The situation after the flop when the winning combination you want to and on the turn and the river (the fourth and fifth community cards) came 2 must be cards, called Texas Hold’em bekdoor (backdoor draw), or runner-runner. For example, you have at the hands of 2 hearts and the flop came another. Then for a flash is necessary that the thorn, and the river were hearts. This bekdoor flash. Usually strong players «do not go» for his two, because the probability to obtain them is very small. In the example on the turn you want to come one of the remaining 10 worms from the 47 cards unknown to us. The probability of 10/47. If this happens, then on the river need the following worms, the chance appearance of which 9 out of 46. The overall probability of the arrival of his two worms is (10/47) * (9 / 46), ie approximately 4.2%, or 1 to 23. Therefore, in most cases the most appropriate solution for bekdoor flash is folded. However, in some situations, especially when there is a chance to improve his hand high, and buying other cards, it makes sense to take the risk. This decision also affects the ratio of the size of the bank and the necessary rate position in the game, the number of remaining players, their strength and your familiarity with the tactics of their games, and other factors. As an illustration, I would like to cite a few examples. They are taken from real games in limit hold’em, and, although not as academic as a specially devised sketches, quite revealing.
Example 1 (limit $ 15 – $ 30, blinds are $ 10 – $ 15). In the hands of the 7 A peak of the peak of the big blind. Solid player for us makes a raise. We know that he is attacking with a couple dozen or older, as well as AK or AQ. A player in middle position calls, as well as sitting on the button. Others fold. We call. 4 players left in the bank $ 130. The flop comes 9 Peak 8 Peak 2 Peak, giving us the opportunity to senior bekdoor flash and straight. We say check, attacking pre-flop bets, and the other two players fold. What?
Answer: equal. The bank had $ 145, and call costs $ 15, ie a ratio of about 10 to 1. In almost 13% of cases on the turn or the river comes A, giving us a couple. At the same time, remembering with some cards before the flop is attacking our opponent, we can assume that he will win if the two A (one possible combination), AK (8 combinations) and AQ (8 combinations), so in 17 cases. But in 24 cases, he may be couple K, Q, J or 10. Thus the probability of victory by the appearance of A is 13% * 24 / (24 +17) = 7.6%. At the opening 7, we are winning, with 24 possible combinations of enemy AK or AQ, and play any of the alleged pairs (27 combinations), so this gives another 13% * 24 / (24 +27) = 6.1%. More than 4% – a chance to bekdoor flash, plus almost 4% bekdoor straight. Of course, this is a game, and can be mass variety of scenarios, but the probability of victory of more than 20% rate in 1 / 10 the bank is fully justified.
Example 2 (limit $ 30 – $ 60, blinds are $ 20 – $ 30). We in the big blind 9 of Clubs 8 of Clubs. The player starts on the left raise, the two meet, the small blind – pastured. Attacked the enemy, according to our information, so usually comes in early position with a pair of J and older or AK and AQ. We call, in the bank $ 260, and the flop comes 10 clubs 5 diamonds 2 peak. We bekdoor straight flush, respectively, as the chances of just a flash and just straight. Our word – check next bet, pass-pass. What?
Answer: equal. We make several assumptions. The opponent or one of the 24 possible pairs, or A with K or Q (32 versions). At the opening of 8 or 9 more likely that the best hand, get at us. Also there is a nonzero probability that the arrival at the turn of one of the cards are not satisfied with his opponent will not raise rates before the River and has a real chance to see the fifth card for free. In this case, we reiterate the opportunity to pull 8 or 9. If on the turn Q (but not the enemy and not a pair of AQ Q) or 6, then we straight to the hole, and there’s a free chance to pull the “chokes” it on the river card. It is also worth considering that after our collagen on the turn you can buy an amicable Clubs (10 cards), J (no clubs, it has already considered – 3 cards), 7 (same as – 3 cards), and referred to 8 or 9 (6 more maps) . Total 22 out of 47, not counting «leaky» chance.
