# Example of cut card effect using combinatorial analysis

Discussion in 'General' started by k_c, Dec 25, 2008.

1. ### k_cWell-Known Member

Here's an example of the exact calculation of the cut card effect when the cut card is placed after the fifth card from the top. It shows that when the cut card is conditionally encountered dealer's edge is increased and why.

Single deck, H17, double any 2 cards, no double after split, no resplit, 1 card to split aces, full peek, no surrender

full shoe EV = -.2051%

Game is heads up, one player versus dealer.If cut card is placed after the fifth card from the top, then the cut card will only be encountered whenever player, dealer, or both take a hit on the first round. If both player and dealer are pat then the cut card will not be encountered.

DATA WHEN NO CARDS ARE DRAWN IN ROUND 1; CUT CARD WILL APPEAR IN ROUND 2
prob(dealer BJ and player BJ) = 0.1773017%, EV = 0%
prob(player BJ and no dealer BJ) = 4.649245%, EV = +6.973864%
prob(dealer BJ and no player BJ) = 4.649245%, EV = -4.649245%
prob(pat player & dealer & no player BJ or dealer BJ) = 7.535815%, EV = +0.1748389%
EV(round following round 1 when both player and dealer are pat) = -0.2494087%

DATA WHEN CUT CARD IS ENCOUNTERED IN ROUND 1; THIS WILL BE THE ONLY ROUND PLAYED
prob(either player, dealer, or both are not pat) = 82.98782%, EV = -2.704534%

EVs WHEN PLAYING THROUGH TO THE CUT CARD USING TOTAL DEPENDENT BASIC STRATEGY
patHandEV: +2.499459% (prob(pat hand))=0.1701218; cut card is not encountered)
nonPatSingleRoundEV: -2.704534% (prob(non-pat hand))=0.8298782; cut card is encountered)
afterPatEV: -0.2494087% (ave EV=-1.4661%; prob=0.1701218; cut card encountered in 2nd round)
totEV: -0.4544837%

EV WHEN PLAYING ONE ROUND AND NO MORE USING TOTAL DEPENDENT BASIC STRATEGY
full shoe EV = -.2051%

Above data is an exact calculation using combinatorial analysis. Placing the cut card after the fifth card in the above heads up game results in reducing a flat betting basic strategy player's EV from -.2051% to -.4545%.

SUMMARY
If player plays one round and quits:
a) 17.01218% of the time both player and dealer are pat; edge to player = 2.50%
b) 82.98782% of the time player, dealer or both are not pat; edge to dealer = 2.70%
c) overall dealer edge = ~.20%

If player plays until cut card is encountered:
d) a, b and c above apply without change
e) 17.01218% of the time an additional round is played when both player and dealer are pat. The player's average EV for this round is -1.4661% because on balance more high cards than low are spent when both player and dealer are pat; edge to dealer = ~.25%
f) overall dealer edge = ~(.20% + .25%) = ~.45%

Playing through to the cut card rather than quitting after one round gives dealer an extra ~.25% edge versus player using total dependent basic strategy in the above case.

2. ### KasiWell-Known Member

Very very cool post k_c