Trips

Anyone know the odds of making trips by the river with a pocket pair? All the sites I have looked at only show odds to the flop.

I found another thread on this forum which quotes around 22%

personally, I have a pocket pair put triple the Bank or put it all on the line in 80% of cases win well draw your own conclusions

I believe it is 1 in 7 roughly to hit a set by the river

Here's the post I found, the first reply has the details

https://www.cardschat.com/forum/general-poker-13/pocket-pair-v-pocket-pair-odds-195744/

It cant be worth the time for me.

Basically, 1 in 8 times

fa1920 said:

Basically, 1 in 8 times

Click to expand...

That's for the flop, by the river it's 1 in 5

With having pocket pair, it is 11% chance to hit trips or better (like full house) at the flop.
There are sites that offer exact percentages, not that hard to find. The 11% probability I know in head, but the source is long forgotten

The 11% probability I know I knew, it's not very profitable to believe that you hit the river that way.

basic probability theory.

there are 2 outs and 5 cards

the odds of not hitting trips is

(48/50)*(47/49)*(46/48)*(45/47)*(44/46) = 0.80816

So the probability of hitting trips is 1 - 0.80816 = 0.19184

I found when holding pocket pair - Odds/probability of making a set or better by the river 4.2 to 1 or 19.2% chance

Just tried to search for the answer and everywhere only lists for the flop.

Thank you for doing the math for us. I've wanted to know this answer for a very long time but never bothered to figure it out myself. Cheers!

Thanks for the info.

Rule of thump for quick calculation:

We only know our pocket cards, so i calculate with a 50 card deck left. For each out you have you get a 2% chance of hitting it with 1 card being dealt. So you get 0,02 per out and multiply by the number of cards that are left to be dealt. This is not 100% accurate but good enough for better decisions at the table where you have no time to go and look up odds.

With a pocket pair you have 2 outs, so two times 0,02 = 0,04
Multiply by 5, because 5 cards will be dealt = 0,20
Which means 20 % chance to hit trips by the river.

With AK preflop you have 6 outs, so 6 times 0,02 = 0,12
Multiply by 5, because 5 cards will be dealt = 0,60
Which means 60 % chance to hit an Ace OR a King by the river

With AK and the flop already dealt you have
(6*0,02)*2 = 0,24
or a 24% chance of still hitting an Ace OR a King on the turn or river.

(Your Outs * 0,02) * Number of Cards to Come = your chance of hitting at least one out

it depends on your playing style

amxvulcan said:

Anyone know the odds of making trips by the river with a pocket pair? All the sites I have looked at only show odds to the flop.

Click to expand...

hi hi amxvulcan
if have pocket pair (odds dealt any pocket pair 5.9%, once in 17 times)
remains 50 unknown cards, two of those give success
and is five opportunities (flop, turn, river) to attain success, make magical set...
however probability depend at what stage of the hand

on flop
if have say 77 ... now to flop a 7, make a set is: 11.76% (once in 8.51 times)

on turn
now is 47 unknown cards left, with one to come, make a set is 4.3% (once in 22.26 times)

on river
now is 46 unknown cards remain, with one to come, probability make set is: 4.3% (once in 22 times)

the mathematical formula to calculate make my head want explode lol

as well explained by kraemer (brilliant guy) above... after flop is convenient think of outs (the number of cards which give you desired result)...
good estimate is: (outs x 4) for turn, & (outs x 2) for river

i think best answer your question ..
you dealt a pocket pair: achieve a set by the river: 11.75% (once in 7.5 times) achieve at least a set incl quads and boats too)
make exactly set: 8.4% (once in 11 times)
interesting to achieve quads by river 0.84% (once in 119 times)

this may be of interest
http://www.pokerology.com/charts/poker-math-and-probability.pdf

(note: i believe correct is say, a set is when you have 2 in hand, 1 one on board...
trips be when have one in hand, board has other two)

About 11% to hit a set on the flop. Good hand to call with in multiway pots from late position (small pairs) if, by the river, you can expect to win 9x or more of your preflop investment in the pot.