Flop decision

[RoodyPooh]

Everyone folds around to you and you complete in the SB with the 6 /images/graemlins/club.gif 7 /images/graemlins/club.gif and BB checks

Flop: 5 /images/graemlins/spade.gif 8 /images/graemlins/heart.gif 9 /images/graemlins/heart.gif

Just as the flop comes out the BB fumbles his cards and shows the T /images/graemlins/heart.gif J /images/graemlins/heart.gif and you decide to give the guy a break and show him your cards also.

What's the correct play for each player?

[Bozeman]

nuts should check call, jt should bet. on the turn, situation is reversed if a blank comes.

Who is better off in this situation?
Suppose there are only 2 small bets in the pot (sb limped and bb checked preflop).
14/45*3=+.933sb for jt when he hits on the turn
31/45*(30/44*-3+14/44*5)=-.313sb
total=+.62sb
(therefore 67 makes 14/45*-1+31/45*(30/44*5+14/44*-3)=1.380sb, so they add to 2 as they must). So, even though JTs is the favorite to win the hand, and will always see the river, 67 does better because of implied odds on the turn. If 76 would never fold, he actually loses money on average (imagine the situation where his hand is apparent, but he imagines bb has twopair or a flush draw).

Craig

[bigpooch]

The J /images/graemlins/heart.gif T /images/graemlins/heart.gif is a slight dog, isn't it? Of the
C(45,2)=990 combinations of cards that can show up, this
hand misses on C(31,2)=465 combinations since one of the
sevens is in the other hand.

Thus, the 76 just keeps betting until he gets beat. The big
draw just has to keep calling until the end.

How thin is this edge? Well, suppose the 76 checks and the
JT checks. Now when the JT misses the turn, the 76 bets
and wins (since there are now only 14 outs of the 44 cards
remaining which isn't quite 1/3). Even though the 76 plays
the hand suboptimally, his expectation is (+31-14)/45 x 0.5
BBs= +17/90 BBs. On the other hand, if the play is proper,
his EV would be 14/45(-1.0 BB)+(31/45)x(14/44)(-2.0 BB)+
(31/45)x(30/44)(+2.0 BB)=94/495 BBs. The difference is just
1/990 BBs, which is just 1/C(45,2)!

[Bozeman]

465/990=46.97%<50%

So JTs is a favorite to win by the river.

But now we have a weird situation: 76 does (slightly) better if there is a bet on the flop, even though he is an underdog on new money going in on the flop. But he definitely doesn't want to be raised on the flop (14/45*-1.5BB+31/45*14/44*-2.5BB+31/45*30/44*2.5BB= 79/495<17/90. So neither player should bet this flop! Then EV76=17/90, EVJTs=-17/90, or discounting the preflop sunk cost, EV76=17/90+1/2=31/45=.689BB, EVJTs=1/2-17/90=14/45=.311BB.

So my first answer was wrong, for this unusual case, 76 benefits from having a pot small enough than he can make JTs correctly fold.

If there is any more than x SB (x VERY slightly larger than 2) in the pot preflop, then my original analysis holds.

Craig

[Mike Haven]

i found this to be a very interesting situation indeed, and i changed my mind several times during my analysis, (which
i hope is correct!), which led to a somewhat incredible conclusion

from a simulation programme we see that JTs will win 53% of the time if two cards are taken, and 32% of the time if the turn card misses

as there are only 14 cards out of the 45 available that help JTs, the odds on JTs hitting on the turn are 31 to 14 or 2.2 to 1

there are 2sb in the pot, so if 76s bets then JTs is getting 3 to 1, more than the 2.2 to 1 needed to chase

therefore 76s can't bet into JTs

it looks like JTs can bet as if it is called JTs is getting 3 to 1 for its 2.2 to 1 shot

but then 76s could raise because it would be forcing JTs to lay 2 to win only 4 on that round, less than the required 2.2 to 1

this makes it look like neither hand can bet on the flop

however, we know that JTs will win 53% of the time if two cards are taken, so therefore we know that JTs needs to receive odds of only 47 to 53 or 0.89 to 1, less than evens, to see both cards, to win

