A No Blind Game

Sorry for the dumb question, but I'm not sure I understand this properly.


Suppose you were playing in a 20-40 hold'em game with no blinds and zero rake. Would it be correct to play anything less than AA? What if there were a few players who would? Suppose half your opponents will play hands such as 55, JTs, etc. NOW would it be correct (or MORE profitable) to lower your starting requirements and play hands less than AA? Thanks.

I'm not asking the safest way to play, but how to maximize your profit. Obviously, if all of your opponents will only play KK through AA, you would only want to play AA.


I'm asking this because there's been much talk in my poker circle about how a loose playing strategy can run rings around a tight player. I appreciate any responses. Thanks again.


Kevin

I would be willing to play this game headup against anybody, with a substantial side bet that they cannot beat me at this game. Any takers?


Dirk(MildManneredMathMan)

Thats funny! n/t

Kevin,


I think you are missing something here. If you only play AA, your opponents will soon realize that you only play AA. If your opponents know what you have, you can't win.


You can find a good example in Sklansky's Theory Of Poker," Chapter Eight, The Value of Deception, p. 65.

Soh,


But there's NO ante! Why do you need deception? That was the point. You can simply wait for a player (or players) willing to play a worse hand, and virtually be gauranteed the best of it by only playing AA. It wouldn't matter how predictable you are, since if you never played a hand in this game it wouldn't cost you anything. You couldn't lose. My question was, can you make more by adding additional hands assuming they will still play worse hands on average.

Here is what you would do in a simplified case. Suppose you just get a 5 card hand with no draw. You just have one round of betting then show down. Let's simplify it more and say there is no raising.


Also, suppose you KNOW what hands they will bet. You simply call with any hand that will beat a random one of their betting hands at least 50% of the time. I.e. list all their hands in descending order and call with any hand that beats at least half of the hands in that list. Of course, they are making a mistake by ever betting.


Dirk(MildManneredMathMan)

In a pot which has zero money in it, there is no reason to ever play or bet a hand which is anything less than the nuts (AA). Why would you be willing to incur the risk of losing to a better hand? If the other players also realized this (and realized YOU realized this), you would never play anything less than AA, since you could go forever and not play a hand in this game without losing a dime. So here, deception is not even a factor.


However, if other players in this game did not realize this and would play and bet worse hands than AA before the flop, it might start becoming profitable to play less than the nuts yourself.

Kevin,


Let's say you and I play 10-20 hold'em heads up with no blinds. I know you only play AA, and you know that I know it. You wait, wait, wait and finally get AA. You bet. I call. You have no idea what I have.


Flop comes QcJh7h. You have one heart. You bet. I raise. What's your play?


How do you play when I know exactly what you have but you have no idea what I have?


Am I missing something here?


Soh

You are not missing anything. This is exactly what I was getting at. The precise math aspect is over my head, but I would think that if you were to play any two cards here AND use proper game theory, it is impossible for me to have an edge even though you are purposely putting $$ in with what you know to be an inferior holding.


This is the topic of conversation between a few players whom I play with. What if you were to take a good but tight player who raises or even limps UTG? His hands are very narrowly ranged, yet yours are not. Even if you add blinds to this game, is it possible to play very loosely against him if you still employ good game theory? Does the fact that his hand is within a very narrow range, while your's is not, give you an automatic edge against this player, since he cannot put you on a hand? I say, there must be ways for the tight player to combat this yet, but I am not good enough to come up with a compelling argument to the contrary. I sure wish others would jump in here and give their thoughts...

Soh wrote: "Flop comes QcJh7h. You have one heart. You bet. I raise. What's your play? How do you play when I know exactly what you have but you have no idea what I have? "


I look at the frequency you make this sort of raise. Maybe you can push me off a pot, but if you keep doing this, I know you are bluffing too often. I will start calling and you will lose more. If instead your bluffing frequency drops down low, then I begin to make money off the preflop calls.


