question on partnership trumps

[jogs]

I made a tough calculation which says a partnership should hold all 13 cards in one suit about once every 15,000 boards. If this is true anyone who has played over 50,000 boards should have had the partnership hold 13 cards in one suit at least once.

I was wondering if there is anyone who has played over 50,000 boards who has never held all 13 cards(for partnership) in one suit?

Some of the online players playing 500 hands a week are playing over 25,000 hands a year.

 

Thanks,

jogs

 

ps. My partnership has held all 13 cards in one suit before.

[manudude03]

I don't think I've ever had all 13 before, had 12 a few times, but not 13. My opps have had it twice though. By the way, after 50k hands, there's still a 3.567% chance of never having it happen.

[Hanoi5]

My partner once led my suit and gave a ruff and discard. It's not the only time it's happened to me.

[JLOGIC]

I've seen it multiple times, guess I run good.

[Free]

I made a tough calculation which says a partnership should hold all 13 cards in one suit about once every 15,000 boards. If this is true anyone who has played over 50,000 boards should have had the partnership hold 13 cards in one suit at least once.

Sorry but this statement is wrong. There will always be a very small percentage that won't hold 13 cards in 1 suit after 50000 boards, even after 100000 boards. If you check enough players, then you'll always find one. If there aren't enough players now, you can use "time" to get more players involved, so over a certain period of time (= multiple generations) there will be one for sure.

 

Btw, do you care to explain how you get to that 1 out of 15000? And is that really the chance per pair and not per board?

 

I was wondering if there is anyone who has played over 50,000 boards who has never held all 13 cards(for partnership) in one suit?

Probably. I'm not interested in doing the math (too complicated because many people play the same boards), but if you calculate percentages and how many players there are who have played 50000+ boards I guess you can calculate there's a big chance there's at least 1 somewhere in the world.

[jogs]

I don't think I've ever had all 13 before, had 12 a few times, but not 13. My opps have had it twice though. By the way, after 50k hands, there's still a 3.567% chance of never having it happen.

 

Hadn't occurred to me to do the math on it. Didn't realize the chance of it not happening was so high.

Just ran it through Excel. I got

3.779% chance of never for 50k hands.

0.143% chance of never for 100k hands.

[jogs]

 

Btw, do you care to explain how you get to that 1 out of 15000? And is that really the chance per pair and not per board?

 

There's a math function in Excel called hypgeomdist.

Choose 13 cards of one suit among 26 cards of the partnership.

Sample s(uccesses) is number of successes.

13 in this case.

Number_sample is the size of the sample.

26 cards for partnership.

Population s(uccesses) is number of possible successes within the population.

13 cards in a suit.

Number pop is the population size

52 cards in a deck.

 

Then multiple that number by 4, since there are 4 suits in a deck.

 

That's the chance of one pair holding all 13 cards in one suit for one board.

[gnasher]

The chance of dealing a specific partnership all of a specific suit is

26/52 * 25/51 * 24/50 ... * 13/41 * 14/40

= (26! / 13!) / (52! / 39!)

~= 1/61055

There are four suits, so I agree with 1/15000.

[Flameous]

Haven't actually happened to me but once in friendly games opponent opened weak two in hearts. His partner smirked and bid 3♥ with 7 card support cause he was sure partner had psyched and was going to bid 3♠ or something over 3♥ and he could play it in four. So there they played 3♥ in 13 card fit, making exactly. Good stop :o

[mfa1010]

Curiously there was a 13-card spade fit on a board we played against Fredin-Upmark of Sweden last Friday in the Nordic team championships. We held 29 of the 30 remaining hcps and were cold for grand in either minor. The Swedes had no problems finding their NV save in 7♠, however. The board was pushed at -1100.

 

Board 5 from the BBO vugraph archive:

Link to hand viewer

[mycroft]

I had two leads into ruff-discards in a month. I remember one before in decades. I think I remember having 13 trump on offense a couple of times. I probably play enough that 1/15000 sounds about right for that memory.