because of the 2sb already in the pot, it doesn't matter how much 76s bets for JTs to receive more than evens - if 76s bets "x" then JTs receives "x+2" to "x", which is better than "x" to "x", which is evens

so, we have to go back to the situation where it looks like JTs can bet but shouldn't in case 76s raises

it turns our that it doesn't matter to JTs if 76s raises, because JTs knows that it will always have the odds on any turn bet to call (if JTs has not already won the hand on the turn) to see the river, (only needs 2.14 to 1), and we know that if JTs sees both the turn and the river then it will win 53% of the time in total

in fact, i shouldn't say "it doesn't matter to JTs if 76s raises" - JTs would love 76s to raise because then JTs wins 53% of a bigger pot

(of course, 76s knows this now, so 76s wouldn't raise)

therefore, the answer to the question is that JTs will, if given the opportunity, bet the flop and bet the turn, winning 53% of all hands played

which leads us to the amazing conclusion that as soon as JTs bets the flop the made straight must fold!

QED

[sublime]

[ QUOTE ]
which leads us to the amazing conclusion that as soon as JTs bets the flop the made straight must fold!


[/ QUOTE ]

Gotta love poker. Math tells you to fold the best hand(at the time)

Would/Could you?

[Mike Haven]

Math tells you to fold the best hand(at the time)Would/Could you?

In this particular situation, no, I would not.

For two reasons.

First, that I would hope he didn't know the best course of action, and would fold to my "bluff" bet on the flop.

And second, that this is close enough to being evens, (for me, personally), to gamble that I would come out on the right side of the gamble. (When we talk about 53% we are looking at thousands and thousands of exactly similar hands being played. If we played three such hands in our playing lifetime, which is probably a huge over-estimate, we could easily win two out of the three - "if our luck was in on the day"!)

[chief444]

The straight has a 47% chance to win (as you said). There are two small bets in the pot now (on the flop). If JT bets and the straight calls, there are 4 small bets in the pot. If JT wins on the turn, the straight folds, therefore losing one small bet (on the flop) and no more. If JT misses on the turn then the straight bets and JT calls taking the pot to 4 BB's and costing the straight so far 1.5 additional BB's. Obviously, there will be no more bets called on the river.

So,
31.1% (14 outs/45 unseen cards) of the time the SB loses .5 BB's.
21.9% (53%- the 31.1% chance JT wins on turn) of the time the SB loses 1.5 BB's.
47% of the time SB wins 4 BB's.

Therefore EV of the straight calling the flop is:
.47*4-.311*.5-.219*1.5 = +1.396 BB's

So by my calculations, the straight should check/call the flop and either bet or fold the turn. Is this correct?

I suppose my actual reply to this would be to ask...What is the Rake?

[sublime]

[ QUOTE ]
In this particular situation, no, I would not.

For two reasons.

First, that I would hope he didn't know the best course of action, and would fold to my "bluff" bet on the flop.

And second, that this is close enough to being evens, (for me, personally), to gamble that I would come out on the right side of the gamble. (When we talk about 53% we are looking at thousands and thousands of exactly similar hands being played. If we played three such hands in our playing lifetime, which is probably a huge over-estimate, we could easily win two out of the three - "if our luck was in on the day"!)

[/ QUOTE ]

Well those reasons are good enough for me /images/graemlins/smile.gif

[Mike Haven]

Oops.

Thank you - that's yet another twist I missed.

47% of the time the made straight will win the pot of 4BB, 2.5BB profit.

With the scenario so far he loses 31 x 0.5 = 15.5

And 21.9 x 1.5 = 31.85

And wins 47 x 2.5 = 117.5

Total win = 70.15BB in 100 hands.

I guess he does play after all! Sorry for my previous bull.

With this result, I'm now suspecting the strategy has to change for JTs! ...

[chief444]

Thanks Mike.

[ QUOTE ]
With this result, I'm now suspecting the strategy has to change for JTs! ...

[/ QUOTE ]

I had the same thought.

