the simulation. Different frequencies will yield different answers.
gordonm888
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November 21st, 2021 at 9:58:09 AM permalink
Having a correct optimal strategy as a function of the size of the active multiplier is what we were basically try to achieve. If they give us that, and we can reproduce it here and in the WOO site, then we will have achieved our basic goal.

The issue of frequency of multipliers is only important if we want to achieve any of these goals:

1. independent confirmation of the house edge

2. evaluate the game against other criteria, e.g., volatility, or issues with casinos reporting large payouts to the IRS

3. study the game design to learn from it

4. evaluation of the published optimal strategy to see if we can identify an even better strategy
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
gordonm888
• Posts: 5264
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November 21st, 2021 at 9:58:10 AM permalink
Having a correct optimal strategy as a function of the size of the active multiplier is what we were basically try to achieve. If they give us that, and we can reproduce it here and in the WOO site, then we will have achieved our basic goal.

The issue of frequency of multipliers is only important if we want to achieve any of these goals:

1. independent confirmation of the house edge

2. develop a simpler basic strategy that is easier to memorize and that gives up only a very small amount of EV.

3 evaluate the game against other criteria, e.g., volatility, or issues with casinos reporting large payouts to the IRS

4. study the game design to learn from it

5. evaluation of the published optimal strategy to see if we can identify an even better strategy
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
NeilLCC
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November 21st, 2021 at 11:51:47 AM permalink
I think it unlikely Evolution could or would reveal more than they already have.
The multipliers are meant to be selected randomly, anything else could be considered manipulation, unless of course they publish the frequency, which they haven't.
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LC1
• Posts: 14
Joined: Nov 21, 2021
November 21st, 2021 at 12:13:02 PM permalink
Quote: NeilLCC

I think it unlikely Evolution could or would reveal more than they already have.
The multipliers are meant to be selected randomly, anything else could be considered manipulation, unless of course they publish the frequency, which they haven't.

As I mentioned, the multipliers apparently only occur in six possible combinations. The implication seems to be that these are all equally probable, but that is not entirely clear.
LC1
• Posts: 14
Joined: Nov 21, 2021
November 21st, 2021 at 12:41:22 PM permalink
Quote: gordonm888

Having a correct optimal strategy as a function of the size of the active multiplier is what we were basically try to achieve. If they give us that, and we can reproduce it here and in the WOO site, then we will have achieved our basic goal.

The issue of frequency of multipliers is only important if we want to achieve any of these goals:

1. independent confirmation of the house edge

2. evaluate the game against other criteria, e.g., volatility, or issues with casinos reporting large payouts to the IRS

3. study the game design to learn from it

4. evaluation of the published optimal strategy to see if we can identify an even better strategy

I confess some of the complexities have been giving me a headache. I need to look through this thread in detail to get a better understanding. I've been unclear in my own mind whether the optimal strategy is purely a function of the current multiplier, or whether the frequencies are also a factor. [Given that a higher frequency of the bigger multipliers for high totals will cause you to be more likely to aggressively hit the next hand, chasing such a multiplier, and thus will make the win percentage on each hand lower, meaning the value of carrying forward a multiplier from the current hand is reduced accordingly.]

I'm not sure how much sense the above makes, and apologies if it seems like rambling. :-)
OnceDear
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November 21st, 2021 at 1:47:14 PM permalink
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'.]

BRILLIANTLY WELL SPOTTED

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
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
charliepatrick
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November 21st, 2021 at 1:55:05 PM permalink
The optimal strategy will be a function of both the incoming multiplier and the set of multipliers for the next hand. Knowing the distribution of the ratios will give an idea of the former, there may be some recursion needed, but unless there are multiple minimums it will give the strategy and house edge. It would be great if someone could copy their strategies here.
Thanks for the above post which crossed with mine.
OnceDear
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November 21st, 2021 at 2:01:26 PM permalink
Quote: charliepatrick

The optimal strategy will be a function of both the incoming multiplier and the set of multipliers for the next hand. Knowing the distribution of the ratios will give an idea of the former, there may be some recursion needed, but unless there are multiple minimums it will give the strategy and house edge. It would be great if someone could copy their strategies here.

To copy Evolution's strategy here would infringe copyright. But here's a link
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
charliepatrick
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November 21st, 2021 at 2:14:41 PM permalink
Quote:

To copy Evolution's strategy here would infringe copyright. But here's a link

I agree - when I get back off holiday it will be easy for me to plug in the various factors and see, as an exercise, how close infinite decks gets to their strategies - the difficulty will be working out how often you get the various multipliers into the next hand; i.e. how often the player gets 17, 18, etc.
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November 21st, 2021 at 2:23:10 PM permalink
Protect it

Fees
I’d rather have to be a lucky player than good one.
gordonm888
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November 21st, 2021 at 8:08:41 PM permalink
I have done some spot sampling of Evolution's posted strategy table on Lightning BJ.

1. I found it confusing.

2. It is not formatted in a way that is useable for 99% of humans on Earth; it is far too massive and complex.

3. It does seem to recommend Doubling Down on unconventional hands such as (12-17) and (5-8) when you have a large enoughg multiplier active, so we have that aspect of it correct.

4. It calls for splitting everything but 5-5 with most multipliers. It calls for splitting TT versus 2-7 starting with a multiplier of 2!
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
billryan