Proof/Same True Count / Different Shoe
Composition proof

Same True Count. Different Shoe. Different Decision.

Two internally validated OOB states share the same rules, player hand, dealer upcard and exact Hi-Lo True Count. Their remaining compositions differ — and so do their highest-EV actions.

Internally validated Independent validation: Not yet performed.
What stays the same

Identical rules, identical hand, identical count.

Both states share the same game rules, player hand, dealer upcard, Hi-Lo Running Count, Hi-Lo True Count and number of cards remaining.

Player hand 10 + 6 = 16
Dealer upcard 10
Cards dealt 7
Cards remaining 409
Running Count +3
True Count +0.38
Rule configuration 8 decks · ENHC · S17 · DAS No · Double any first two cards · Split to a maximum of 2 hands (one split, no resplitting) · Resplit aces No · Hit split aces No · Surrender None · Blackjack 3:2
True Count = +3 ÷ (409 / 52) = 156 / 409 ≈ +0.38
The two states share the same True Count before rounding, not only in the displayed value. Both have a Running Count of +3 with 409 cards remaining, so the exact quotient 156/409 is identical. The difference between them is not hidden in the second decimal place.
What changes

Different cards were removed, so different cards remain.

In each state, four Other Cards are removed in addition to the two player cards and the dealer upcard: seven cards in total. Both sets of Other Cards sum to the same Hi-Lo contribution, but they are not the same cards. The highlighted ranks differ between the two shoes.

OOB-RS-0009 STAND
Other cards removed
3, 4, 5, 5
Exact remaining shoe
A
32
2
32
3
31
4
31
5
30
6
31
7
32
8
32
9
32
10/J/Q/K
126
Total remaining: 409
Action EV
Stand -0.5791
Hit -0.5824
Double -1.1647
Split Unavailable
Surrender Unavailable
Highest-EV: STAND · margin 0.0033 over Hit
Per original bet, including any additional wager. The highest-EV action is selected from the unrounded internal values, before display rounding.
Margins are calculated from the displayed, rounded action EVs.
OOB-RS-0010 HIT
Other cards removed
2, 3, 6, 6
Exact remaining shoe
A
32
2
31
3
31
4
32
5
32
6
29
7
32
8
32
9
32
10/J/Q/K
126
Total remaining: 409
Action EV
Stand -0.5804
Hit -0.5720
Double -1.1440
Split Unavailable
Surrender Unavailable
Highest-EV: HIT · margin 0.0084 over Stand
Per original bet, including any additional wager. The highest-EV action is selected from the unrounded internal values, before display rounding.
Margins are calculated from the displayed, rounded action EVs.
What this demonstrates

A count summarizes the shoe. It does not replace it.

The same number, two different shoes.
Hi-Lo summarizes card removal in a single number. Different remaining compositions can share that number without producing identical action EVs. In this pair, OOB selects Stand in one state and Hit in the other.
What this pair does not show
These examples do not show that card counting is useless, measure how frequently decisions differ, or establish an average profit improvement.

True Count remains a useful summary of the shoe. This pair shows what a summary necessarily leaves out.

Reproduce this pair

Recreate both states and compare for yourself.

These steps recreate each state manually, in OOB or in any independent tool supporting the same rules. They do not import anything into the application.

OOB-RS-0009 → STAND
  1. Set the rule configuration: 8 decks · ENHC · S17 · DAS No · Double any first two cards · Split to a maximum of 2 hands (one split, no resplitting) · Resplit aces No · Hit split aces No · Surrender None · Blackjack 3:2.
  2. Start a new 8-deck shoe.
  3. Enter the other cards in the published order: 3, 4, 5, 5.
  4. Enter the two player cards: 10 + 6.
  5. Enter the dealer upcard: 10.
  6. Stop before playing the hand.
  7. Check that Cards Dealt reads 7 and that the remaining shoe matches the composition above (409 cards).
Then calculate the EV of each available action independently, using the same EV convention, and compare with the published values only after your own result is recorded.
OOB-RS-0010 → HIT
  1. Set the rule configuration: 8 decks · ENHC · S17 · DAS No · Double any first two cards · Split to a maximum of 2 hands (one split, no resplitting) · Resplit aces No · Hit split aces No · Surrender None · Blackjack 3:2.
  2. Start a new 8-deck shoe.
  3. Enter the other cards in the published order: 2, 3, 6, 6.
  4. Enter the two player cards: 10 + 6.
  5. Enter the dealer upcard: 10.
  6. Stop before playing the hand.
  7. Check that Cards Dealt reads 7 and that the remaining shoe matches the composition above (409 cards).
Then calculate the EV of each available action independently, using the same EV convention, and compare with the published values only after your own result is recorded.
OOB-RS-0009 in the State Library → OOB-RS-0010 in the State Library → Read the Methodology →
Technical context

Both states carry the same verification record.

Engine Version
OOB-ENG-b0681ede84a3
Methodology Version
Methodology v1.0
Verified on
2026-09-06
Validation Status
INTERNALLY VALIDATED
Verified runtime: OOB-RT-a209a03d7b2d · Python 3.14.4 · Production. Running runtime: OOB-RT-77a6e87094d3 · Python 3.14.4. Independent validation: Not yet performed.
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