Help with 3bet 4bet, math question

Re. Help with 3bet 4bet, math question

So, lets see my wrong thoght process [img]http://en.donkr.com/Content/Scripts/v1/tinymce/plugins/emotions/img/smiley-cry.gif[/img] Some parts are directly copy pasted from: http://en.donkr.com/forum/optimal-3-bet4-bet5-bet-strategies-in-nlhe-6-max---part-1-533561 Lets say Alice and Bob both have 50bb stack, and Alice bets 3.5 into 1.5 pot. Alice starts betting, we know Alice openbets form UTG with 15%.In pot is allready 1.5bb(sb+bb) Alice bets 3.5 bb, Bob 3bets to 12bb, Alice folds or 4bets allin , then Bob calls all in bet or folds. [i]"Alice can[apostrophe]t fold so much that she gives Bob an opportunity to make a profit by 3-bet bluffing any two cards"[/i] So Alice need to defend 30% of her starting range ( 12/(12-4,5))=cca 70% fold.[i][/i] [i]We know what is her range 0.3 * 15%=top 4.5%, so she doesnt have bluff range, I mean she is not playing hands like A5s,A4s but best 30%. ( ok, we can say that she is palying QQ+,AK for value and AQ,TT+ for bluff )[/i] [i] [/i] Next step. When Alice 4-bets to 50 bb, she is risking 46.5bb (50bb minus she 3.5bb raise) more to win a 17bb pot (1.5bb from the blinds + Alice[apostrophe]s 3.5bb raise + Bob[apostrophe]s 12bb 3-bet). 46.5/( 17 +46.5)=73%, and this part is confusing. [i] [/i] Bob can[apostrophe]t allow Alice to 4-bet bluff any two cards profitably, so he defends optimally by folding exactly 73% of the time ???, and calling ( as BOB can not 5 bet, only way he can win is by calling, so there is no need for polarized range like A5s, A4s, Bob calls with best 27% of his range. Now, this part doesnt sounds right, because Bob would lose to much by folding 73%, because he is geting good odds. He needs to put 38 more to win 81,5 that means he need to win 46,6% of time.[i]( in stove that means 5,6% vs 4,5% alice is shoving). [/i] The biggest problem I can not understand is how to calculate range for BOB, ofcorse he can only 3bet with QQ+, thats allwys EV+ with no blufs, but that is not optimal. How to culculate VB/ bluf range for BOB( we know open bet, and 4bet range of alice), and what is optimal frequencie. Probably I made some stupid rocky mistake, so I am asking You for help.[img]http://en.donkr.com/Content/Scripts/v1/tinymce/plugins/emotions/img/smiley-undecided.gif[/img]

kuky84

Re. Help with 3bet 4bet, math question

First, one important thing to keep in mind is that optimal play is generally not the most profitable play. Optimal play is designed to prevent an aggressive opponent from automatically making a profit by betting and raising at every opportunity. So if you see an opponent shoving a lot with bad hands, you should call with the appropriate range of hands that is profitable for you. If he isn[apostrophe]t shoving blindly, and you believe he is shoving with a good plan behind it, play optimally (at least until you find mistakes in his strategy that you can exploit). Anyhoo, you have the math you need for Bob, and you are on the right track. If you want him to defend optimally, you know how many % of his 3-betting range he should call the 4-bet with, and then the rest of his 3-bets are bluffs. Begin by letting him value 3-bet the hands that are a favorite against Alice[apostrophe]s shoving range and then add bluffs.

Bugs

Re. Help with 3bet 4bet, math question

Ok, I done some math and for this case if they open 15% I rr 3.7%,2.6 for value,1.1 bluff, or in other words, VB/bluff 0.7 / 0.3 I see correlation between VB/ bluff frequency and how deep we are, but I dont know how to calculate exactly. For example what if we have 70bb and alice allways goes all in. What if we have 20bb. for 20bb, this math is wrong, for example if alice 4bets, that means she risks 16.5 to win (16.5 +17), or she needs 50% fold to bet any 2. But Bob is making really huge mistake if he is calling only 50% with given odds. So my conclusion, if we have 30bb stack, we should VB 90%, with 50bb VB 70% and with 75 bb VB around 50% of our 3bet range. But still I dont know excatly how to calculate that. Maybe we can get this number if we tell that alice knows that we will not fold if we invested 12 bb, and have 22 behind,so there is different math. Not 12/ ( 12+1.5+3.5)=0.7, but 30/(30+1.5+3.5)=0.86 From this we can see that stack size determine our opponent optimal fold frequency. So, Bugs pls tell me if this logic is right and comment if I wrote something wrong.