Assuming one player plays only aces, and the later player knows this ... In order for the looser player to show a profit overall, he has to cover the -equity he put in preflop. He has to outplay the tight guy post flop by a LOT because the preflop call was so bad. I don't think there are enough opportunities for value bets to make back the loss. Yet, if you bluff more than the pot odds dictate, AAs have a profitable call on your bluff, and you will only lose more.


The scenario is headsup, with no blind. I will only play AA, and I will raise with it. I will never bet or fold postflop. Against optimal play, I will win 2 SB when I win, and lose at most 7 SB when I lose (I only lose 7 when you win on flop, 5 when you win on turn, and 5 on the river). Only hands that are better than 3.5:1 underdogs (it's actually going to be worse since you will sometimes win less than 7 bets) are profitable. Are there any such hands? Regardless if there are any or not, this is just showing how much of a disadvantage you have because of inferior cards. Keep in mind in actual play, I will have the chance to deny free cards, as well as fold according to game theory guidelines to make it worse for you.

I prefer larger blinds rather than smaller blinds because the larger blind structure (say 15/30 vs 10/20)livens the game up. In a big blind structure the rocks/super nits, really have a big problem, which allows the more creative player to have a more equal playing field with the plodders and forces the plodders to play some hands they are not confortable with.


Rocks can't just sit and wait for the nuts, the blinds will eat them up. Big blind structure play is more like playing a short game (which I love and look for); I prefer playing California poker over Las Vegas poker (i.e. faster games) and 15/30 over 10/20. When I pl;ay 10/20 I have to play classical hold em to beat the game, but 15/30 allows me to stretch my mind a bit and for me is much more fun and profitable - many rocks just can't play fast games very well, or short games for that matter.


In fact, I would guess it takes more general poker skill to play 15/30 than 10/20 because hands have different values in the bigger blind games. It will be interesting to see how the blind structures evolve in the context of trying to figure what is the optimium blind structure for stimulating both action, and skill. In the future we may find ourselves playing with blind structures that change during the game because as the blind structures change so do hand values, making recipe playing very tough.

And why is this? Because you would play against the player who would only play AA? Or because you would only play AA yourself?

"I will never bet or fold postflop."


I understand never bet post-flop. But not the never fold part. If you NEVER folded, then your opponent would only bet when he has you beat and take free cards the rest of the time. This doesn't seem right either...

You can just raise preflop, only with AA, fold everything else, and then call the correct game-theoretic frequency, as if you were playing with your hand face up. Of course, this doesn't answer the question of whether or not you would make more by playing hands other than AA. I would guess that you would almost certainly make more playing other hands, provided your opponents were doing the same and that you could outplay them. If your opponents all played only AA, playing hands less than AA would be wrong, because your added equity from bluffing would not be enough to make up for the amount of money you are putting in with much the worst of it.

Finally someone hit on the point of my post. This is no doubt a no-brainer for Sklansky and others proficient in math. Since I'm not, please bear with me..


You wrote: "If your opponents all played only AA, playing hands less than AA would be wrong, because your added equity from bluffing would not be enough to make up for the amount of money you are putting in with much the worst of it."


Suppose you only play AA in a $20-$40 game with no blinds. I know this. Why shouldn't I call you every time? You cannot play proper game theory against me because I know what you have. However, I am able to play proper game theory against you. How would you go about gaining an edge after the flop? Is your edge before the flop great enough to overcome your disadvantage for the remaining streets? Thanks.

I can use proper game theory against you, because I know you know what I have, so I don't have to bother thinking about whether you are making a mistake or playing in some way that I should exploit. All I have to do is check and call on the flop and turn, then call often enough on the river that your bluffs are unprofitable, heads-up with bets on each street and a raise preflop, that would mean there is $200 in the pot in a $20-$40 game, so I would have to call 83.3% of the time. If you didn't bet the turn, there would be only $120 in the pot, so I would only call 75% of the time, if you bet the turn, but not the flop, there would be $160 so I would call 80% of the time, and if you bet nothing after the flop, there would be $80 in the pot, so I would call 66% of the time.


