Pot of Gold

1The rules, as data

Pot of Gold rides on an ordinary Free Bet blackjack game and adds no cards and no randomness of its own.

Free Bet blackjack is Geoff Hall's variant where the house funds your splits and doubles. You can split any pair except tens for free and double hard 9, 10, or 11 for free. In exchange, a dealer 22 pushes. Each free split or free double comes with a physical button, called a coin or lammer, placed next to your bet. Pot of Gold pays by how many lammers you end the round with, win, lose, or push. Zero lammers loses the stake, and every wager loses to a dealer natural under the Nevada rules of play.

The configuration behind every number here: six decks, dealer hits soft 17, free splits to four hands (aces once, one card each), free re-splits, free doubles on hard 9/10/11 after splits. Two paytables circulate, so both get priced. This page leads with Pay Table 2 and covers the jackpot table in its own section further down.

2The published-figure gate

The machinery matches every published number that can be right, and one of them can't be.

First the boring checks. The engine matches Wizard of Odds on the main game's house edge (0.99% measured against their 1.04% for these rules), on dealer-22 frequency (7.354% against 7.3536%), and on the split-fives delta, a published number that depends on the whole resplit process: +3.080% ± 0.185 measured against +3.019% published, over ten independent runs of two million rounds each.

Then the gate turned up a problem. The chance of ending a round with zero lammers doesn't depend on strategy at all, and it has an exact closed-form answer: P(0) = 0.838228071… The published table says 0.833420, sourced to a "random simulation" with no stated method. Those two can't both be right, and one of them is an exact fraction. My simulator, run on shoes it had never seen, landed on the exact figure (z = −0.41). My best guess at what happened: the published simulation let lammers survive a dealer ten-up blackjack, which contradicts the Nevada rules-of-play filing.

What this means for someone reading the rack card: the jackpot paytable costs about 8.25% (± 0.13), and the advertised 5.77% is wrong. Splitting 5s instead of free-doubling them (a strategy explained in step five) brings it to 5.17% against the advertised 2.75%. I'm confident in the correction because the same machinery reproduces the published deltas, the numbers that don't depend on the disputed convention, to a third of a standard deviation.

3The oracle

Evaluated on the fresh shoe, the oracle prices the bet exactly: −7.07% on PT2, −8.25% on PT1. Past the fresh shoe it has to be measured, and that shapes the whole analysis.

The oracle's fresh-shoe evaluation comes in two exact pieces. The zero rung has a closed form: P(0) = 0.838228071. For the paying rungs, I recorded how often each lammer count occurred over the twenty million validation rounds. Expected value is linear in the paytable, so those frequencies price any paytable anyone prints with no new simulation, and the two circulating tables can be compared on literally the same rounds. The numbers below are the off-the-top table.

The same linearity settles which rungs matter. The 300:1 rung fires once per 39,000 rounds, and the 1000:1 once per 435,000. Together they're worth 0.72% of a unit. The 2-lammer rung fires once per 74. The jackpot rungs are decoration, and that fact runs the paytable comparison below.

One limit matters for how the rest of this page reads. Some bets get a full oracle: 21+3 and the baccarat side bets have exact EV formulas at any composition, so their human systems get scored as a percent of a true ceiling. Pot of Gold doesn't. Its mid-shoe EV depends on free-split chain dynamics with no closed form, so past the fresh shoe the oracle is measured, as the EV-by-state curve in the next step. That's why this page's capture number is scored against the best divided benchmark rather than against a perfect-play ceiling: for this bet, nobody knows the true ceiling, including me.

4The state dataset

Twenty million cut-card rounds, binned by the pre-deal hi-lo true count. The curve comes out upside down.

Small cards feed everything about the lammer distribution. Free doubles need hard 9/10/11 in two cards. Free splits need pairs below ten. The long chains that reach the upper rungs need clusters of small cards. One 5,5 split into re-pairs and free doubles can eat half a suit of low denominations in a single round. The ten-rich shoes a blackjack counter waits for are the shoes where this bet starves.

So the signal runs opposite to hi-lo (the correlation between free-double probability and hi-lo true count is −0.937), and the bet wakes up at counts a blackjack player considers garbage. The curve below is monotone and statistically overwhelming, with per-bin z up to +20. The lammer rate roughly triples across the range, and the paytable's convex payouts multiply it. The zero crossing sits between TC −1 and −2.

5The fit, and the count

The bet's own removal effects look wrong to a blackjack eye, and aren't. The fitted card is pog2, an unbalanced count whose pivot sits exactly on the trigger.

I regress side-bet profit on the per-rank composition of the remaining shoe, checked against main-game removal effects I derived separately by an independent method (agreement +0.9956). The fuel is 2 through 8: removing any one costs the side bet 6.8 to 9.2% of a unit, and the 7 weighs as much as the 3, because 7s make the free-double totals. The 9 is worth about half. Aces and tens are dead. And the best human count ignores the 5 completely, which no blackjack count in print does.

Most counts need true-count division because a running count means different things at different depths of the shoe. An unbalanced count has one exception: a single running-count value that means the same thing at every depth. Card counters call it the pivot. I searched every whole-tag count whose pivot sits exactly on the staking trigger, and the search lands on pog2. The card is below: the tags, the ideal weights they quantize, and the rules that run it. Correlation with the exact removal effects: −0.9726.

