Risk of Ruin, Computed

Risk of Ruin, Computed is part of the cash-game specialization because bankroll sizing, stake movement, ruin risk, staking, and pro cash economics changes the value of otherwise familiar no-limit hold'em decisions. The curriculum scope for this lesson is: Presents the risk-of-ruin formula for poker — RoR = e^(-2 * winrate * bankroll / variance), with winrate in bb/100, bankroll in bb, and variance as the square of standard deviation per 100 hands — and builds intuition by computing it across realistic combinations. Works through four computed cells: a 5bb/100 winner with 90bb/100 std dev at 20 buy-ins (~8% ruin), the same player at 40 buy-ins (under 1%), a 2bb/100 grinder at 40 buy-ins (the uncomfortable double-digit answer), and the sensitivity check showing that halving winrate hurts far more than doubling the roll helps. Covers the formula's assumptions (fixed winrate, no moving down, normal approximation) and why real-world discipline beats the raw number. The quiz should test plugging stated winrate/std-dev/roll values into the formula and ranking scenarios by ruin risk. That scope matters because cash games do not forgive vague strategy. A tournament player can sometimes hide behind stack-pressure shortcuts, but a cash player repeats the same spot thousands of times against a rake structure that quietly taxes every marginal mistake. The aim here is to turn the concept into an operational rule: identify the economic constraint, identify who makes the mistake, and choose the line that keeps the mistake in the opponent's range while removing it from yours.

Start with the environment. Cash poker is not one game. A 50NL online pool with 5 percent rake capped at several big blinds, a $1/$2 live game with a jackpot drop, a $5/$10 time game, and a private app game with agent credit risk all produce different correct answers before anyone sees a flop. The same hand can be a profitable defend in a low-rake heads-up pot and a disciplined fold in a high-rake multiway trap. The professional habit is to define the unit first: big blinds, straddle units, dollars per hour, hands per hour, or buy-ins at risk. Once the unit is clear, emotional labels like good game, bad beat, deep, cheap, or soft become testable claims.

The baseline range file used by this project lists 42 UTG open labels, 60 CO labels, 89 BTN labels, and 78 SB labels for 100bb 6-max cash; this lesson treats those as a starting map, not as a rule that survives every rake model, stack depth, or lineup. The practical use of that baseline is comparison. If a lesson tells you to widen, tighten, flat more, 3-bet more, or leave the table, it is always relative to that default and to the stated assumptions. Do not memorize the conclusion without the condition that produced it. Cash specialization is mostly the skill of noticing when the condition changed: the fish left, the straddle made 300bb play like 150 units, the cap made the bigger game cheaper in big blinds, or the opponent behind you turned a standard open into a reverse-implied-odds problem.

The first decision point is preflop, because preflop creates the pot that rake, position, and stack depth will act on. In clean 100bb 6-max, many marginal hands can realize enough equity to continue. In a raked cash game, that realization is not free. You need to win the pot, pay the rake, and still have enough left for the call or raise to beat folding. That is why the weakest offsuit broadways, dominated aces, small suited kings, and speculative calls out of position are the first hands removed when the game becomes expensive or the lineup becomes aggressive. They do not just lose when they miss; they also lose when they make a second-best pair and pay off.

The second decision point is stack depth. At 100bb, top pair top kicker can sometimes drive three streets in the right range configuration. At 250bb, the same hand is often a two-street hand unless the opponent is dramatically overcalling. Deep money shifts value toward hands that can make the nuts or block the nuts: suited aces, suited connectors, pocket pairs with clean set value, and broadways that can make nut straights and flushes. It shifts value away from hands that make dominated one-pair bluff-catchers. That does not mean you become passive deep. It means your aggression needs better candidates and more coherent sizing across streets.

The third decision point is seat quality. The phrase money flows clockwise is shorthand for a concrete edge: you profit when weaker players act before you and reveal their intentions. A whale on your right gives you isolation raises, thin value bets, and controlled calls. A maniac on your left taxes every open and forces you to defend wider in uncomfortable nodes. A tight regular on your left may be tolerable because they let you steal; a creative 3-bettor on your left can destroy a table that looks soft by average pot size alone. Good cash players table-select first and seat-select second, but they do both continuously.

Quantitatively, every lesson in this track uses simple checks rather than fake precision. If a bluff risks 50 into 100, the repo odds tool gives a 33.3 percent break-even fold threshold and a 66.7 percent MDF. If a call is 10 into a final pot of 40, it needs 25 percent equity. If a nine-out flush draw sees both cards from the flop, the exact hit rate is 34.97 percent, not the rounded story your memory might prefer. These numbers do not decide the hand by themselves. They keep the discussion honest so that exploit reads, implied odds, rake, and future-street leverage are added on top of a real base.

Hand Example 1 below is intentionally generic enough to transfer. Read it by asking which factor is doing the work. If the answer is rake, a line that looks close should usually become tighter. If the answer is depth, ask whether your hand can win stacks or only win a medium pot. If the answer is opponent type, ask whether you are punishing a real leak or projecting one because you want action. The better you become, the less you need heroic river guesses, because many of those guesses disappear when preflop entry, seat choice, and flop sizing are already disciplined.