If you have only a 25% chance of making the best hand by the river, and you check all the way to the river, then bet only when you have me beat, I win $40 from you 9 times out of 12 (when you don't outdraw me), I lose $80 to you 2 times out of 12 (when you have me beat and I call), and I lose $40 one time out of twelve when you have me beat and I fold. So I end up winning $360 and losing $200, for a net profit of $160 over 12 plays.


With the same 25% chance to make the best hand, and with $120 in the pot at the river, I win $60 12 times out of 16, I lose $100 3 tims out of 16, and I lose $60 1 time out of 16, for a net profit of $360 over 16 plays, which is worse for you. So you would like to check it all the way, then bluff appropriately on the end.


Since you have the option to bet when your hand has me beat on the earlier streets, you might decide to bet every time your hand has improved to have a better than 50% of chance of winning at the showdown, this allows you to win anywhere from a little over $6.66 from me to $66.66 when you flop a hand, depending on my chances of outdrawing you, and you can win anywhere from $5.33 to $45.33 extra when you make your hand on the turn. These numbers are based on you winning some percentage of the bets on the turn and flop, depending on my chances of outdrawing you (note that if I have a 10% of outdrawing you, you are only winning 80% of the bet, since you win a bet from me 9 times, but lose one once for a net profit of 8 bets in 10 tries). The extra $6.66 when you make it on the flop and $5.33 when you make it on the turn comes from the extra calling frequency I have to use.


So what does this all mean? If we figure that on average I will have to catch an ace to outdraw you (sometimes I'll be drawing dead, sometimes I can catch any pair or a flush or str8 card), then you can expect to average $55.66 extra whenever you flop a hand that beats me and $41.50 extra whenever you turn a hand that beats me. To simplify things a little bit, let's say that any time you make a hand before the river you extract an extra $48.50 from me. If x is your chance of making the best hand by the river, and y is your chance of making a hand by the turn, your expectation is as follows:


y*(48.50 + 200/3) + (x-y)*(200/3) - 40*(1-x)


The 200/3 comes from you winning $80 each time I call on the end and $40 when I fold. The adjusted calling frequency is already included in the 48.50, so the rest of the calculation ignores it.


So we have: 48.5*y + 106.66x - 40, so if x is greater than 40/106.66 you should call, and if y is greater than (40 - 106.66x)/(48.50) you should call. Are there any hands (besides, AA, obviously) that fit this criteria? I'm not sure, but you could write a program to make the calculation, a hot and cold simulation would work well. Of course, a hot and cold simulation of this type could just go through the entire betting strategy also and give you the figure.


I don't think there are any hands that will beat AA more than 40% of the time, and since the odds of making your hand by the turn are supposed to be greater than about 5/6 - 2.2x, you are pretty much toast as soon as x drops below 25%, which I think includes just about every hand. So based on this (admittedly rather rough) analysis, I don't think you can make money playing less than AA against someone using proper strategy with only AA.


Hope this helps,

Lenny

"You can just raise preflop, only with AA, fold everything else, and then call the correct game-theoretic frequency, as if you were playing with your hand face up. "


I don't think you can completely exclude the case that AA should bet after the flop - to avoid giving free cards.


It's a common scenario in real poker: You are betting a hand that only might be the best hand to avoid giving free cards to a draw.

A Somewhat Solution ! to an Interesting problem !


Changing the PROBLEM slightly to prove a point:


1. You bet and show me your two black Aces.


2. I call w/ red suited connectors (45 - TJ) and almost any red pair - something like that - giving me about 20 % to out-drew on you.


3. On the flop we see all cards !


4. We are playing pot-limit.


SOLUTION:


On the river: I have 20 outs and 10 bluff-outs.


On the turn: I have 20+10=30 outs and 15 new bluff-outs.


On the flop: I have 20+10+15=45 outs and 22,5 new bluff-outs.


