What are the odds, how big does the pot need to be

3-6 Mirage game.


I am on the button with 7h6h 4 people limp before me, I very gladly call sb completes and bb checks. - 21 in pot


Flop comes Kh, 4d, 3c. sb bets, bb calls, 2 more callers to me. 33 in pot


so anything better than 11:1 I call - right?


two cards to come,

inside straight draw is 4.1:1 (16.5%)

runner runner flush draw (although a weak flush) is 25:1 (4%)

so I am already at 3.9:1 right?

I assume SB has some king - maybe two pair with the rags on the board, so I know that it would take at least trips to win.


what are the odds for a runner runner 3 of a kind?

how do I figure that for both the 6 and 7 to add ot the pot odds. I am sure that it is a long shot (is it 4/46 * 4/47 for each - if so, how does that calculate into odds) I can add an additional 1.5% to the 20.5% that I already have and I am to about 3.5:1 - it seemed like a very easy call. + the implied odds for the nut st8


Long story short, turn and river come heart rank is insignicant to the outcome because no one came alive and the board didn't pair, with everyone calling the turn (now it is a 4.1 (19.6 with the flush draw and 10.5:1 (8.7%) 13 outs for for a 2.5:1 the and the sb called the river - so I took down a pretty nice sized pot (63 at turn, 75 at river). when I turned over the cards, the sb mucks and says HOW COULD YOU HAVE CALLED THAT? I said, just feeling lucky today... In reality, I didn't want to be Mr. Poker at the table because I was getting an Old Man reputation for throwing away 8 of 10 hands preflop and usually raising when I played. Didn't help, still got hammered in the session on some rough rivers, but I just wanted to make sure that I figured that out right and it was not a loose play. The inside st8 draw alone was more than justified with a $33 pot at that point.. right?


Thanks

Kevin

You can probably call the flop with a little less than 11:1--you have implied odds working for you as well. If you make your straight, it is very likely to be good, probably more likely than your typical straight. You made a proper call on the flop, and once the second heart comes in, you certainly see the river. Assuming you raised (or bet) the river, I'd say you played just fine. I wouldn't worry about runner-runner possibilities when calculating odds. If it truly is a borderline situation, the runner-runner possibility might tilt things in favor of calling. And don't worry about what anyone says about how you played your hand.


As for the odds of making a running three-of-a-kind, a possibility that I only consider when my thinking is at its fuzziest, you only have three cards of each rank to hit, not four. There are six cards that you can hit on the turn that will give you a pair (three 7s and three 6s) and having hit your pair, you have two cards to make trips:


(6/47)*(2/46) = .0037 = 269:1


That's like 1/6 of an out. Stranger things have happened. I hit runner-runner quads the other day at $15/30. But I only needed to spike the set on the turn to win.

Super easy call on the flop drawing to the nuts on a rainbow board. The backdoor flush draw is pure gravy. Automatic call. On the turn picking up the heart makes another easy call. Ni han sur.

Good hand Kevin, I think you played it well.


I have a general question for all posters, do you guys often calculate your odds at the table, or do you know approximate odds in certain situations (that you've worked out ahead of time), and use those for a back-of-the-envelope when you have to make a fast decision?


I don't try to work out my odds of making a hand at the table. Rather, I study odds outside of the game to get a feel for them, and then use my gut feel at the table. Of course, I try to keep track of the pot to know what the pot odds are.

thanks for this interesting post


you need to make some very slight adjustments to your calculations - your odds equivalents to your percentages are incorrect


(in fact the following figures are still slightly out because we are looking at a situation where we are actually working out the odds on "a single two card draw" (your runner runner scenario) - but that is not the case in hold'em - you are going to receive two one card draws - and often with two one card draws you won't be able to call the second bet because of pot odds, even though you have included the result of the second one card draw in your initial single two card draw calculations - in other words, the times that the inside straight would have filled on the river where you have had to fold on the turn, because of too low pot odds at that moment, have become partial-bet losers instead of full-bet winners)


an inside straight draw is 43 to 4 = 10.75 to 1 (8.5%) on the turn and 42 to 4 = 10.5 to 1 (8.7%) on the river - therefore it's 5 to 1 (16.5%), (100 divided by 16.5 = 6, 6 minus 1 = 5 to 1 odds), to hit it on either the river or the turn


runner runner flush is 22.8 to 1 (4.2%)