If before Rivera was something potentially better than one pair, will attack themselves, with the pair – just check and call on the bet of the enemy. Assume that the opponent about half the answer to our bet – having initially high pair, having bought it, or suspecting our bluff. As for the life of pessimists, considering also that we lose, that is, fold, if the turn did not come, and the enemy will increase your bid. Nothing – it is one of the 25 remaining cards useless to us, and in this case, $ 30 for the answer will prosazheny. Statistically, it is $ 30 * (25/47), which is about $ 16. But there is a possibility and great troubles – we are buying on the turn you want, we respond to the bid of the enemy and do not buy anything on the river. Under the flash is 10/47 (clubs on the turn) * 31/46 (no clubs and our pair), ie about 14%. Under straight – 6 / 47 (no J of clubs or 7) * 32/46 (not straight and pairs) = 9%. Total in 23% of cases, we will lose $ 90 ($ 30 after the flop and $ 60 after Thorne) – statistically about $ 20.
Our chances to collect flash, straight, two pair or three in total about 8%. If this happens, the prize is $ 290, which are already in the bank, plus $ 60 set on the turn, and in half the cases, we expected an additional $ 60 on the river, which we will now consider both the $ 30. Total $ 380 * 8% = $ 30 rounded up. In addition to these combinations, with a probability of 22% we would get one pair, which in 43% of cases the opponent will lose, and in 57% – will win. (There is still a chance that we’ll buy this pair on the turn and his opponent – on the river and the resulting benefit, but it can happen less than 1% of delivery, and is not taken into account in the imputation.) Respecting the enemy, not we expect that he will respond to our bet after the river with a combination of AK or AQ, respectively, 22% * 57% of our winnings will be $ 350, that is statistically $ 44. We also bring in one pair would have to bet after the river, and we will lose $ 30 on the flop + $ 60 + on the turn and another $ 60 on the river, that is $ 150, in 43% of cases. Result 22% * 43% * $ 150 = $ 14, that is, with one pair of hands, our average gain is $ 44 – $ 14 = $ 30.
Cumulative total: – $ 16 – $ 20 + $ 30 + $ 30 = $ 24, that is, while fitting the rates we have a positive mat. expectation.
Example 3: (limit $ 30 – $ 60, blinds are $ 20 – $ 30). We K peak 10 peak in late position. Nobody comes into play, and attacking the blinds we raise. Player on the button – reraise, both blind pass, we – Call. At the bank $ 230 and two players. Flop – 7 of Clubs 6 of Diamonds 5 peak, we bekdoor flash and Senior straight, and the chances of a high pair. We check the opponent bet. What?
Answer: Pass. Value for the required rate to the bank about 1 to 9, and 6 card suit us for a higher pair. But the problem is that not known whether the couple if it comes, is really the eldest, whether the opponent, who aggressively attacked, AK came with K or A-10 with 10 on the turn. Or simply have the older couples in her arms. 4% chance to buy two peaks on the flash + 1.5% on 8 and 9 for the straight – it is too small to risk the extra money. In this case, seems to bet on the flop is not limited to – if it comes from a seemingly suitable cards on the turn would have to respond to the opponent’s bet, and from early on to it, position.
Example 4 (a limit of $ 10 – $ 20, blinds are $ 5 – $ 10). In early position in our hands A Q tambourine tambourine, and we begin to raise. Next to us, 2 other players in middle position and the big blind for equality. Five players and $ 105 in the bank. Flop K peak 8 of Diamonds 3 trefdaet hopes for a senior flash or a couple. The big blind bet. What?
Answer: Pass. I made a bet on the first hand in a situation where for him, a crowd of 4 players, and even responded to a raise before the flop almost certainly pair, and then set K. Especially with such a colorful and nestreytovom flop. Save (and it is not a fact) can only A, or two of their diamonds. While the ratio of bids to the bank almost 1 in 12, while the probability of A – 1 to 15, but the main problem is that for us three more players who have quietly increased their bets before the flop, and it is quite possible that someone will increase now. I have to pay again. Extraordinary.
Example 5 (limit $ 10 – $ 20, blinds are $ 5 – $ 10). We are in the big blind and play a free call with 10 clubs 6 of clubs. In the game there were 5 players, including the small blind, and formed a bank at $ 50. The flop came 9 Peak 7 of Diamonds 3 of clubs, offering bekdoor flash and straight with one hole. We check, bet-call-call-pass. What?
Answer: Pass. At the bank $ 80, have put $ 10, ie 1 to 8. Buy on Turn 8 it is possible with a probability of 1 to 11, and bekdoor flash, even if they come their two clubs, is likely to be a little older. To all other one of the three opponents can hold J-10 and the opening 8 to receive a senior straight, and it cost us very dearly.
These examples show that the play in situations when you need to buy two of your cards should be very deliberate and calculated manner. However, it can be said about all aspects of the game of poker.
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