Overall odds of being ''Rivered''?

[Dodger]

Please stay with me on this one, I've tried not to ramble too much! Have looked on several sites but can't find an answer...:wall Starting with a definition from Urban Dictionary... Rivered. ''The loss of a winning poker hand on the very last card dealt; it is frequently followed by shock, tears, and a severe need to blow things/people up. 3:36pm All in preflop...equal hands...I hit a better hand on flop and turn and get rivered by my arch nemesis. Anybody with the name of Sandy that you happen to know, go ahead and punch him/her in the face for me. thx...'' :D This problem has been bugging me for quite a while now, regarding wins on the river, so here goes... Texas Holdem...best 5 cards from 7...(7x6x5x4x3)/(5x4x3x2x1) = 21 possible combinations. Not counting the river card there are (6x5x4x3x2)/(5x4x3x2x1) = 6 possible combinations. So in every game you play, your best hand will include the river card 15/21 times...over 70%! So it follows that, when a hand goes to the river, 70% of the winning hands will contain the river card. Of course this is not to say that 70% of all hands are won on the river card, but reckon it is fairly solid maths that there is a 70% chance of the river card being included in that hand. {This statement in itself sounds a bit dodgy to me, but it is not all important to the problem so we can let it slide!} Right...still here?...good...my problem is this: Just what % of games are won on the turn of the river card? or more precisely, what is the % of games where a player gets rivered, the river card gives a win, when on the turn the hand would have been a loser??? {A simplistic example of you holding AA with board AA47 then K...this would be in the ''river card included in winning hand'' count but not in the ''won on the river'' count, so the 70% goes out the window!} With 2 x A Levels in Maths, I can't even start on this one. Reckon it would require analysis of played hands, the maths may be just too complex, for me at least. What prompts me to ask the question is the proliferation of people moaning about being beaten on the river, when I reckon it is mathematically much more likely than most players realise. Personally, I feel that at least 33% of hands that get that far will be won on the river. Sure it is not going to be as low as 20%, nor as high as 50%, just a gut feeling and so frustrated that I can't back it up with the maths. {Thinking out loud here...if say 40% of hands get to the river and only 25% of them make river wins, then that would be 10% of all hands being river wins. So...In a 10 player stt, played over about 60 hands, you would expect to see 6 rivered wins! Play 10 STTs a day for a year and you'll see...Jesus wept, 21,915 rivered hands!}

[Hedonist]

Re: Overall odds of being ''Rivered''?

{A simplistic example of you holding AA with board AA47 then K...this would be in the ''river card included in winning hand'' count but not in the ''won on the river'' count, so the 70% goes out the window!}

If you change the above to holding AA with the board AJ47 then if your opponent is holding TQ the K would river you. He has 4 Kings to win with and 42 cards to lose with so you will expect to win 42 out of 46 games, if you win you forget about them. The 4 games you lose are the ones that are posted on forums as bad beats and will be remembered. To do a mathematical analysis you would need to calculate how many cards can win on the river against a better hand, this is much to complicated for me to work out.