mwebb
mwebb
Joined: Oct 15, 2015
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October 15th, 2015 at 9:20:40 PM permalink
Sorry if this BJ variant question belongs in another forum, but I was just curious about the math behind the Pot of Gold side bet for Free Bet BJ as the current Wizard page on the game has no information on it.

For those not familiar, the PoG pays out based on the number of free bet lammers that a player collects during the round. So the calculation would be the odds of receiving either a free splittable pair (all but 10 rank cards) or a stiff 9-10-11 (hands involving Aces not being countable as "stiff" for this purpose; though some houses do allow for this, none that I have heard of that offer PoG do).

The side bet comes with 2 pay tables:

Table 1:

Free Bet Lammers Collected / Pays:
7: 1,000:1
6: 300:1
5: 100:1
4: 60:1
3: 30:1
2: 10:1
1: 3:1

Table 2:
5-7: 100:1
4: 50:1
3: 30:1
2: 12:1
1: 3:1

If anyone can help with the math on this it would be helpful to me.

Also: if you can tweak the dials:
- How is the bet affected by no resplitting Aces?
- How does the number of decks affect this wager? (FWIW: 6 decks is what I would be interested in looking at).
- How would a continuous shuffler affect the math?

Thanks to anyone who can crunch these numbers!
Wizardofnothing
Wizardofnothing
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October 15th, 2015 at 9:24:57 PM permalink
When you say in a round you mean per hand amongst all players at the table?
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mwebb
mwebb
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October 15th, 2015 at 11:07:01 PM permalink
The Pot of Gold wager is attached to each betting spot and counts the free bets accrued at that spot only. That's why it maxes out at 7, as with max split up to 4 hands (so 3 free bets) with a max double on each of the 4 spots in that case (4 more free bets, total = 7).
Wizard
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Wizard
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November 9th, 2015 at 6:07:35 AM permalink
Link to Free Bet BJ rules, including Pots of Gold in Washington.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Paradigm
Paradigm
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November 9th, 2015 at 8:41:59 AM permalink
Has anyone seen Pot of Gold at a casino? I think it is a great addition to Free Bet, but have not seen in placed anywhere yet.
Wizardofnothing
Wizardofnothing
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November 9th, 2015 at 8:47:55 AM permalink
It was in Washington, however I don't think it's remotely attractive as side bets go, I'm not the math expert but to get seven free bets .... I don't think I have ever been dealt 4 splits with four double, would love to know the odds - I've never gotten it in regular blackjack let alone even more then 3 of them playing greener- especially given the limited double rules like no soft doubles would make it even harder.
It's almost mythical like this casino that offers 100 dollars on any seven card Charlie as a bonus bet - I think they have paid out one TOTAL IN THE LAST 6 months
No longer hiring, donít ask because I wonít hire you either
Paradigm
Paradigm
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November 9th, 2015 at 9:11:45 AM permalink
Where in WA? I will be back up there in early December and will check it out if it is located in I-5 corridor.
Wizard
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Wizard
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November 11th, 2015 at 5:25:06 PM permalink
I just wrote up an analysis of the Pot of Gold side bet. Bottom line is a house edge of 5.76% or 4.64% depending on the pay table, assuming six decks. For a side bet, that is not bad.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
richodude
richodude
Joined: Jul 29, 2022
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February 11th, 2023 at 1:45:24 AM permalink
Quote: Wizard

I just wrote up an analysis of the Pot of Gold side bet. Bottom line is a house edge of 5.76% or 4.64% depending on the pay table, assuming six decks. For a side bet, that is not bad.
link to original post



I think this bet is exploitable. My crude math shows just 3 tens missing from a fresh shoe makes the side bet advantageous. This is pencil and paper work and Iím not sure how close I am. I canít figure out cvdata either. My casino uses pay table 2 with $1-10 and $5 min for main bet. All standard rules too

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