Two rules for the initial bet. One decision model.
Graduated and Selective are the two options under “Bankroll management” in OOB.
Both read the same pre-bet estimate and the balance you confirm, and both express the
suggested initial bet in units of that balance. They differ only in how many units they
suggest. Neither changes how the available actions are evaluated.
Shared and different
The same inputs. Different steps above +0.2%.
Both rules start from the pre-bet EV estimate: OOB’s estimate of the next round,
computed from the composition you have recorded, before the round’s first card. It is
used only for the suggested initial bet. The
Expected Value page
explains how it differs from the EV of an action.
Shared
Inputs, Lower Steps and Fixing
The same pre-bet estimate and the same unit, taken from your confirmed balance. No bet below −1.0%, 1 unit from −1.0% to below +0.1%, and 2 units from +0.1% to below +0.2%. In both, the initial bet is fixed when the round starts, and a double or a split adds the same amount again.
Different
How Far the Bet Rises
From +0.2% to below +1.1%, Graduated rises in steps of 3, 4, 6, 8 and 10 units, while Selective stays at 2 units. From +1.1%, Graduated suggests 12 units and Selective 13.
Selective applies when no choice has been saved. The rule you choose is saved for your
account and remains selected after you log out.
Two separate questions
Switching the rule does not change the action EVs.
OOB answers two questions with separate rules. The decision model ranks the available
actions of the active hand — Hit, Stand, Double, Split or Surrender, where the rules
allow them — by calculated EV. The bet-sizing rule suggests how many units to stake
before the round. The selected rule is not an input to the decision model.
What switching changes
The number of units suggested for a round that has not started yet, and with it the
suggested amount.
What stays the same
The action EVs, the action marked “Highest-EV”, the pre-bet estimate, the
reference count and the recorded shoe. A change of bet rule alone does not reset the
shoe, the count or the current hand.
A percentage is not an amount.
EVs are quoted relative to the stake. A larger initial bet scales the expected amount and
the size of possible wins and losses in the same proportion; it does not make the estimate
more favourable. See Variance.
The unit
The unit comes from the balance you confirm.
Enter a balance in “Balance” and confirm it. Only a positive number is accepted;
commas as thousands separators are allowed. One unit is that balance divided by 100,
rounded to the nearest whole number, with halves rounded up. The suggested initial bet is
the unit multiplied by the number of units the selected rule gives for the pre-bet estimate.
unit=round(confirmed balance100)
initial bet=unit×n
Here n is the number of units the selected rule gives for
the pre-bet estimate (see the steps below), and round takes
the nearest whole number, with halves rounded up.
Confirmed balance
Balance ÷ 100
Unit
1,000
10
10
1,049
10.49
10
1,050
10.5
11
2,550
25.5
26
49
0.49
0
Illustrative balances. Because of the rounding, the same number of units is not always the same share of the balance. Below 50, the unit rounds to 0 and the suggested amount is 0.
The confirmed balance belongs to the live game. CLEAR HAND, NEW SHOE and a change of game
rules keep it; logging out clears it. When you select “New Session”, a valid
“Start Balance” entered at that moment becomes the confirmed balance of the new
session; without one, no balance is confirmed until you confirm one. Check the
“Balance” value before the next round.
The steps
Units by pre-bet estimate, for each rule.
Each lower bound is inclusive. The rules read the unrounded estimate; the displayed
percentage is rounded to four decimals, so a value shown as +0.1000% can still be just below
+0.1%. These are the thresholds of the published
One Million Cards comparison.
Pre-bet estimate
Graduated
Selective
Below −1.0%
No bet
No bet
−1.0% to below +0.1%
1 unit
1 unit
+0.1% to below +0.2%
2 units
2 units
+0.2% to below +0.3%
3 units
2 units
+0.3% to below +0.5%
4 units
2 units
+0.5% to below +0.7%
6 units
2 units
+0.7% to below +0.9%
8 units
2 units
+0.9% to below +1.1%
10 units
2 units
+1.1% and above
12 units
13 units
At the top step, the initial bet is 12 units under Graduated or 13 units under Selective, before any double or split. Its exact share of the confirmed balance depends on the rounded unit. For example, a confirmed balance of 50 gives a unit of 1, so these initial bets represent 24% and 26% of that balance.
