Craps Bankroll Risk — Exposure, Variance, and Session Survival

Craps bankroll risk is the chance that normal game swings exhaust the money assigned to a session before the player reaches a planned stopping point. It is not measured by house edge alone.

A Pass Line bet has a low edge, yet it can lose the full stake. An odds bet has zero house edge, yet it can lose several base units at once. Several individually reasonable bets can create a fragile layout when their combined exposure is too large for the bankroll.

The useful question is not “How much did I buy in for?” It is: How much can the current set of wagers lose, how often can that happen, and how many such sequences can the bankroll absorb?

Start with four separate measures

These measures answer different questions. A bankroll can have many base units but still carry excessive active exposure. A wager can have zero expected loss and still create substantial variance. A session can also be ahead while its remaining bankroll is too small for the current layout.

Base units are only the first screen

Suppose the bankroll is $600.

“Forty units” does not mean 40 rolls or 40 shooters. A Pass Line decision can take several rolls, and additional wagers may win or lose before that decision ends.

A unit count also becomes misleading when the player presses stakes. If the base wager rises from $15 to $30, a $600 bankroll instantly falls from 40 current units to 20 without any dice result.

Total exposure can be much larger than the table minimum

Consider a $15 table and this layout after point 6 is established:

• $15 Pass Line;
• $30 odds behind the line;
• $18 place 8;
• $15 Come bet;
• $5 hard 6.

Total chips at risk or in active contracts are:

$$15+30+18+15+5=$83$$

Not every wager resolves on the next roll. But if 7 appears:

• Pass and odds lose $45;
• place 8 loses $18;
• the Come bet on its first roll wins $15;
• hard 6 loses $5.

The net result is -$53, not -$83. That example shows why raw exposure is a warning measure rather than an exact next-roll loss forecast. Each wager’s state must be modeled.

If the Come bet had already traveled to another number, the same 7 could defeat it instead, producing a larger loss. Craps risk changes as chips move through states.

Low edge and high swing can coexist

The Pass Line’s house edge is approximately 1.414% on the base wager. For a $15 Pass decision:

$$\text{expected loss}\approx15\times0.01414=$0.21$$

Adding $30 odds does not add house edge to that supplemental wager. The expected loss for the combined $45 contract remains about $0.21, assuming standard true-odds payment.

The combined edge as a percentage of total line-plus-odds action is:

$$\frac{0.21}{45}\approx0.47%$$

That percentage looks attractive, but the outcome swings are larger. If point 6 is active:

• point 6 before 7: line earns $15 and $30 odds earn $36, for +$51;
• 7 before point 6: line and odds lose $45.

Conditional on the point already being 6, there are five combinations of 6 and six combinations of 7. The contract wins 5/11 of these decisions and loses 6/11. The fair odds payment balances the supplemental wager mathematically; it does not make the bankroll stable.

This is why price and survival must be analyzed separately.

Several small edges still create large action

Suppose a player keeps these bets working for an hour:

• $15 Pass Line, 25 resolved decisions;
• $18 place 6 and $18 place 8, each producing 35 resolved decisions;
• $5 Field, 60 one-roll decisions.

Using approximate common edges:

The $5 Field chip is the smallest visible bet but contributes the largest theoretical loss because it resolves frequently and carries a higher edge. Repetition matters as much as denomination.

If the Field pays triple on one of 2 or 12, its edge can be lower. The actual table paytable controls.

Proposition bets can dominate bankroll cost

A $5 Any Seven wager seems minor beside a $30 odds bet. Any Seven commonly pays 4 to 1 despite 6 winning and 30 losing dice combinations:

$$EV=\frac{6(4)-30}{36}=-\frac{6}{36}=-16.67%$$

Expected loss per decision is:

$$5\times0.1667\approx$0.83$$

Repeated 30 times, that is approximately $25 theoretical loss. The $30 odds bet is much larger in dollars but contributes zero expected loss when paid at true odds.

This comparison does not mean the odds bet is harmless. It means one wager mainly adds variance, while the other adds both variance and substantial negative expectation.

Session survival is not the same as expected loss

Expected loss is an average. A bankroll can disappear even when theoretical loss is modest because results arrive in uneven chunks.

For a fixed session, risk depends on:

• starting bankroll;
• stake size and betting multiples;
• number of simultaneous wagers;
• point distribution;
• odds multiples;
• frequency of one-roll and proposition bets;
• table speed;
• pressing or regression rules;
• stop-loss and stop-time rules;
• correlation among wagers on the same dice result.

