Hello all,
We know that one way to win the 21 + 3 side bet is to combine my first 2 cards with the dealer upcard to form a flush. I have used an online simulator to find out that, on average, one will find a set of any 3 cards side-by-side (6 deck) about 7 times in any 244 card shoe.
For the purposes of this post, I am looking at only heads-up play and therefore counting ANY set of 3 side-by-side cards as a flush. (As you know, when playing heads-up, the first 3 cards - that is, my 2 plus her 1 up card - out of the shoe per round are eligible to make a flush.). So, for example, in the sequence K, Q, 5, 2, A, 4, 5, 6, 4, 9, we count 2 three-card flushes (the 4, 5, 6, and the 5, 6, 4, even though it is not possible for the player to win both of these 2 flushes because they are too close to each other in the shoe.). I am counting the flushes in this counter-intuitive manner simply because that's the way I began counting them, and I now want to maintain consistency.
When playing at home with my 6 deck shoe, I have been able to identify certain shoes that, when I play the 21 + 3 side bet, I count not 7 but 11 (on average) of these sets of 3 side- by- side sets of cards that form a flush.
Again, assuming that a typical shoe of computer play yields 7 of these flushes, and, at home, I am able to play only those shoes that yield, on average, 11 of these flushes, by how much does my EV increase (assuming that all of the other manners in which I can win the 21 + 3 side bet - e.g., 3 of a kind, straights - remain the same as what a sim would predict. In other words, assume I can only identify those particular shoes which contain more flushes but not necessarily more straights, three of a kinds, etc.).