Suggested, then fixed
The bet is fixed by the round’s first accepted card.
Between rounds, the display shows “Suggested bet”: a preview from the current
pre-bet estimate, the confirmed balance and the rule selected now. After you choose another
rule or confirm a new balance, the preview is updated once the current calculation has
finished.
A round starts with the first card accepted after CLEAR HAND, NEW SHOE, New Session or a
change of game rules — including a first card entered under “Other Cards”.
At that moment OOB fixes the rule, the estimate of the composition before that card, the
confirmed balance, the unit and the initial bet. When an amount is available, the display
then shows “Bet this hand” until the round ends.
A different rule during the round is saved and shown as “from next hand”; the bet of this round stays as fixed.
A newly confirmed balance during the round applies from the next round; the bet of this round is not resized.
Doubles and splits use the fixed initial bet: each adds that amount again. The fixed bet is not a cap on the total stake of a hand.
UNDO of every card since the round started means the round has not started after all; the next accepted card fixes it again, with the rule and balance current at that moment.
Selective, balance 2,550→unit 26; first card accepted at an estimate of +0.62% → 2 units, “Bet this hand: 52”
During the round→you choose Graduated and confirm 3,000: this round stays at 52; a double adds 52
Next round→Graduated, unit 30; if its first card is accepted at +0.62% again → 6 units, 180
Illustrative estimates and balances. In practice the estimate changes as cards are recorded.
When there is no amount
“Do Not Bet” and a missing balance mean different things.
Below −1.0%
Do Not Bet
Both rules suggest no bet, and the display shows “Do Not Bet”. If a round starts at that estimate, the guidance stays “Do Not Bet” for the round. OOB still records the cards and calculates the action EVs; the guidance does not predict the outcome of the hand.
No confirmed balance
Units Without an Amount
The display shows the number of units with “Confirm Balance”, for example “6x — Confirm Balance”. The amount appears once a balance is confirmed. If the round is already fixed, a balance confirmed now applies from the next hand.
Worked examples
One balance, five estimates, two rules.
A confirmed balance of 2,550 gives a unit of 26. The estimates below are hypothetical.
Pre-bet estimate
Graduated
Selective
−1.30%
No bet
No bet
−0.40%
1 × 26 = 26
1 × 26 = 26
+0.15%
2 × 26 = 52
2 × 26 = 52
+0.62%
6 × 26 = 156
2 × 26 = 52
+1.25%
12 × 26 = 312
13 × 26 = 338
Illustrative arithmetic of the two published rules. It is not a forecast and not a risk estimate.
Limits
A suggested bet is a rule, not a forecast.
No guarantee and no protection from losses.
Neither rule guarantees a profit or removes losses. A favourable estimate can still be
followed by a losing hand, session or longer run. Neither rule is presented as safer or
more profitable in general.
Not a personal risk-of-ruin estimate.
OOB does not calculate a risk of ruin for either rule or assess what you can afford to
lose. The Risk of Ruin
page explains the concept.
The published comparison used a fixed unit.
The One Million Cards
comparison applied these thresholds on simulated tracks with a fixed $10 unit on every
round. It does not test the balance-based version described on this page, and it is not
independent validation.
The estimate has open limits.
The pre-bet estimate comes from OOB’s production model, with an empirical
calibration inside a defined domain, described in the
Methodology. Its internal
audit, recorded in the
Validation Register, V-009, has not
reached a verdict.
Continue
Related pages and published evidence.
Risk of Ruin
Bankroll, bet size, horizon, and the money doubles and splits can require.