seven
Joined: Oct 1, 2013
• Posts: 151
July 4th, 2019 at 7:45:13 AM permalink
Hello all

I hope someone can help me to find the chances for winning ( or losing) for the following game

it is a poker variant envelope game which gives players five different ways to win. the player selects five envelopes from a total of 20, each filled with a card (four Aces, four Kings, four Queens, four Jacks and four 10s). If he draws a three of kind he wins \$10, a straight is worth \$20, a full house is \$30, while a four of a kind is worth \$250, a Royal Flush \$10k

as I like the idea of the game I thought I can be the house in a private game event

cheers
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4759
July 4th, 2019 at 7:54:30 AM permalink
Quote: seven

Hello all

I hope someone can help me to find the chances for winning ( or losing) for the following game

it is a poker variant envelope game which gives players five different ways to win. the player selects five envelopes from a total of 20, each filled with a card (four Aces, four Kings, four Queens, four Jacks and four 10s). If he draws a three of kind he wins \$10, a straight is worth \$20, a full house is \$30, while a four of a kind is worth \$250, a Royal Flush \$10k

as I like the idea of the game I thought I can be the house in a private game event

cheers

There are (20)C(5) = 15,504 different hands. Of these, I count:
4 Royal Flushes
80 Fours of a Kind (e.g. AAAA and 16 possibilities for the fifth card)
480 Full Houses (5 possibilities for the 3 of a kind rank; 4 sets of three of those cards; 4 possibilities for the pair; 6 sets of cards for the pair)
1020 Straights (4 choices for the 10, 4 for the Jack, and so on, but subtract the 4 Royal Flushes)
1920 Threes of a Kind (5 possibilities for the 3 of a kind rank; 4 sets of three of those cards; 6 pairs of ranks for the other two cards; 4 of each of these ranks)
The sum of the payouts = 114,000, or about 7.353 per possible hand
seven
Joined: Oct 1, 2013
• Posts: 151
July 4th, 2019 at 8:01:57 AM permalink
[q...................................
The sum of the payouts = 114,000, or about 7.353 per possible hand

thank you very much for the answer. I am confused, what do you mean with the sum of the payouts = 114,000 ? is this according to what I wrote for 3 - 4 of a kind straight, full house and RF?

what would be best payouts for the house in such a game?
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4759
Thanks for this post from:
July 4th, 2019 at 8:21:05 AM permalink
Quote: seven

I am confused, what do you mean with the sum of the payouts = 114,000 ?

4 Royal Flushes, each paying 10,000 = 40,000
80 Fours of a Kind, each paying 250 = 20,000
480 Full Houses, each paying 30 = 14,400
1024 Straights, each paying 20 = 20,480
1920 Threes of a Kind, each paying 10 = 19,200
That adds up to, er, 114,080, doesn't it? Hard to tell the difference between 0 and 8 on my calculator sometimes...
But that's what I mean; the expected value of a hand = 114,080 / 15,504.

The "best" payouts depend on a number of things, but mainly, what it costs to play, and how much you want to make.
seven
Joined: Oct 1, 2013
• Posts: 151
July 4th, 2019 at 8:24:46 AM permalink
Quote: ThatDonGuy

4 Royal Flushes, each paying 10,000 = 40,000
80 Fours of a Kind, each paying 250 = 20,000
480 Full Houses, each paying 30 = 14,400
1024 Straights, each paying 20 = 20,480
1920 Threes of a Kind, each paying 10 = 19,200
That adds up to, er, 114,080, doesn't it? Hard to tell the difference between 0 and 8 on my calculator sometimes...
But that's what I mean; the expected value of a hand = 114,080 / 15,504.

The "best" payouts depend on a number of things, but mainly, what it costs to play, and how much you want to make.

great thanks again,
now I understood it very well and as you mentioned it is now question of cost to play and payouts