Analyzing Casino Bets Systematically

The process

A card that leaves the shoe is information. Any bet built on the shoe can be priced from that information, and the same pipeline can do it for any game. It runs from rules to verdict in eight steps and always ends at the same three numbers: the ceiling, the capture, and the price. If you'd rather see it by a small example first, the same eight steps run on a six-card toy game where you can check every number by hand.

1. Encode the rules as data

   Every rule of the game (decks, dealer behavior, payouts, variant toggles) goes into one configuration object, and one engine plays every variant. This matters because validation carries over. The engine that reproduces standard blackjack's published numbers is the same code playing the exotic variant, so the exotic results inherit that credibility.

2. Reproduce the published figures

   Before anything new, the machinery has to match what's already known for the exact ruleset: house edge, dealer outcome frequencies, known rule-variation deltas. Every bet page carries those checks as a row of pills linking to the source they were checked against, so you can go read the published number yourself instead of taking my word for it. Sometimes this step finds something on its own. One side bet's published edge table turned out to be arithmetically impossible, and the gate caught it because part of that table has an exact closed-form answer. A check that came out that way gets a red pill and keeps its link.

3. Build the oracle

   The oracle is the bet's expected value when you know the full remaining shoe. Where the bet's structure allows it I enumerate exactly. Otherwise I compute EV from the exact composition, and simulation is the fallback. The oracle is the ceiling. Every human system that follows gets scored as a fraction of it.

4. Simulate states into a dataset

   Deal millions of shoes and record, before every round, the remaining composition and the oracle's price for it. "Is this countable" becomes a curve: expected value against what a player at the table could observe. Some of the best curves run upside down and peak at exactly the counts where a blackjack player would leave.

5. Fit a model a person can carry

   From the dataset I compute each rank's effect of removal and fit a linear count, weighted toward the states where money is actually out, then rounded to whole tags you can keep at table speed.

   Linear is the default, and it has to defend itself. I score the fit against the oracle. If the leftover error is large, or the bet's structure says per-card effects can't carry the value (payoffs on suit clustering, payoffs on cards matching each other), the model grows: interaction terms, second moments, whatever the structure calls for. One bet here needed a four-suit system to reach 78% of its ceiling after rank-only counts stalled. Another has no linear signal at all. Every single-card removal effect is exactly zero, and all of its value sits in how cards leave together.

   True-count division gets the same treatment. A count with its pivot parked on the decision threshold needs no division and reads correctly at any depth, right where the decision happens. When a play has one trigger, that construction has beaten division outright in my measurements. Plays with decisions at many thresholds are where division starts to pay for itself. Either way I measure what the no-division card captures and let that number choose, because a simpler card also means fewer mistakes, and mistakes cost real money.

6. Replay the human system live

   Then the literal card (count, trigger, playing rules) gets replayed on fresh shoes it was never fitted to, the way a person would play it. Its score is the capture fraction: the share of the oracle ceiling it keeps. Competing systems replay on identical card streams, so a difference of a few dollars per hundred rounds shows up cleanly instead of drowning in shoe noise.

7. Put dollars on it

   A real edge can still be a bad bet. The ledger states net per 100 rounds, bankroll at a stated risk of ruin, and how long it takes to clear the noise, under stated assumptions about stakes and penetration. Each page prices one example scenario, in the same format everywhere, because once beatability is settled a menu of configurations is clutter. The betting ramp belongs to the scenario too: the curve from step four is the result, any ramp can be priced from it with arithmetic, and I say what the example ramp was optimized for. This step kills more bets than any other.

8. Deliver a verdict

   Five calls are possible. Highly beatable: a system a person can carry captures a rich edge relative to the bankroll and the waiting it demands. Beatable: a carryable system captures a real edge, priced like work. Not worth it: the edge is real and the income at realistic stakes is pocket change. Not beatable: there's no composition signal to exploit. Not human-beatable: the oracle finds an edge, and no carryable system keeps enough of it to matter. The call describes the game itself. Facts that complicate the story get stated with the numbers, like a bet that turns positive and still pays less than putting the same chips on the main hand.

The bets

One page per bet, same shape every time: verdict first, then the eight steps, with the heavier math folded away where you can open it when you want it.

What this is not

This site sells nothing, and a verdict of beatable here is not a suggestion to go play. Several of these bets can be beaten on paper and then ask for a bankroll, a penetration, or a table maximum that a real floor rarely offers, and two of them turn positive while still paying less than the same chips put somewhere else. Each page prices what the game actually costs to collect.