(calculated from 37 to 10 = 3.7 to 1 (21.3%) and 37 to 9 = 4.1 to 1 (19.6%))

(but including the 5h card already dealt with in the straight calculations, for ease - this won't make a huge difference to the end result)


runner runner trips for the 7 is 332 to 1 (0.3%)

(from 44 to 3 = 14.7 to 1 (6.4%) and then 44 to 2 = 22 to 1 (4.3%))


runner runner trips for the 6 is the same at 0.3%


therefore you need 3.7 to 1 (from the total of 21.3%) to make a single two card draw


in this case the "single two card draw" is in fact two one card draws, made up of a $3 sb and a $6 bb = $9 (assuming no raises)


you will win the $33 plus at least $6 = $39 for the two relevant bets of total $9


so you are getting potentially at least 39 to 9 = 4.3 to 1 at this point so a call is probably ok if you don't expect a turn raise


however, once the turn card is dealt you will have to recalculate to see if you are still getting the odds to call a turn bet


if you didn't turn a flush card or a 7 or a 6, then you need 10.5 to 1 to draw for the insider (you won't be getting these odds so you will have to fold)


if you turned a 7 or a 6 you need 6.7 to 1 to draw for trips or the insider (you will probably just about have these odds to call if there is no raise)


if you turned a flush card you need 2.8 to 1 to draw for the flush or the insider (definite call )

knowing the odds for the "normal" calls is vital in limit poker, particularly


i would hazard a guess that even bobcards would agree with this - even though i have never seen him actually fold a hand, i am sure that bobcards knows instantly and exactly the odds involved with his hand in comparison to his opponent's likely holding


then he factors in the odds of whether or not his opponent will raise or call or fold and he acts accordingly - meaning of course he raises


the easiest way to get to grips with commonly required odds figures after the flop is shown is to turn your hand into likely outs - say, if you think you can only win if you fill your inside straight you have 4 outs - if a flush or a straight will win you may have 12 outs - etc


you know five cards, leaving 47 unknown cards in the deck, so catching one of your 4 outs on the turn is 43 to 4 = 10.75 to 1 or (rounded off) 11 to 1 pot odds required to call a bet


although the odds change a little for the river, they don't change much, so your one set of calculations suffices for all practical purposes


(catching one of your 4 outs on the river is 42 to 4 = 10.5 to 1 or (rounded off) 11 to 1 again)


make and memorise a chart of odds in terms of outs on the flop from 2 outs down to 15 outs and you should have everything you need for most hands

Mike,

Thanks for taking the time to explain that to me. I have a small diary sized book that I carry with me that has outs and odds for 2 cards to come and 1 card to come. For example, It says that a 4 flush is 1.9:1 on the turn and 4.1:1 on the river, likewise an openended str8 draw is 2.2:1 on the turn and 4.7:1 on the river. Is this incorrect as well - or in this case are the odds correct because I am still 4 flushed in and open ended at the turn and river. Thanks again for taking the time to explain. Understanding these odds have helped improve my game 10-fold. I can only imagine how much it improves when I actually start calculating odds correctly! (haha)


Kevin

"it says that a 4 flush is 1.9:1 on the turn and 4.1:1 on the river, likewise an openended str8 draw is 2.2:1 on the turn and 4.7:1 on the river."


