R
Ranger390
Rock Star
Silver Level
I've been meaning to ask this for some time regarding counting outs to a draw, particularly a flush draw. Here's the situation: Texas Hold'em, Full ring game or tournament table of 10 players. You look down at two suited cards and call the preflop bet. The flop shows two additional cards of your suit, so you have 9 outs to your flush. The 2/4 rules (remember, there is a slight error due to rounding) says that you will hit your flush 36% of the time if you see both the Turn and River cards. The odds of hitting on the Turn is 18%. But, if you miss on the Turn, the odds are still 18% that you will hit on the River.
Here's my question, when figuring outs, ALL unseen cards are counted as potential outs and there are 9 remaining cards of your suit that are unseen. However, ALL unseen cards are not currently in the deck, as each player at the table has already been dealt two cards each. That means that there are 18 cards that have been dealt to the to the players that you can not see and that can not be dealt of the Turn or River. In a thoroughly suffled deck, that means that the odds are that 4.5 of the cards of your suit were dealt to other players and are unavailable to be dealt on the Turn or River. So, out of the remaining 29 cards in the deck, only 4.5 of your suit remain. That's an 18% chance of completing your flush on the Turn and River instead of a 36% chance. OR, a 9% chance of hitting on the Turn and 9% to hit on the River. Under these circumstances, the odds of hitting your flush are not as attractive.
While it would be more difficult to figure odds in this fashion for other types of drawing hands, why are the odds of other players already being dealt the cards that you need not figured into odds calcualtions? Why is this reasoning off base? Is my math really fuzzy???
Here's my question, when figuring outs, ALL unseen cards are counted as potential outs and there are 9 remaining cards of your suit that are unseen. However, ALL unseen cards are not currently in the deck, as each player at the table has already been dealt two cards each. That means that there are 18 cards that have been dealt to the to the players that you can not see and that can not be dealt of the Turn or River. In a thoroughly suffled deck, that means that the odds are that 4.5 of the cards of your suit were dealt to other players and are unavailable to be dealt on the Turn or River. So, out of the remaining 29 cards in the deck, only 4.5 of your suit remain. That's an 18% chance of completing your flush on the Turn and River instead of a 36% chance. OR, a 9% chance of hitting on the Turn and 9% to hit on the River. Under these circumstances, the odds of hitting your flush are not as attractive.
While it would be more difficult to figure odds in this fashion for other types of drawing hands, why are the odds of other players already being dealt the cards that you need not figured into odds calcualtions? Why is this reasoning off base? Is my math really fuzzy???