MK
• Posts: 13
Joined: Aug 31, 2022
July 23rd, 2023 at 3:50:16 PM permalink
In the 8 deck baccarat game,
If an ace card (specific card) is not drawn by the end of the game,
The house edge of a pair bet or a tie bet gradually decreases as the game progresses. It may change to (-) eventually.
Baccarat's mathematical analysis data does not take this into account.
Do you agree with this idea?
gordonm888
• Posts: 5196
Joined: Feb 18, 2015
Thanked by
July 23rd, 2023 at 4:33:53 PM permalink
Yes.

In general, as the shoe draws down, if there are one or more ranks that have a disproportionately large number of cards remaining then the probability of drawing two or more cards that are a pair will be increased over a case with a 'flat distribution' of ranks.

This table gives the probability of getting a pair in two dealt cards as a function of the number of cards(decks) remaining and the distribution of ranks.
Total cardscards/rank; 2-K# of acesProb of a pair, 2 cards dealt
41632320.074698795
20816160.072463768
52440.058823529
523160.117647059

The first three rows show the probability of a pair in two dealt cards for 8 decks, 4 decks and one deck, assuming that all the ranks have an equal number of cards remaining. The pair prob. goes from about 7.5% down to about 5.9%

The last row shows a case in which there are 52 cards remaining, but there are 3 cards each of the ranks 2 -K and 16 Aces. The pair probability vaults up to about 11.8% for this case.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
MK