Following through from JT's perspective and assuming the straight will check/call the flop:

EV of bet on flop:
31.1% of time JT wins 2BB
21.9% of time JT wins 4BB (assuming straight will bet turn)
47% of time JT loses 1.5BB
EV = .311*2+.219*4-.47*1.5 = +.793

EV of checking through on flop:
31.1% of time JT wins 1BB.
However, JT would now be correct in folding on the turn (2BB's in pot including straights turn bet for 2:1 pot odds, but 2.14:1 chances of making hand on the river)
EV = .311*1 = +.311

So it looks like JTs should bet the flop. I'm thinking that this works out exactly as one would expect at first glance. That is the more money that goes into the pot on the flop the better it is for JTs (with a 53% chance of winning) and the worse for the straight. But because of the money already in the pot plus the fact that the straight has better implied odds for the turn (JT actually has reverse implied odds for the turn) the straight is clearly staying in the hand.

Very interesting hand. I'm sure if I was playing either one live I would be betting/raising the flop. It is interesting though to see an example where you should check/call with the nut hand.

Moral of the story....always bet/raise your straight flush draws.

[chief444]

Actually, I need to edit my comment somewhat. Based on the numbers it looks like the straight actually makes out best if there is exactly 1 SB from each player on the flop. So even though J10 is a 53% favorite, the straight wants J10 to have the odds to chase to the river. But any raises on the flop beyond the initial bet and call benefit J10.

But looking again,
Straight's EV with no bets on the flop is
.689 (turn odds of J10 missing) * 1 BB already in pot = +.689

And I already calculated the straights EV with one bet from each going into the pot to be +1.396 BB.

So how can exactly one bet from each on the flop benefit both? Now I'm just confusing myself. Can someone straighten me out here or explain this? I must have made a mistake somewhere.

[AJo Go All In]

[ QUOTE ]
there are 2sb in the pot, so if 76s bets then JTs is getting 3 to 1, more than the 2.2 to 1 needed to chase

therefore 76s can't bet into JTs

[/ QUOTE ]

you are fundamentally misunderstanding the concepts at work here. if you are the favorite, you by definition making money with every bet that goes in to the pot. the pot size is completely irrelevant. if you are a 2-1 favorite, and there are 10 million bets in the pot, you should still bet. of course, you would rather the other guy fold than call, but betting still makes you money. this is actually pretty basic and important to understand.

[TomCollins]

JT wants as many bets as possible on the flop. Once he bets and is called, he has the odds to stay til the end.
67 wants no money in until the turn, which he wants as much as he can get in if JT doesn't hit.

Supposed somehow 2 bets got in on the flop. JT will have a higher EV now than before. Because if he misses, 67 will bet, and he is getting 4-1 on his call, plenty to chase.

So he strikes out 47% of the time, and loses 2BB
He hits on the turn 31% of the time, and wins 3BB
He hits on the river 22% of the time, and wins 5BB.
So his EV is 1.09BB

Whereas he he strikes out 47% of the time, and loses 1.5BB
He hits on the turn 31% of the time, and wins 2BB
He hits on the river 22% of the time, and wins 4BB.
His EV is .795. So JT would love for 2 bets to get in, he just needs help from 67, which he won't get.

[chief444]

That much is clear, I agree. Where I am confusing myself is how the straight can have a higher expected value if two small bets go in on the flop than if it checks through and JT does not have the odds to chase to the river. My numbers showed that one bet from each on the flop is better for both players. Either I made a mistake in my numbers that I can't find or someone needs to explain how that is possible. I understand that more bets are better for J10, being the favorite at that point.

