Every week someone rediscovers doubling after a loss and thinks they solved roulette.

Here is the actual ledger.

European roulette, even money, $10 unit, double after every loss until you win.

The "win" after a 6-loss streak is $10. The money you put at risk to get it is $10 + 20 + 40 + 80 + 160 + 320 + 640 = $1,270.

Probability of 7 reds (or blacks) in a row on a 37-pocket wheel is not mystical. Each spin is 18/37 to hit your color. The table max is built so that streak hits you before you recoup.

Expected value per spin does not care about your betting pattern. EV on even money is −2.70% of whatever you put out. Martingale just correlates your bets: many small wins, one session-ending loss.

If you want a number that actually moves: play European not American (2.70% vs 5.26%), skip the 00 wheel, and never bet a system that requires the table to not have a max.

Math first. Then the table.

People treat blackjack like a streak game. It isn't. Over a night, four spots leak the money:

Standing on 12–16 when the dealer shows 7 through ace. You feel "safe." The dealer is making a hand more often than not. Hit.

Hitting 12–16 when the dealer shows 2–6. Now you're busting so the dealer doesn't have to.

Splitting 10s because "two 20s would be nice." You already have 20. Leave it.

Taking insurance every time you have blackjack. Insurance is a separate bet with a house edge around 7%. Your 21 does not make that bet smarter.

If you only fix those four, you are playing closer to basic strategy than 90% of the table — without a chart on your phone.

That's the whole Simple Blackjack product. Four rules. One bankroll cap. $7. Not counting, not a 20-lesson course.

Most people pick a blackjack table by minimum bet. That is the wrong number.

A $10 table that pays 6:5 on blackjack costs you about 1.4% extra versus a 3:2 table with the same rules. On $500 of action that is seven dollars in extra expected loss — before you make a single strategy mistake. The $25 3:2 table is often the cheaper game.

House edge is a function of rules, not of how friendly the pit looks.

Before you sit, check five things:

• Blackjack pays 3:2, not 6:5

• Dealer stands on soft 17 if you can find it

• Double after split is allowed

• How many decks

• Whether late surrender exists

If you cannot name those five, you do not know the edge you are paying. You are guessing.

Basic strategy exists because every hit, stand, double, and split has an expected value. The chart is not a superstition. It is the higher-EV action for that total versus that upcard. Play without it and a 0.5% game becomes a 2% donation.

I wrote a full blackjack-only course on this — EV for each decision, why insurance is a 2:1 bet that is not fair off the top, and how a true count actually changes the remaining shoe. It sits next to the broader Casino Math Course if you want every table game.

If you only take one thing: leave 6:5 felt. The rest of the math is easier when you stop lighting 1.4% on fire before the first hand.

People still sell "double after a loss until you win" as a system. Here is why it is mathematically dead.

Take American roulette, even money, house edge −5.26%. Each spin is independent. Changing the bet size does not change the sign of EV. It only changes the shape of your results: a pile of small wins, then one loss that is larger than all of them combined.

Work a 7-step Martingale on $10 units:

• Sequence: $10, $20, $40, $80, $160, $320, $640

• Total risked if you lose all 7: $1,270

• Win at any step: profit = $10

• P(lose 7 even-money spins on a 38-pocket wheel) is (20/38)^7 ≈ 1.1%

So about 1 in 90 sessions, you are down $1,270 to make $10 the other 89 times. Table max usually stops you before step 7 anyway. Then you cannot "get it back."

Same logic on baccarat and red/black. If the trial is −EV, progressive sizing is still −EV. The only number that matters is expected value of the bet, not the story you tell after a win streak.

If you want the actual formulas (EV, house edge, blackjack basic strategy, pot odds, bankroll), I put them in the Casino Math Course.

If you can't tell me the implied probability of -137 in five seconds, you're guessing.

American odds are just a price. Convert them:

• Negative odds: implied % = odds / (odds + 100)

• -137 → 137 / 237 ≈ 57.8%

If your true probability is higher than that number, you have +EV. If it isn't, walk.

That's one page of the Betting Math Guide. The rest covers EV, Kelly-style sizing, and why parlays are usually a tax.

Pay once. Download the PDF. Use it on the next card.