The split-5s rule on the card needs its own explanation. A pair of 5s is the only hand in the game offering a choice of free bets: it's a hard 10, so it qualifies for the free double, and it's a pair, so it qualifies for a free split. The double is the better blackjack play, and it ends the hand at one lammer. A split does more for the side bet: it makes two new hands, and each can re-pair into another free split or draw into a hard 9, 10, or 11 for a free double, every one another lammer. So while the side bet is out, split the 5s. I call it farming. Measured with paired seeds (identical shoes, the two runs differ only at the 5,5 decision), farming breaks even below a one-dollar side stake at every count against a $15 main, and it lifts the trigger window from +7.37% to +11.78% ± 0.09 per unit.

I looked at higher-order terms and didn't need them. The linear count already beats the divided hi-lo benchmark (next section), and the structure that remains, the paytable's convexity in chain length, is what the trigger-plus-farm design already collects. Other bets go the other way. 21+3 needed suit-interaction terms to reach most of its value, and War Blackjack's tie leg has no linear signal at all.

6Certified live

The literal card, replayed end to end on ten million fresh rounds per penetration.

A curve assembled from bins carries approximations, so I replayed the exact card above (start 24, stake at 12 or below, farm while out, flat main, straight Free Bet basic strategy, no insurance) on ten million fresh rounds per penetration, none of which the fit had ever seen. It staked 16.49% of rounds against a binned prediction of 16.5%. It earned +10.39% ± 0.39 per unit against a predicted +10.13% (z = +0.66). The unstaked main game came in at −0.946% against the assumed −0.95%.

Head to head on identical card streams, pog2's no-division trigger takes 106.6% of what hi-lo takes with true-count division. A pivot sitting on the decision threshold reads correctly at any depth, right where the decision happens. The Red 7 family gets the same free lunch. Move the pivot and it degrades fast. Offsetting it by 0, 2, 4, and 6 points keeps about 100%, 100%, 70%, and 35% of the value, which is also why KO's tags don't work for this job.

Depth helps twice, through more trigger windows and better ones: at a one-deck cut (penetration near 0.833) the card stakes 18.6% of rounds at +11.18% ± 0.36 per unit. The seven-lammer jackpot landed seven times in 1.65 million staked rounds, in line with the arithmetic. Farming doubles the main bet's exposure in the same rounds where lammers land, so main and side profits correlate at +0.72 units².

7The ledger

Income scales with the side stake, but the main bet toll doesn't. The posted side maximum decides the money.

The toll is the main game's negative expectation, charged every round whether the side bet is out or not. The income arrives only in the staked window and scales with the stake. So the side maximum, and whether the side bet is tied to the main wager, move the bottom line more than anything else on this page. The scenario below puts $100 on the side, which is the bet's own ceiling wherever a floor posts that maximum without tying it to the main wager. Everything else is the site's standard: shoe game, 0.75 penetration, 5% risk of ruin. Both this scenario and the jackpot table's below come from one live run of the literal card, so the two paytables are compared on the same shoes with their real main-side covariance, not an independence assumption.

8The verdict

Highly beatable, with a count a hobbyist can carry.

The count avoids division and the farm rule is easy. What varies is the room: the side maximum sets the income, the paytable sets the variance, and penetration sets both. The attention this play draws is built into it. The system puts money out at visibly bad counts and splits 5s against basic instinct, which an ordinary bet spread never does.

§The jackpot paytable

PT1 advertises 300:1 and 1000:1 and treats the player worse. The jackpot rungs almost never fire, and a workhorse rung pays for them.

Pay Table 1 reads 3 / 10 / 30 / 60 / 100 / 300 / 1000. You'd expect the jackpot rungs to matter to an attack that harvests the deep-negative tail, where the long free-split chains live. The measurement says they don't. Expected value is linear in the paytable, so the gap between the tables is just payout differences weighted by how often each lammer count occurs. The 300:1 fires once per 39,000 rounds and the 1000:1 once per 435,000, together worth 0.72% of a unit. The 2-lammer rung, which PT2 raises from 10 to 12, fires once per 74 and covers both. PT1 costs 8.25% off the top against PT2's 7.07%, and the rung table below reproduces the independently measured gap to the third decimal.

The count transfers as-is: same tags, same trigger, same farm rule, and the threshold search picks the same pivot on both tables. The bigger difference is variance. The 1000:1 rung carries most of the side bet's volatility while contributing 0.21% of a unit, so on identical shoes at the same $100 stake PT1 earns $10.60 less per hundred rounds and asks for $15.8k more bankroll, a two-thirds larger stake in the game for less money. The stingier-looking table is the better one for the player.

One note on where these numbers come from, since the two tables were measured at different times. The certification in step six ran on this paytable, which is why that section's figures are PT1's. Both scenarios on this page come from a later run that played the same literal card on both paytables, shoe for shoe, so the comparison between them is exact and neither one is assembled from parts.

§What this verdict depends on

• Six decks, H17, dealer 22 pushes, free splits to four hands (aces once), free re-splits, free doubles on hard 9/10/11 after splits. Validated against the published main-game edge. The four-hand resplit cap matters, because the farm leans on it.
• Every Pot of Gold wager loses to a dealer blackjack (the Nevada rules-of-play settlement). A floor that pays lammers through a ten-up natural is playing the convention the published table appears to assume, and every number here gets better for the player under it.
• Cut-card shoes only. A continuous shuffling machine kills this attack, like every attack.
• The scenario is written at a $100 side maximum, untied from the main wager, which is the bet's best posted form. Income scales with that maximum and the toll does not, so a smaller maximum, or a placard tying the side to the main, changes the money more than anything else on this page. Both cases are priced above.
• Both scenarios come from one live run of the literal card on both paytables, carrying the measured main-side covariance, with no independence assumption. The comparison between the tables is exact, since it runs on the same rounds card for card.

Last updated 2026-08-10.