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06-30-2020 , 12:53 PM

Bhark85

stranger

Join Date: Jun 2020 Posts: 2

New to stud but have an easy question for someone out there.
Say you get dealt rolled up trips. Assuming no knowledge of other players cards. What are your odds to either upgrading to a full house or 4 of a kind by the end of the hand?

If you can show your math, that would be helpful too.

Last edited by Bhark85; 06-30-2020 at 12:54 PM. Reason: Typo

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06-30-2020 , 06:30 PM

PoteauMtn

stranger

Join Date: Jun 2020 Posts: 10

with [ K K ] K your percentage chance :

Quads 8.16 percent

Full House 32.02 percent

The math for quads

49 unknown cards And 4 more cards to complete your hand
4 Card Combinations
49c4 = 211,876
one out for quads (1) King
48-1=47
47c4 = 194,580
combinations with a king
211,876 - 194,580 = 17,296
probability = 17,296 / 211,876 = .081633
8.16 percent chance
odds 12.25
The full house takes more time than I have at the moment
you can google the combination formula there is at least two formulas
for 49c4 that is 4 card combinations for 49 cards
here is one of them
49*48*47*46/24=211,876
49*(49-1)*(49-2)*(49-3) / factoral of 4 (4*3*2*1) = 24

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06-30-2020 , 09:00 PM

Bhark85

stranger

Join Date: Jun 2020 Posts: 2

Thanks, I ran my math at 1st and got 38% earlier. I was close but thought something was still off.

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06-30-2020 , 09:15 PM

PoteauMtn

stranger

Join Date: Jun 2020 Posts: 10

I got to thinking the odds for quads in my reply is off by 12 combinations I did not count the hands where the last four cards dealt are all of the same rank for example

[ K K ] K A A A A , 2222 thru QQQQ

SO for quads : 8.17% odds = 12.2

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07-01-2020 , 04:34 PM

PoteauMtn

stranger

Join Date: Jun 2020 Posts: 10

Below is the math for probability of making a Full House

[ A A ] A Starting Hand, 4 more Cards to come from 49 : containing the following combinations that make a full house : 1 pair, 2 Pair and 3 of a kind

1 Pair Combinations : 12 x 4C2 x 11C2 x 4 x 4 = 63,360

2 Pair Combinations : 12C2 x 4C2 = 2,376

3 of a kind combinations : 12 x 4C3 x 11 x 4 = 2,112

Total = 67,848

49C4 = 211,876

probability : 67,848 / 211,876 = 0.320225

ODDs = 3.122803

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