forking the thread: tth5's take on sklansky's question

[astroglide]

since the thread has gotten long and confusing enough i'll open this one for those of you interested in discussing the simulation aspect of it. here are my tests using turbo texas holdem 5.0.

for those of you just joining, the scenario is a 20/40 game with only 1 big blind. it is folded to the button. the blind will always call your raise preflop, reraise a healthy amount with good cards, and generally play well post-flop.

rake: 5% up to $4 taken in $1 increments.
jackpot: none
tokes: $0.50 for any pot bigger than $50

10-handed table. seats 1-8 fold every hand and play w/o adjustment.

seats 9 and 10 are the same sim - bret the maverick, player #1 in tth. the profile is modified so that he will always openraise if he is playing and the pot is not yet opened, and always see the flop. this will force the dealer to always openraise and the blind to always call (at a minimum, reraising with a healthy percentage of hands).

the limit is $20/$40 and there is only 1 big blind.

the button is fixed on seat 9.

i have verified that their play is average at a minimum and they will make moves. k5o openraises, blind bets k9t flop and k5o calls, calls ace turn, folds queen running-flush river - blind had 68o. this is done with a healthy but not often frequency from both sides.

the blind always gets random cards. listed ev is for the button. 500,000 iterations of each.

k5o: 50.1% win rate, -$3.54 per hand average. button lost 1.77m, blind lost 478k.

75o: 51.8% win rate, -$5.42 per hand average. button lost 2.72m, blind lost 462k. i was surprised to see jj and qq over aa in the win rate dept, but then i noted they were fractions higher than each other. pairs in 57's straight zone (88/99/tt/etc) did better than the other overpairs, giving more credit to how often a 1-gapper makes a straight.

random cards: button lost 105k, blind lost 2.14m. now we're talking!

from the ev analysis here is where you would start if you wanted to beat the rake and the toke EVERY TIME:

pairs: 33, worth $4.75

suited connectors: 78s, worth $4.58. j7s, j8s, etc also showed a profit so it's pretty clear to see where to begin with any suited cards.

offsuit cards: a8o, worth $4.99. any 2 cards HIGHER than a 9 are worth playing as well.

you can clearly go lower than this because of the ev given by certain hands like big pairs and still show a profit. i'm too lazy to actually modify behaviors on the sims so that they follow those exact guidelines unless sklansky himself asks.

rest assured, those hands will win you money every time unless you play them wrong.

regardless of how you feel about sim's play behavior, these are identical players. with you on the button and your clone on the blind, your results should be identical unless you're superstitious about certain hands and play them differently. of course, assuming you call every blind.

it can also be observed that i'm not an expert by any means at tth sims :O) 500k runs may not be enough, especially on the random cards. i'll do a run of 10m on the random cards and see how it differs.

[astroglide]

forgot a big note: this is assuming an openraise every single time, so those are the hands that can show a profit after raising. i can do a run of always limping to contrast the ev...ugh this gets complicated [img]/forums/images/icons/frown.gif[/img]

[astroglide]

ok over 10 million hands the button loses 2.8 million and the blind loses 41.1 million.

results:

pairs: 44 and up
unsuited aces: a8o and up
suited aces: a2s and up
suited random: any 2 suited cards 9 or higher (e.g. q9s)
suited connectors: 98s and up
unsuited random: any 2 cards 10 or higher (e.g. jto)

if you're raising every hand and the blind plays the same as you post-flop, all of those hands will beat the rake+toke.

k5o was dealt 90,238x and turned in a win rate of 50.3% with an ev of -$3.20

75o was dealt 90,907x and turned in a win rate of 52.3% with an ev of -$4.25.

[M.B.E.]

Thanks - that's very interesting.

What happens if you run the sim with no rake or toke?

I guess I could approximate it from the results you've given. For K5o you give an EV of -$3.54. You said that the button always openraises and the players always see the flop. That means the pot will always be at least $80, so the rake+toke will always be the maximum of $4.50, correct? That suggests an EV disregarding rake/toke of +$0.96 for K5 (in other words, just barely profitable).

For 75o you give an EV of -$5.42. Adjusting for the rake+toke, this suggests an EV of -$0.92 (in other words, just barely unprofitable).

Also if I understand it correctly in your sim the button always raises. How do the results change if the button just limps? And how do they change if the button can fold preflop when the blind raises? (My theory was that the button could show positive EV in this scenario by always limping with 75o, and folding if the blind raised. That's assuming the blind will raise with 20% of his hands, which is what David stated. My basis for playing like that is so against a pocket pair the 75o would lose only $20. Also I think that in this scenario, against a blind who never folds preflop but sometimes raises, K5o too might do better limping preflop than raising. I'm not sure about that. In any event it should be clear that 75o will do better limping preflop than raising if the blind never folds.)

[tewall]

"regardless of how you feel about sim's play behavior, these are identical players. with you on the button and your clone on the blind, your results should be identical unless you're superstitious about certain hands and play them differently."

This isn't true. For example, position may be more valueable for good players than poor players, so the sims could be undervaluing position.

[M.B.E.]

<font color="purple">ok over 10 million hands the button loses 2.8 million and the blind loses 41.1 million. </font color>

That's a total loss of $43.9-million. I assume that's because of rounding error? (It should really be $45-million, since the rake+toke is always $4.50, correct?)

<font color="purple">k5o was dealt 90,238x and turned in a win rate of 50.3% with an ev of -$3.20 </font color>

That's +$1.30 adjusting for rake+toke. Considerably better than my estimate of -$7.20 (http://www.twoplustwo.com/forums/sho...;Number=223969).

<font color="purple">75o was dealt 90,907x and turned in a win rate of 52.3% with an ev of -$4.25.</font color>

This suggests positive EV -- by a hair -- adjusting for rake+toke. I think it would do even better limping preflop instead of raising.

[tewall]

I think you're right. I think K9 would be about the cutoff (to where you should raise instead of limp). I also think K5 would do a little better in the hands of a good player (who can take better advantage of the position than a poor player).

[astroglide]

'more valuable' in what way? position is completely intuitive heads up. you always know if you're first or last. i can somewhat understand subjective doubts about valuing position in a full game, but these guys are playing EVERY HAND. there isn't a decision about position preflop, and the rest is straightforward.

[astroglide]

i have to question on a theoretical level why raising vs calling even matters if you're only playing +ev hands and both players are seeing the flop every time you play. if 67o shows a profit calling, you're simply doubling your bet preflop that you hand will win. in the long run, raising vs calling may not matter if it's hu in a always-play situation.

at least signifigantly less. implied odds are pretty much out the window.

[tewall]

There's no reason to believe that modeling poor players will be exactly like modeling good players. If you took different profiles from TTH for example, and tested them playing the hand, surely the results would be different (that is, put different profiles in for Brett). I have no idea how different, but you could try it out and see. There surely would be some difference.

I gave the value of position as one example of the difference between good and bad players playing. There are many other factors that go into playing well. Because a bad player earns such and such against another bad player with a given hand in a certain situation in no way implies that a good player will earn exactly the same amount against a good player.

It is reasonable to assume that a good player will be able to take advantage of position more than a bad player.

Your argument about playing every hand and position doesn't make sense. The value of position pre-flop is very small compared to the value during the rest of the hand.

In HEFAP21 in the shorthanded section, the authors suggest playing 40% of the hands when defending the blind. If you run TTH sims you will find that a much larger pct of hands will be +EV defending the blind than this. Why is this? One possibility is that Sklansky is way off and just plain wrong. Another possibility is that position is more valuable to good players.