That last item matters. Pass Line, place bets, Come numbers, and hardways can all lose together on 7. Treating their variances as independent would understate downside clustering.

A generic “risk of ruin” formula designed for independent equal-size bets is therefore not reliable for a changing craps layout. Simulation or exact state modeling is more appropriate, and even then assumptions about strategy and table pace must be explicit.

A three-shooter stress test

A player begins with $300 and uses:

• $15 Pass Line;
• up to $30 odds;
• $18 each on place 6 and 8 after the point.

A fully loaded point cycle has $81 in action. Consider three short hands where the player establishes a point, takes odds, places 6 and 8, and then 7 appears before any helpful number.

Each such sequence can lose:

$$15+30+18+18=$81$$

Three consecutive versions would cost:

$$3\times81=$243$$

Only $57 remains. That sequence is not the average, and a point can be 6 or 8 so one place bet may overlap with the line contract under the player’s actual rules. The example is a stress test showing that a $300 buy-in is thin for $81 of loaded exposure.

A plan should survive plausible bad sequences without requiring an immediate deposit, ATM visit, or desperate stake increase.

Odds multiples and bankroll choice

Taking more odds lowers the combined house-edge percentage but raises peak exposure.

With $15 Pass Line:

The final column is the bankroll issue. A smaller percentage does not mean smaller dollar variance.

The correct odds multiple cannot be chosen from house edge alone. It must fit the session bankroll and the player’s tolerance for losing the full line-plus-odds amount repeatedly.

Rules and procedures affect risk

The Massachusetts approved craps rules illustrate standard Pass, Don’t Pass, Come, Don’t Come, place, buy, lay, and supplemental odds contracts, including true-odds payouts for points 4 through 10. Casinos can set table limits and approved optional wagers within their jurisdictional framework.

Before estimating risk, verify:

• minimum and maximum wager;
• maximum odds allowed by point;
• whether place and hardway bets are working on come-out rolls;
• Field special payouts;
• buy and lay commission amount and timing;
• rounding rules for improper betting multiples;
• whether an electronic, stadium, or hybrid game resolves at a different pace.

A model built for 3-4-5x odds and 80 rolls per hour does not describe a terminal offering 10x odds and much faster decisions.

Bankroll management without pretending it beats the game

A bankroll rule can limit damage; it cannot change negative expectation. Useful controls include:

1. Set the session bankroll before arriving. Do not treat access to more money as part of the plan.
2. Choose a maximum loaded layout. Define the largest total line, odds, place, and side action allowed.
3. Count action after every press. A win can increase risk if all proceeds are added to working bets.
4. Separate odds from reserves. Fair pricing does not make those chips unavailable for loss.
5. Limit one-roll repetition. Small center or Field bets accumulate quickly.
6. Use a time boundary. More rolls create more action and more opportunities for drawdown.
7. Stop when current units no longer support the planned layout. Do not keep the same bets after the bankroll has been cut in half.
8. Record cash in and cash out. Chips remaining on the felt are still part of the bankroll.

A stop-loss does not improve EV. It caps one session’s loss and can reduce the chance that emotional decisions expand exposure.

What a simulator must disclose

A useful craps bankroll simulation should state:

• exact bet sequence and working rules;
• odds multiples by point;
• payout and commission assumptions;
• number of rolls or resolved decisions;
• whether bets are pressed, regressed, or replaced;
• bankroll and table limits;
• stopping rules;
• number of simulated sessions;
• outputs such as median result, drawdown percentiles, and bust frequency.

One simulated path proves nothing. A distribution of many modeled sessions can show how often the bankroll survives under the stated assumptions. It still cannot predict the next real session.

Use the variance simulator and expected loss calculator as planning aids, not promises.

A final pre-buy-in test

Before playing, calculate:

• starting bankroll;
• base units at the current minimum;
• maximum line-plus-odds contract;
• maximum total layout exposure;
• largest plausible one-roll loss;
• expected hourly action by bet type;
• planned time and loss boundary;
• whether the bankroll still supports the plan after a 30%, 50%, or 70% drawdown.

Craps offers some of the lowest-priced wagers in a casino and some of the most expensive, all on the same felt. The bankroll does not care which chip felt small or which bet had a good percentage. It experiences the combined cash flow of every active contract. Continue with craps expected value, craps house edge, one-roll bets, and odds bets.