? on Royal Match

DD game, bet pays 2 1/2 to 1 and 25-1 for the Royal.
Three or four other players at table. After two rounds, no Kings or Queens
have been played. Any way to estimate the house advantage for the next round?

shadroch said:

DD game, bet pays 2 1/2 to 1 and 25-1 for the Royal.
Three or four other players at table. After two rounds, no Kings or Queens
have been played. Any way to estimate the house advantage for the next round?

Click to expand...

Absolutely if you just made the assumption that everyone used 2.7 cards. (Obviously, this isn't the sort of calculation you want to be caught making at the table).

EV = (Probability of Lose)(Wager) + (Probability of Suited hand not K,Q)(2.5 x wager) + (Probability of Suited K,Q)(25 x wager)

However, it may or may not be positive EV, yet, as I may be wrong, but I think most of the EV in this bet is tied up with the outcome of getting a suited pair. Despite the higher payout, the suited K,Q is really an infrequent chance event.

Spaw

Snyder says the majority of your money comes from suited pairs, which is why he says play only the game that pays 3-1 on them. I'm curious how many non- KQs must be out of play before the bet becomes EV positive in the 2 1/2 and 25 payout mode.

shadroch said:

Snyder says the majority of your money comes from suited pairs, which is why he says play only the game that pays 3-1 on them. I'm curious how many non- KQs must be out of play before the bet becomes EV positive in the 2 1/2 and 25 payout mode.

Click to expand...

EV = (Probability of Lose)(Wager) + (Probability of Suited hand not K,Q)(2.5 x wager) + (Probability of Suited K,Q)(25 x wager)

Well, for the above equation if you set EV = 0 (break-even situation) and rearrange it so that it is in terms of (Probability of Suited K,Q), then you can solve for what the probability of getting suited K,Q needs to be for the bet to be break-even. Of course, you'd make the simplifying assumption that the probability of getting a suited hand (not K,Q) is always the same as off the top of the shoe.

Once you have found what the probability of getting suited K,Q needs to be in order for the bet to be break-even, then you can compute what percentage of the remaining decks need to be K's and Q's (assuming there is a normal suit distribution) for the bet to be break-even.

Perhaps I might have time this weekend to work this out if someone else (or you) don't get to it first.

Spaw

shadroch said:

After two rounds, no Kings or Queens
have been played. Any way to estimate the house advantage for the next round?

Click to expand...

The attached spreadsheet will let you look at any deck composition and see what the house edge is. Just adjust the payouts in the light green section and adjust the deck composition in the light blue section.

With 22 cards removed (about 2 rounds with 3 players) you could still be at about a 5% disadvantage. As you said, the suited matches can make or break you. If the other suits are equally distributed then the excess Kings and Queens aren't going to get you out of the hole.

-Sonny-