Value of Baccarat Dealer Error - Gambling and Probability

WheelDraw1020 · 07-02-2012, 05:42 AM

If there's a Baccarat dealer who never gives the banker a card if leading after the player's 3rd and always hits the banker if behind after the player's 3rd but follows all other rules correctly how much is a Banker bet worth?

**BruceZ** · 07-02-2012, 05:50 PM

Quote:

Originally Posted by WheelDraw1020

If there's a Baccarat dealer who never gives the banker a card if leading after the player's 3rd and always hits the banker if behind after the player's 3rd but follows all other rules correctly how much is a Banker bet worth?

I did a simulation of 10 million hands, and I got that a bet on the banker would have a positive EV with an edge of about +0.9%. That should be accurate to within 0.1% to about 99.9% confidence. That's for an 8 deck game with 5% commission. You didn't explicitly specify what the dealer does when the player takes a 3rd card and he is tied with the player, so I assumed that he follows the normal rules in that case based on his total and the player's 3rd card.

The R simulation is below. I first checked it without the dealer error and got the right value, which is about -1.06%, to within the accuracy of the sim. The dealer error lines are marked in the comments.

Code:

sims = 10000000
decks = 8

cards = c(rep(1:9,4*decks), rep(0,16*decks))

hit = c(1,1,1,1,0,0,0,0,
1,1,1,1,0,0,0,0,
1,1,1,1,1,0,0,0,
1,1,1,1,1,0,0,0,
1,1,1,1,1,1,0,0,
1,1,1,1,1,1,0,0,
1,1,1,1,1,1,1,0,
1,1,1,1,1,1,1,0,
1,1,1,0,0,0,0,0,
1,1,1,1,0,0,0,0)

dim(hit) = c(8,10)

wins = 0
losses = 0

for (i in 1:sims) {
  deal = sample(cards, 6, F)
  player = (deal[1] + deal[2])%%10
  banker = (deal[3] + deal[4])%%10
  if ( (player < 8) & (banker < 8) ){
    if (player <= 5) {
      player = (player + deal[5])%%10
      if (banker < player) {    #Dealer error
        banker = (banker + deal[6])%%10  #Dealer error
      }
      else {
        if (banker == player) {  #Dealer error - should always do next line
          if (hit[banker+1,deal[5]+1] == 1) {banker = (banker + deal[6])%%10}
        }
      }
    }
    else {
      if (banker <= 5) {banker = (banker + deal[5])%%10}
    }
  }

  if (banker > player) {wins = wins + 1}
  if (player > banker) {losses = losses + 1}
}

(wins*19/20 - losses)/sims

WheelDraw1020 · 07-02-2012, 10:49 PM

Thank you Bruce.