if online poker is random, why did I find this with a sample of 562.742 showdown hands?

Amount of hands where
- holecards match 100%
- boardcards match 100%
- flop not in order
Result: 5 (0.00000888506633590526 %)

Amount of hands where
- holecards match (suited or offsuit)
- boardcards match 100%
- flop not in order
Result: 50 (0.00008885066335905264 %)

What result were you expecting?

Actually I wasn't expecting to see any of those hands, where holecards and boardcards match 100%.

Why not? What's the probability of it occurring?

1 in 96Mio / 1 in 6Mio...

Seems more like 1/26 million by my estimate (1326 hole cards * 19600 flops)

However, I'd want to look at the data also - in my database I have more than one instance of a hand that due to an error was loaded twice.

the data consits of hands with unique hand numbers...I will double check...

double checked...50 unique matches where both holecard values are the same and both boards match 100% (including the suit, flop order doesn't matter).

e.g.

Player1:
HC: AsJc
Flop: 5c3s2h
Turn: Js
River: Td

Player B:
HC: AsJh
Flop: 5c3s2h
Turn: Js
River: Td

Assuming the prob. is 1 in 26Mio vs 50 in 562742 we get:

0,000088850663359 (actually occured)
vs
0,000000038461538 (expected)

Wait, is this for all players (that have hole cards exposed)? That changes things quite a bit (every hand with a showdown will have at least 2 sets of hole cards exposed. If it isn't the hero going to showdown, then it'll be 3)

Is this akin to the birthday paradox where chance of any two people having same birthday is small, but it only takes 23 people in a room to have 50% chance of any pair of people having same birthday?

this is for all showdown hands. I have 562.742 of those hands. I take one specific showdown hand and search for the same hand in my sample. I found 100 results in my database. I have to divide this result by 2 because I get each result twice.

How many players at the table?

What does it mean for the boardcards to match? Match with what? The board form the previous hand?

he means matches another "entry" in his hand history database

but he has not answered if he is only looking at his own hole cards or the hole cards of any player shown at showdown

any player

How about if you just tally how many deals went to showdown, and how many of these had the exact same board (flop could be in any order)? That removes the element of how many players were in the hand at showdown (and/or including yourself even if you did not have a live hand at showdown) and which hands are shown down at showdown, etc.

Of course, boards that get to showdown are not entirely random, but let's leave that issue to the side for a moment.

see my initial post.

562.742 hands (single player hands) went to showdown.

50 of those hands matched another hand (different hand number,same site) with the same board cards (flop unordered/all cards same suite) and the hole cards (just observed if both starting hands are suited or offsuite).

A match would be:

Player A:
HC: AJo
Flop: 5c3s2h
Turn: Js
River: Td

Player B:
HC: AJo
Flop: 5c2h3s
Turn: Js
River: Td

This is still not clear (at least to me). The word "hands" is ambiguous in poker. Do you mean "deals"?

Clearly, if four players go to showdown on the same deal, there is only one board (of course). So I suggested removing the players' hole cards from the inquiry so that everything is apples to apples.

See my previous post. I am not trying to be difficult, but do you understand what I asked for (and why)?

yes...i am refering to 50 single deals that saw showdown, each deal connected to 1 player name. Each deal has a match as described with another single deal (different player, different hand number).

The actual result quering my database was 100, but that will count each match twice:

Deal A matches Deal B
Deal B matches Deal A
...

So I had to divide by 2 and the correct result is 50.

I think you need to use the total number of displayed hole-cards as your denominator, not the number of hands. Let's say for example that you played HU and every hand went to showdown. If you played 100 hands, you'd see 200 sets of hole cards, and so you'd see such occurrences twice as often.

I think at the very least you'll find that the number of shown hole cards is 2x the number of hands.

To use any combinatorics as part of the analysis, the events under study should be independent. Of course in Texas Hold-Em, the seven cards that players make their hands from are not independent. Another way of saying this is that the "deals" that OP is querying are not independent presuming that each "entry" in his query is the 7-card collection of cards of each player which went to showdown (may or may not include his own hole cards if he did not go to showdown).

I am sure that this is obvious, but just in case it isn't, suppose poker is played with a 200 card deck and there are 75 players in each hand. Two deals go to showdown and everybody is all in on both deals. Then, by one tally, there are 150 "entries" in the hand history database (75 * 2). And you can see how many of these "match" any other entries. However, of course, there were really only 2 boards dealt so that saying that the matches could come from 150 entries is not quite correct when we perform the standard independent events calculations.

That is why it is much better to simply look at each deal's board as the "entry" under consideration. This would assure that meaningful analysis be undertaken to look into whether the deals are "random enough".

I have made the same point several times in this thread without any headway, so I don't expect any positive movement in this direction.

Peace.

why so complicated?

I have selected only those matches where the deal (even my own deal) went to showdown.

1. i have a sample from pokerstars (texas holdem)
2. with my sample i have 562.742 unique deals (each deal connected to a player name) that saw showdown
3. what is the expected probability of finding a match with the following pattern...

- the 2nd deal matching the specified one and they have been played in two different hands.
- suits matter for board cards
- hole cards are the same (suited/offsuit)
- flop is unordered
- order of turn/river matters.

Example:

Deal A:
Holecards: AJo (just focusing on suited or offsuite)
Flop: 5c3s2h (order doesn't matter)
Turn: Js
River: Td

Deal B:
Holecards: AJo (just focusing on suited or offsuite)
Flop: 5c2h3s (order doesn't matter)
Turn: Js
River: Td

HandNumber Deal A != HandNumber Deal B

You mean I can't use the amount of independent deals (562.742) for my calculation. Instead I have to count the amount of hands played within this sample?

If you are just considering the ranks of the hole cards, there are only 91 unique combinations of ranks (13c2=78 plus 13 pairs), not 1326.

If you are just considering the ranks of flops, there are only 442 unique combinations of ranks (13c3 plus 13*11 paired flops plus 13 triplets), not 19,600. And I'm pretty sure that's overcounting the ones that are reduced in probability by the hole cards that are already shown down that hand, so it varies by number of hands shown.

So for ranks only, we have something less than 91*442=40,422 possibilities.

If you did consider suits on the flop only, the combos is still less than 19600 for the same reason as above. 19600 is when only one hand is known, and we always know at least two. You have to group them to get the real probability for each number of hands shown. Considering suits, with two hands shown down, there are 48c3=17296 flops. With three hands shown down, there are 46c3=15180 flops. Math for full board is the same, just choose 5. I couldn't tell if you are just matching flops.



No, just the ones where the hole cards are known and examined. Count all shown hands for your denominator.

OP, can you tell us how many different deals in your database went to showdown? Is it 562,742?

For example, if two players went to showdown, one with (Ah, Ks) and the other with (Qs, Qc) and the board was [8d, 4h, 2c, Js, Kh], does this count as one or two in your 562,742 tally?

Thank you.

Think its you that's making things complicated...