[Mike Haven]

i've looked at it again, and, without listing the simple individual calculations, i'm now confident that there is no better strategy than both checking the flop and if JTs does not win on the turn, 86s betting the turn, forcing JTs to fold - JTs winning 0.62sb, 86s winning 1.38sb

i can find no other strategy where either player can win more if the opponent acts in a certain way

if JTs bets the flop 86s will bet the turn with JTs calling for the same win results but with unnecessary betting

if 86s bets the flop JTs will raise and win slightly more - so 86s can't bet the flop

if no one bets the flop or the turn JTs wins a lot more

[chief444]

I see my mistake now. Isn't it funny how you can look over the obvious so many times. /images/graemlins/confused.gif

I had before for straight's expectation:
[ QUOTE ]
31.1% (14 outs/45 unseen cards) of the time the straight loses .5 BB's.
21.9% (53%- the 31.1% chance JT wins on turn) of the time the straight loses 1.5 BB's.
47% of the time straight wins 4 BB's.

Therefore EV of the straight calling the flop is:
.47*4-.311*.5-.219*1.5 = +1.396 BB's


[/ QUOTE ]

But actually 47% of the time straight wins 2.5 BB's (4 minus the 1.5 he puts in).

Therefore:
EV = .47*2.5-.311*.5-.219*1.5 = +.69 BB's or 1.38 SB's

Now it all makes sense. /images/graemlins/laugh.gif I'm sure I made a similar mistake in my J10 numbers.

So yes I agree that it doesn't matter, as long as no one raises the flop. Thanks Mike. That one was driving me crazy.

[Bozeman]

"i've looked at it again, and, without listing the simple individual calculations, i'm now confident that there is no better strategy than both checking the flop and if JTs does not win on the turn, 86s betting the turn, forcing JTs to fold - JTs winning 0.62sb, 86s winning 1.38sb"

True, but you are not the first to present the correct strategy.

"if JTs bets the flop 86s will bet the turn with JTs calling for the same win results but with unnecessary betting "

Not quite the same results, the numbers round to the same with 2 decimal places, but JTs does better with 0 bets on the flop (and much better with 2, so 76 must check the flop).

With a larger than 2sb preflop pot, proper play is 76s check the flop (JTs bet) then call, bet the turn if blank (JTs calls), check/fold a turn that hits JTs.

Craig

[Mike Haven]

if you are the favorite, you by definition making money with every bet that goes in to the pot

JTs is favourite to win the hand

when i wrote "therefore 86s can't bet into JTs" i was meaning that as JTs was favourite, by betting, 86s was leaving itself open to a raise it did not want - things have changed since i wrote the post, but, in principle, that is correct and agrees with your statement

also, by not betting, 86s would be manipulating the pot odds so that JTs would have to fold to a bet on the turn

[Mike Haven]

True, but you are not the first to present the correct strategy.

Sorry - I didn't realise it was a competition.

Who won?

/images/graemlins/wink.gif

[TomCollins]

JTs has the pot odds to call as long as one bet gets in on the turn by each player. There would be 2BB in on the turn. If he misses, 67 bets, and JT is getting 3-1 on his call, plenty to call.

67 can't manipulate anything here.

[chief444]

If the flop is checked through, JTs would not have the pot odds to call on the turn. Pot odds would be 2:1 and odds of JTs catching the river would be slightly worse.

[Mike Haven]

as chief444 has explained, there is 1bb in the pot pre-flop

if 86s didn't bet on the flop but bet 1bb on the turn then JTs couldn't call as he needs 2.14 to 1 to break even and is only getting 2 to 1 offered

so, yes, 86s can manipulate the pot odds here

i know it's confusing using the term 1bb for 2sb pre-flop, but the amount is the same

[BigBiceps]

In no-limit JTh should push all-in. 67c should call only if there was already sufficient money in the pot such that it is correct for him to play when he will only win 47% of the time.

Ie. there has to be at least $12.77 in the pot if the bet is $100.

pokenum -h 6c 7c - th jh -- 5s 8h 9h
Holdem Hi: 990 enumerated boards containing 5s 9h 8h
cards win %win lose %lose tie %tie EV
7c 6c 465 46.97 525 53.03 0 0.00 0.470
Jh Th 525 53.03 465 46.97 0 0.00 0.530

[TomCollins]

But JT can always bet, and should.

[Mike Haven]

But JT can always bet, and should.

JTs won't get an opportunity to bet on the turn because 86s will bet so that JTs can't call.