Doubts about Free Bet Blackjack Math

Hi everyone,
Recently, I’ve been studying Free Bet Blackjack and analyzing some data from the wizard website. According to Wizard's standard rules and basic strategy (which aligns with my own strategy validation), I found the house edge to be 1.01%, which slightly differs from (and is actually lower than) the 1.04% listed on the website. I suspect that unspecified rule details on the website might include: there is a hole card and the dealer peeks for blackjack (my assumption), and the rule that split Aces can receive only one additional card(but splits up to 4 hands).

Furthermore, a simple verification shows a discrepancy: both my simulation and theoretical calculations yield a probability of 0.838228071 for "0 tokens" in the Pot of Gold side bet (calculated by determining the probabilities for dealer blackjack and non-FD/FP hands). This is a notable gap from Wizard's random simulation result of 0.833420. Has anyone else researched this? Could this be due to rule inconsistencies or potential errors in my calculations?
Here are my simulation results for reference

Game Nums 1,000,000,000
Total Real Bets 1,005,037,723.00
Total Free Bets 186,178,244.00
Total Pays 994,902,597.50
RTP 98.99%
Total Hands 1,050,249,652
Real Money Hand
BlackJack Win Hands 45,320,847
Win Hands(except BJ) 270,563,448
Tie Hands 124,526,226
Loss Hands 428,347,887
Double Win Hands 2,079,509
Double Tie Hands 733,936
Double Loss Hands 1,886,768
Free Double Win Hands 54,712,746
Free Double Tie Hands 20,345,713
Free Double Loss Hands 51,820,430
Surrender Hands 0
Free Money Hand
Win Hands(except BJ) 13,555,731
Tie Hands 5,475,572
Loss Hands 21,493,626
Free Double Win Hands 4,060,884
Free Double Tie Hands 1,505,887
Free Double Loss Hands 3,820,442
Banker Push 22 Game Nums 73,535,474
Free Bet Nums
0 Free Bet 838,233,902
1 Free Bet 143,412,297
2 Free Bet 13,575,090
3 Free Bet 3,742,567
4 Free Bet 822,491
5 Free Bet 185,768
6 Free Bet 25,933
7 Free Bet 1,952

The probability of getting 7 gold coins on the side bet is about 1 in 500,000, so you'll be losing until you hit that a few times early for the 1,000 to 1 payouts.

I have just completed my precise theoretical calculations, and they are in perfect agreement with my simulation using basic strategy. The RTP of basic strategy is essentially the same as that of the perfect optimal strategy. I am confident that my calculations are correct under these rules. Wizard's results may be due to lower precision requirements, random simulation, or indeed slight differences in the rules.
Total 100.0000%
Total Bet 1.005056442
Total Profit -0.010144
Total Pay 0.994912
Rtp 98.99069%
House Way 1.00931%

I researched pot of gold a few years back for AP purposes. I was scratching my head trying to think how my lammer numbers were different. It's not too hard to work out on paper or spreadsheet the probability of a dealt 9,10,11, or pair, and making sure not to include tens or double count pair of 5s. 6 decks returns an ~83.001% chance for 0 lammers. Since the dealer has blackjack 4.75% of the time, about 0.816% of hands dont get a lammer that would have otherwise qualified. I also made a program which I'm sure is broken but chatGPT says is perfectly fine. In 100m hands off a 6 deck shoe, it spits out:
0 lammers: 0.83790823
1 lammers: 0.14405028
2 lammers: 0.01334308
3 lammers: 0.0036528
4 lammers: 0.00082783
5 lammers: 0.00018968
6 lammers: 2.619e-05
7 lammers: 1.91e-06
and a house edge of 7.3%, and free bet HE of 3.3%
or if I split 5s:
0 lammers: 0.83794116
1 lammers: 0.14185929
2 lammers: 0.01499198
3 lammers: 0.0040623
4 lammers: 0.00091141
5 lammers: 0.00020391
6 lammers: 2.793e-05
7 lammers: 2.02e-06
with a house edge of 3.9%, and free bet HE of 3.9%
this is on the 3, 12, 30, 50, 100, 100, 100 paytable. 6 decks H17

As for why yours and wizards numbers differ. I have a hard time seeing how wizards PoG number could possibly be correct. My best explanation is when there are only 2 decks, you have 4464/5356 (83.3458%) chance of no dealt qualifying free hand, which doesn't even account for dealer BJs.
For the house edge, I'd expect in a billion hands your result to be +- 0.01%. Maybe it's variance, maybe it's a slight rule difference. I'm siding with the game creator. Practically, the difference doesn't matter, but definitely frustrating if it's a real difference.

In my card removal testing, I didn't get far, but I believe for removal to have this effect on the sidebet house edge:
2,3,4,6,7: 0.65% per card removed (bad for player)
5,8: 0.25%
9: -0.13%
ten: -0.8%
Ace: -0.5%
I didn't get far enough to properly compute the main game's HE or the removal effect on the main game's HE. I'm interested to hear your findings if you are researching the same

I saw Victor (from the Slot Lady channel) playing a Free Bet game in Canada (in Ottawa, Ontario) and he didn't have to put money down on a Pot Of Gold side bet. He was given 7 lammers by the dealer when he bought-in and he could use them when he wanted according to the rules. It just gave him free splits and doubles on his original bet.
So are you saying the HE on that type of game is in the 3% to 4% range?

You get those lammers as part of the game. The side bet pays if you get those lammers, win or lose the hand. House edge on the sidebet is 7.033% according to Allen's findings. About 7.3% on my less precise sim. BUT, if you split 5s always, you sacrifice a bit of EV on the main hand to be in the ~3.9% HE range, with an added 0.3% HE to the main hand

All those pushes on 22 wreck the game. It's kind of a novelty game when you just want to try something else. With that kind of HE and long odds at 1,000:1, I shouldn't be interested. But some people value free splits and doubles over betting extra, so there's that.

I agree with your calculations and probability of 0 lammers. I doubt you have made any errors, and the original math was a tad off.