i'll try not to repeat too much of what i said earlier but i'll do every stage of the calculations so that you can check others yourself with the same methods - if you want any help off the boards my e-mail address is simplyred_2000@hotmail.com and my home is always open to other poker enthusiasts


if you've got a four-flush after the flop you have seen five cards


there are 9 flush cards in the 47 cards you haven't seen - they might well all be out in other players' hands in reality but that does not affect odds calculations in theory


the next card being your flush card results in odds of 38 bad cards to 9 good cards = 38/9 = 4.2 to 1


to turn this into a percentage you add 1 to the 4.2 and divide it into 100 = 100/5.2 = 19.23% chance of being a flush card - which means out of every 100 deals you will get a flush card 19.23 times in the long run (you don't need to understand why, you just have to do it! if you want to do the opposite and turn percentages into odds you take the percentage from 100 and divide it into this new figure : 100-19.23 = 80.77; 80.77/19.23 = 4.2 to 1)


so if you are in a 3-6 game and you have a 4-flush you need 4.2 x 3 = 12.6 in the pot to call a 3 bet to break even in the long run ( you will lose 4.2 times and win once :- you will lose 4.2 x 3 = 12.6 and you will will 1 x 12.6 = 12.6)


of course you then have a second bite at the cherry on the river if the turn doesn't flush you


this time you have seen 6 cards and there are still 9 flush cards in the 46 cards you haven't seen, so your odds on filling your flush are now 37 to 9 = 4.1 to 1 = 19.6%


so if you are in a 3-6 game and you have a 4-flush you need 4.1 x 6 = 24.6 in the pot to call a 6 bet to break even


this is the reason i keep saying you should only look at the next card, not the next two cards, when you are seeing if you have correct pot odds at any point in a game (forgetting the concept of implied odds - likely odds - for a moment)


in our example, you could easily have $10 in the pot at the flop - someone bets $3 - you have your $12.60 necessary to call - pot becomes $16 - you don't turn your flush - he bets $6 - pot is now only $22 - you don't have your required $24.60 in the pot to call and you "should" fold ...


(... of course, you can argue here that if you make your flush and then win another $6 on a river bet your implied odds or implied pot is $22 + $6 = $28 = over your required $24.60 - but that is not a definite mathematical fact - that brings us back to gambling that other players will give you money even though they see 3 flush cards in the centre; see you jumping up and down; see you grinning from ear to ear; etc, etc)


... if you don't fold you will lose 4.1 x 6 = 24.60 and win 1 x 22 = 22 = loss of 2.60 every 5.1 hands in the long run = 2.60/5.1 = 0.51 per similar hand played -- play 100 similar hands and you have lost $51


now, to calculate the odds of getting your flush on the turn or the river, the easiest way is to look at the percentages - but, strangely, in reverse


you are 19.23% likely to get your flush on the sixth card


which means you are 80.77% of the time NOT going to flush


and 80.40% of the time you are not going to flush on the river either


so for 80.77% of the times you haven't flushed on the turn you end up without a flush after the river too


which is 80.40% of 80.77%


which is 80.77 x 80.40/100 = 64.94% of all two card draws


turning this into odds (see above) then it's 64.94/35.06 = 1.85 to 1 that you WILL flush if you take two cards


however, this is the crucial bit you have to understand , as i said earlier, and if you don't understand it you will lose a fortune in the long run


these odds, while correct in one respect, are only correct if you get the two cards in one go


if you have a pot of $5.55 and you call the $3 bet thinking you are getting your necessary 1.85 to 1 pot odds, what happens in the 4.2 cases out of 5.2 deals where you miss you flush?


the pot is now $8.55 - your opponent bets $6 - you are only getting pot odds of $14.55 to $6 = 2.4 to 1! a long way short of your necessary 4.1 to 1 to catch your flush on the river


the only way you can possibly go along with this "flush in two" odds is if you are getting 1.85 to 1 against $3 + $6 = $9, or $16.65 on entry into the pot


in other words, if the pot is $16.65 you can call the $3 bet only if you KNOW that you will get the chance to call only $6 on the turn ( = no raise is allowed!!)


the pot will then become 16.65 + 3 (your call ) = 19.65 + 6 (his bet) = 25.25


BUT the irony to all of this is ...


... what odds are you getting to call the last $6 bet?


25.25 to 6


which equals 4.2 to 1!


SO, you are back to the easier square one "next card" odds!


forgive me if i have over-simplified the calculations - my intentions are good - i don't know what level your math skills are


please let me know if i have helped at all


thanks


mike