kuky84

Re. Help with 3bet 4bet, math question

Start by determining which hands Bob wants to get all-in with when Alice shoves. Just make it simple and say that he wants to value raise the hands that are a 50% favorite against the range Alice plans to shove (Bob knows this range). Then add the appropriate amounts of bluffs and see what you get. Note that Bob knows his value range before he puts a single chip in the pot. The hands not quite strong enough to 3-bet and call a shove with he flats. Also note that although you are getting pot odds to call with many hands [i]once Alice shoves,[/i] it can be a mistake to [i]3-bet and plan to get all-in from the get-go against her shoving range[/i]. This is a subtle point, so think it through. The hands that can profitably call a shove but that loses money overall by 3-betting and getting it in, are better played as flatting hands when you are trying to approximate an optimal strategy Raise the best hands for value, flat the next best hands, bluff with the best hands not strong enough to flat, fold the rest.

Bugs

Re.

Hello guys. Bugs I really enjoyed reading your optimal preflop strategy I[apostrophe]ve also watched Mathew Janda and Alan Jackson series and think you did a great job of explaining preflop play. Here is my thoughts on this situation. So lets say 30BB effective stacks and MP opens the following range: 198 combos (14.9%) 22+ A8s+,AJo+ KTs+,KQo QTs+ J9s+ T9s 89s 78s 76s 65s Definition: MP opens to 3BB, BU 3-bets to 9BB, MP 4-bets to 30BB(all-in) or folds and BU calls or folds. SB and BB always fold. BU risks 9BB to win 3BB+1.5BB, so his 3-bet-bluffs need 67% folds to show immediate profit, so MP needs to defend his opening range 33% of the time by 4-betting. So that is how we find MP 4-bet shoving range: 33% of 198 combos =66 combos. Best 66 combos are: [99+;AQ+] =68 combos (close enough) Now we find all hands that have more than 50% equity vs this range, which turns out to be: [JJ+, AK] =40 combos, and that is the value component of BU 3-bet range. Now we have to calculate how many bluffs to put in BU 3-betting range. Here is how I decided to approach the problem but I am not sure if it is correct. At the bottom of MP[apostrophe]s 4-betting range are 99 and AQ and here is how they fare vs our 4-bet calling range. 99 vs [JJ+,AK] =33,17% AQo vs [JJ+,AK] =28,15% When MP shoves his worst hand AQo and is called by BU, he is getting back 28% of 61,5BB =17BB. Which means that MP is risking 27BB - 17BB to win 13.5BB in the pot. So his 4-bet (semi) bluff with AQo needs folds 43% of the time to break even and that equals to BU 3-bet value to 3-bet bluff frequency. Here is BU 3-betting range: Value: [JJ+AK] =40 combos Bluff: [ATo,A9] =32 combos And BU can still call with his flat IP range, defined by Bugs in optimal 3/4/5 betting preflop. I am confused by one fact though. We said that MP is 4-bet bluffing to make BU indifferent to calling with worst hand in his 3-bet value range, so that is why MP is shoving AQ, 99,TT. But BU have pot odds to call anyway. JJ vs [JJ+AK] =36.6% equity, and BU needs to call 21 for 40.5, which means his pot odds are: 34% MP on the other hand has no other chance but to 4-bet 33% of this range otherwise he will be exploited by 3-bet bluffing with ATC. Maybe MP needs to open a tighter range with such shallow stack, not sure though. @Bugs: I read your "More about 3-betting" post and liked it alot. I have difficulty playing 3-bet pots postflop though, can you suggest more resources to check or a game plan how to improve faster. What has helped you most? Also is there more articles on this site written by you. I found optimal preflop and optimal postflop series so far.

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