Hand Example 2 focuses on the second-order mistake: using the right concept at the wrong table. A deep-stack bluff with a nut blocker is attractive against a thinking regular who can fold strong one-pair hands. It is usually torching money against a tilted caller who came to see showdowns. A thin value bet is mandatory against a station and reckless against a range that arrives condensed and trap-heavy. A seat-change fee is trivial when it buys position on a splashy straddler and wasteful when the apparent target is short-stacked or leaving. Always connect the concept to the player who must respond to it.

A useful study routine for this lesson is to tag hands by failure mode rather than by street. Use labels such as rake-marginal, deep-one-pair, bad-seat, missed-table-change, short-handed-overfold, straddle-unit-error, promo-chase, and fatigue-punt. Those labels are more valuable than simply marking won big pot or lost big pot. A database full of emotional tags teaches nothing. A database full of structural tags tells you which cash-game costs are recurring and which are just variance. The same routine works live: write the hand, stack depth, lineup, rake/drop, and your physical state before judging the decision.

The exploit layer is where cash games become profitable. Population tendencies matter because they repeat. Many low-stakes pools overfold to large turn bets but underfold rivers after calling twice. Many live $1/$3 games produce too many limped multiway pots, which means isolation and value betting outperform fancy balance. Many regular-heavy online games punish open seats with aggressive players on your left, which means quitting is an EV decision rather than a mood. The correct exploit is not maximum aggression; it is the smallest reliable deviation that captures the opponent's repeated error without opening a larger error in your own strategy.

Do not confuse bankroll comfort with strategic permission. A 50-buy-in roll does not make a bad seat good. A rakeback deal does not make a bot-infested pool worth grinding. A three-buy-in win does not require you to stay after the whales leave. A deep stack does not require you to stack off top pair because you are afraid of being bluffed. Cash poker rewards the boring discipline of declining slightly losing offers. Most players study spectacular all-in spots because they are memorable; most long-run winrate comes from all the small offers you correctly refuse.

For this specific lesson, reduce the topic to a checklist before playing. First, name the game conditions: stake, rake, stack depth, table size, and whether a straddle or promo changes the unit. Second, name the target: which opponent is making which mistake, and where are they seated relative to you. Third, choose the default line from the baseline range or standard postflop heuristic. Fourth, adjust only for a stated reason. Fifth, write down the result-independent review question. If you cannot state the reason before clicking, the adjustment is probably a feeling rather than strategy.

The two most common advanced-player errors are overfitting and under-accounting. Overfitting means taking one showdown and building an entire exploit around it. Under-accounting means ignoring the quiet costs: rake, tips, travel, fatigue, time charge, cashout risk, opportunity cost, and confidence-interval noise. This track is deliberately accounting-heavy because cash specialization is businesslike. The best players are not merely better at check-raising rivers. They are better at deciding which games deserve their attention and which close technical spots are not worth entering in the first place.

When you review the quiz, treat every answer as a policy statement. A correct answer should tell you what to do next time, not merely what happened in the example. If a response says tighten, it should identify the tax or range pressure causing the tighten. If it says call wider, it should identify the price, opponent aggression, or short-handed blind pressure causing the call. If it says quit, it should cite game quality or decision quality. This habit protects you from the main cash-game trap: turning a sophisticated concept into a slogan and then applying it everywhere.

The final standard is simple. You have learned Risk of Ruin, Computed when you can explain the profitable adjustment in one sentence, show the arithmetic that bounds the decision, and describe the opponent or game condition that makes the adjustment valid. Without all three pieces, the idea is incomplete. With all three pieces, the lesson becomes part of a repeatable cash-game process: pick better games, enter better pots, pressure better targets, and protect the bankroll that lets your edge compound.

Worked Hand 1

{
  "id": "risk-of-ruin-hand-1",
  "hero": "As Kd",
  "villain": "loose BTN caller",
  "board": "Kh 7c 2d 4s 9h",
  "pot": "$68",
  "action": "Hero raises preflop, value bets flop and turn, then checks river when worse kings are thin and raises are nutted.",
  "decision": "Bet flop small, bet turn for value, check-call reasonable river sizing, fold to huge river raise from passive profile."
}

The key is not whether this exact holding won. The key is whether the line matches the lesson condition and whether the pot size being built is appropriate for the hand class.

Worked Hand 2

{
  "id": "risk-of-ruin-hand-2",
  "hero": "9s 8s",
  "villain": "aggressive blind defender",
  "board": "Ts 7s 2c 4d Qh",
  "pot": "$112",
  "action": "Hero has pair-plus-draw pressure early and arrives river with missed spades but relevant straight blockers.",
  "decision": "Continue flop, barrel high-equity turn candidates, abandon river without blocker advantage against calling-station profile."
}

Use this hand as a review template: write the stack depth, price, opponent profile, and reason for the final action before checking the result.