odds question about a game

[abc4000]

Hi pros, i think most professional bj players here are extremely good mathematician, so i dont know if you can help me solve this simple odds problem about a game people play around my area, i try to solve it for couple of days, but just cant get it, i think im just too dumb for this ?(

Game rule

one deck of cards, no picture cards and jokers, so only 1 to 10. 40 cards

4 spots on table, each spot deal 2 cards

Dealer takes one spot randomly, and player can bet on any other three spots

1 is one point 2 is two points … " 10 is zero"
So 10 + 2 = 2 and 5+4 =9

So two cards total "9" is highest, but "pair" beats single number, and two 10s is the biggest in pair. Which beats anything.

The payout is, 1)if dealer and player push, then dealer wins, 2)if player get pair and beats dealer then player get pay double, if he doesnt beat dealer then he lose the hand, no matter what he gets. And dealer always win one to one.

Can someone tell me whats the odds for the dealer and player

Tried few days, i believe dealer has better odds, but cant get number right


??? iPhone ????? Tapatalk

[terry0222]

Without working out the odds, my 'intuition' is that the dealer has the edge because the dealer wins any push. The player won't get a winning pair (that also beats the dealer) often enough to compensate for the fact that the player loses any push.

[Dog Hand]

1/13th (3/39) of the time you get a pair and win an extra unit.

House Edge is the tie rate minus 1/13 (or .076923).

The tie rate is best figured out by simulation but if you want to take a shot mathematically go for it. It is complicated and thus more than I want to do mathematically.

Three,

The player doesn't automatically win with a pair: his pair must beat the dealer's pair, as the dealer wins ties. I found that the player gets a pair but loses 0.30638...% of the rounds.

Dog Hand

P.S. What happened to the "t"? Did I miss a memo?

[Three]

P.S. What happened to the "t"? Did I miss a memo?

I got rid of the typo in my handle.

[Dog Hand]

Hi pros, i think most professional bj players here are extremely good mathematician, so i dont know if you can help me solve this simple odds problem about a game people play around my area, i try to solve it for couple of days, but just cant get it, i think im just too dumb for this ?(

Game rule

one deck of cards, no picture cards and jokers, so only 1 to 10. 40 cards

4 spots on table, each spot deal 2 cards

Dealer takes one spot randomly, and player can bet on any other three spots

1 is one point 2 is two points … " 10 is zero"
So 10 + 2 = 2 and 5+4 =9

So two cards total "9" is highest, but "pair" beats single number, and two 10s is the biggest in pair. Which beats anything.

The payout is, 1)if dealer and player push, then dealer wins, 2)if player get pair and beats dealer then player get pay double, if he doesnt beat dealer then he lose the hand, no matter what he gets. And dealer always win one to one.

Can someone tell me whats the odds for the dealer and player

Tried few days, i believe dealer has better odds, but cant get number right


??? iPhone ????? Tapatalk

abc4000,

I analyzed this game via the "brute force" method using MS Excel: I enumerated each of the 10,000 possible combinations, calculated the probability of each, and decided whether the combination resulted in a +2, +1, or -1 (from the player's viewpoint).

I found that the player wins 2 units 7.3859...% of the rounds, wins 1 unit 38.2828...% of the rounds, and loses 1 unit the other 54.3313...% of the rounds, for an Initial Bet Advantage of -1.2766%.

The Tie probability turns out to be 8.6625...%.

If you'd like a copy of the Excel spreadsheet, let me know.

Hope this helps!

Dog Hand

P.S. I deleted an earlier post in which I mistakenly had a Player's edge... I missed the "baccarat-style" scoring, and so under-calculated the Tie (and, thus, dealer wins) probability.