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Math experts, question about pre flop Math experts, question about pre flop

10-09-2017 , 01:41 AM
Is there any way of possibly finding whether or not raising a hand pre flop is +ev or not in just a standard 100BB deep cash game? For example raising KQd UTG in a 9 person table
Math experts, question about pre flop Quote
10-09-2017 , 06:35 AM
Not really any way other than a big sample size which is very hard to get. Even that only tells you if YOU are profitable with a hand in a specific game rather than a more general answer. Also, by the time you get a relevant sample, it's probably outdated because both you and the game you're playing have changed.
Math experts, question about pre flop Quote
10-09-2017 , 12:37 PM
You can't calculate the exact EV without a complete solution to multiplayer holdem, which doesn't exist, and such a solution would only be valid in theory (against rational opponents, not real-life players who make mistakes). Probably the closest you can get with a commercially available tool is PokerSnowie. Snowie says that in 9-handed NLH at 100NL, KQs has an EV of 0.16bb as a raise UTG. i.e. It's theoretically profitable if you play it optimally. (By contrast, AA is worth 6bb, and 88 is break-even).
If your opponents are much worse than you, it should be more profitable. If you don't have a skill edge, it probably loses as a raise.
As thorfather points out, you can track your own results with a database/tracker to find out what works for you, but this requires a massive sample size because of the variance in results. You could also hunt down the massive hand history databases some coaches used for datamining. FWIW, Snowie simulated billions of hands, but that still doesn't prove it would beat real people at 100NL.
Math experts, question about pre flop Quote
10-10-2017 , 12:49 PM
I'll add that it depends on villain tendencies (i.e. in what what way they are bad).

e.g. conventionally big broadways, ATo etc go up in value vs fish since they flop good tps and you can get more value with tp vs fish than regs (they defend pre and call down K2o on KT6 more e.g.). But if you get a table of fish that 3bet very wide vs ep open, then you have to be tighter there. Obviously you would make much more than "gto" with hands like QQ+, AK, and maybe even AJo if you can gii pre for value. If they are tighter post, then suited connectors go up in value (either win a big pot with straights/flushes or bluff them out).

At a 6 max table it's not so easy to know exactly what cutoff of hands is +EV to open, and for a human it mostly comes from experience and database analysis.
Math experts, question about pre flop Quote
10-10-2017 , 01:55 PM
You can do analysis to provide some guidance using an equity calculator like Equilab. I’ll simplify a bit and assume a cash game with three opponents (equivalent to 5 of 8 opponents folding). Decision criterion is make a +EV bet.

Assume an all-in bet by hero holding KdQd– all-in is a major assumption for it avoids future betting which would generate a complex decision tree. Two analysis examples follow:

1. Assuming a random hand for the 3 opponents. The EV if all call is

EV = eq(3* Bet) –(1-eq)Bet = eq(4*Bet) - Bet = Bet*(4eq-1) >? 0

Equilab tells us that KdQd has 38.2% equity against 3 random hands so clearly an all-in bet is +EV in this case.

The next example is more realistic in not assuming random villain hands.

2. Assume the button folds to an all-in bet, the small blind will call a top 15% hand and the big blind will call with a top 25% hand. The EV equation is

EV = 0.85 * 0.75 *1.5 + 0.75 *0.15*Bet*(3*eq1-1) + 0.85*0.25*Bet*(3*eq2-1) + 0.15*0.25*Bet(4*eq3-1) > ?0,

where eqi is hero equity against player i and eq3 is equity against both callers.

Using the equities provided by the equity calculator (49%, 52%, 34%), you will find that this is a +EV bet decision for any bet size. Because KQs is a very good hand, this will be true even for tighter villain ranges but at some point, very tight villain ranges will dictate a max bet size to insure +EV.


Clearly the above is a strictly EV math-based approach and may not properly account for such factors as real player mistakes as Arty noted.
Math experts, question about pre flop Quote
10-12-2017 , 06:50 PM
I don’t know why I didn’t include this before, but to further answer OP’s question on pre-flop analysis, here is a summary of some aspects of a sample hand such as AQs, which can certainly aid in deciding if a bet or raise is +EV.

https://imgur.com/a/IRs06

The picture is from the Hold ‘em Calc Excel program I wrote, which has some 32 modules doing all sorts of analysis. This particular example summarizes all applicable results pertaining an AdQd hand . Particular values shown, such as number of opponents or opponent range can be changed, of course.

So, to summarize, the notion that pre-flop analysis of a hand or even a range cannot be done is, in my opinion, not valid.
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