I win 45+22,5 = 67,5.


CONCLUSION:


AA is a big loser in this game - only wins 32,5 % of the time (when called).


I admit that I in PROBLEM have done everything to give AA a hard time - but I still think it somewhat prove 'Kevin's Point' !?


PS: I don't think it will work in limit !?

You are probably right, but I was making the point that you don't even have to do this in order to beat someone who is not playing only AA. I believe that you would win more money if you do this, especially when the board is such that it is highly unlike you are currently beat, but I don't think you have to do it to make a profit if insists on playing weaker hands against you.

***On the river: I have 20 outs and 10 bluff-outs.


On the turn: I have 20+10=30 outs and 15 new bluff-outs.


On the flop: I have 20+10+15=45 outs and 22,5 new bluff-outs.


I win 45+22,5 = 67,5. ***


You don't win nearly this often. Since you are bluffing at the correct frequency, we can assume the result when AA always calls is essentially the same as if the AA were to call with the correct frequency. If the AA always calls, then here's the situation:


You lose whatever the preflop bet was 32.5% of the time, because you are only going to bet the 67.5% given above. Let's call the preflop bet $100 to simplify the math. So you lose $3250 so far over 100 trials.


22.5% of the time, you will bet on the flop then lose (again, according to the above), which now costs you a total of $300 (the preflop bet, plus the pot sized bet on the flop), bringing your overall total to -$10,000.


15% of the time, you bet again on the turn and lose, which now costs you $900, bringing your total to -$23,500.


10% of the time, you bet again on the river and lose, costing you $2700, bringing your total to -$50,500.


20% of the time, you win after betting the river. You win $2700 each time, bringing your total to +3,500. Thus you do have a positive expectation, assuming that a) you always had a 20% chance to outdraw your opponent, b) the AA couldn't tell anything about what hand you might have and c) you are playing pot limit and bluffing correctly. This is basically true because in pot limit the implied odds are so big that it can be profitable to play hands that are getting terrible pot odds. So in a pot limit game with no ante, it would be a little trickier to win by only playing AA. However, I'm not sure that this edge given above would be the true figure, because AA has the option of reraising in situations where the opponent is highly unlikely to have him beat, and the AA might be all-in at some point, which would be to his advantage, since each round of betting drains EV from his hand. For instance, in the example above, if the AA never had more than $1000 going into the river bet, the betting hand would not be able win back enough to cover its earlier losses. Likewise, if the AA was all-in from the start, it would simply win 60% of the preflop bet on average.

"... bringing your total to +3,500".


I agree ! Over 100 trials:


(0,675*200 -100)*100 = +3,500


PS: I like your math-related posts. So keep on posting !

No. I would simply fold every hand.

Certainly, never folding post flop would not be correct. My point is that even with this inferior strategy, I am laying you 3.5:1 to beat aces. My strategy makes that a take it or leave it proposition, and removes your chance to outplay me. By never folding post flop, I take away all of your bluffing equity. As Lenny points out, you need bluffing equity to make up for the preflop call. With my strategy, you are only able to maximize your value equity. I just don't think that's enough.


Realistically, I will sometimes fold postflop. It's intuitive that this will help the AA player.


But the real point, overall, about playing with the AA face up - you would think this gives you the chance to outplay me, and get me to lay it down. This is not true most of the time. You will only be able to do this occasionally. You won't get me to lay it down enough to cover the terrible preflop call. All I have to do is track my folding frequency. If it is too high, then you *must* be bluffing too much simply because I am favored to have the better hand so often. In this case, I can revert to check and call mode, and take the best of it.

This question is less one of weather or not your opponents are going to play hands less than AA. Since there are no blinds and no rake that means that means that you must change the name of this game to "THE WAIT FOR ACES GAME". Sure you could play 5-5 or 10-10 or even KK but what the hell would you call a bet with????????????? if you call with anything less than AA you are a total FOOL?!?!?! right? so it would still be called "THE WAIT FOR ACES GAME"