Simple "dice roller" for live games

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sxm59

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Hello,

Playing sound poker can involve using a "mixed strategy" in certain spots. For example, a player who is first to act and who has a weak hand my decide to bet (as a bluff) 50% of the time and check (with the intention of folding) the remaining 50% of the time. The player is "mixing" between betting and checking because he (or she) wants to be unpredictable and hence not to be exploited. If the player always checks in that spot (that is, never bluffs) then other players eventually will realize that his (or her) hand is always strong whenever he bets, which will enable them to "print money" by calling less when he bets (and betting more when he checks).

In online games, a 50:50 mixed strategy can be implemented by flipping a coin and picking one or the other action (say, bet or check) depending on whether the coin lands on heads or tails. Or by rolling a dice and betting if it's a high number (4, 5 or 6) and checking otherwise.

In live games, however, flipping a coin or rolling a dice is not practical! A better way to implement the mixing is to use the suits of your own cards. For example, suppose you are going to play hold'em and you anticipate that there will be situations during the game where you will want to mix 50:50 between, say, calling and folding. Suppose your favorite suit is spade. Then, the following are simple ways to do the 50:50 mixing:
  • If you are holding unsuited cards, call if you have a spade (and fold otherwise).
  • If you are holding suited cards, call if they are black (and fold if they are red.
What about re-raising 25% of the time and calling 75% of the time?
  • If you are holding unsuited cards that are not a pair, re-raise if the highest of the two cards is a spade (and call otherwise).
  • If you are holding a pair, re-raise if the first card you received is a spade (and call otherwise).
  • If you are holding suited cards, re-raise if they are spades (and fold otherwise).
Finally, note that preflop you only see two cards (and hence two suits), and thus it may be difficult to extend this approach and implement, say, a 10:90 mixed strategy preflop. However, a 12.5:87.5 is easy to implement if you are not holding a pair. Do you see how?
 
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Hermus

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Nice thanks for posting! Just want to add that your watch is also a tool for randomising just about any frequency (e.g. seconds hand between 12 and 3 = 25%, 12 and 6 = 50%, 12 and 9 = 75%).
 
skoldpadda

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You can do what the high stakes guys do if you shuffle chips. look at a certain marking or rotation/orientation of your top chip and use that as a randomizer relative to its 12 o'clock position.
 
Kenzie 96

Kenzie 96

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Dan Harrington used to advocate using your watch for random bluffs.
 
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sxm59

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Great points. Thanks. Note that using a watch or shuffling chips can be "dangerous" unless we do that all the time, even when our optimal action is obvious and does not involve any randomization. For example, suppose Hero raises from UTG, Villain 3-bets from UTG+1, all other players fold, and Hero 4-bets. Suppose further that Villain has figured out that Hero, in this particular spot, is 4-betting for value with AA and KK all the time, and is 4-betting as a bluff with AK 50% of the time. Suppose also that Villain has observed that Hero acted relatively quickly without looking at his watch and without shuffling his chips. Then, Villain could infer (from his knowledge of Hero's range and his observation that Hero did not randomize) that Hero is not bluffing in this spot. If, instead, Hero uses the suits of his cards as the randomizer (instead of a watch or a chip shuffle), then this "tell" cannot arise because Hero always looks at his cards before acting (in this spot).
 
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Hermus

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Great points. Thanks. Note that using a watch or shuffling chips can be "dangerous" unless we do that all the time, even when our optimal action is obvious and does not involve any randomization. For example, suppose Hero raises from UTG, Villain 3-bets from UTG+1, all other players fold, and Hero 4-bets. Suppose further that Villain has figured out that Hero, in this particular spot, is 4-betting for value with AA and KK all the time, and is 4-betting as a bluff with AK 50% of the time. Suppose also that Villain has observed that Hero acted relatively quickly without looking at his watch and without shuffling his chips. Then, Villain could infer (from his knowledge of Hero's range and his observation that Hero did not randomize) that Hero is not bluffing in this spot. If, instead, Hero uses the suits of his cards as the randomizer (instead of a watch or a chip shuffle), then this "tell" cannot arise because Hero always looks at his cards before acting (in this spot).


Well, presumably we're playing a mixed strategy to approach the GTO equilibrium which in theory is unexploitable so we don't care if they know we have a mixed strategy hand. If we don't we shouldn't play a mixed strategy anyway because any exploitable tendency in our opponent very often if not always (I didn't do the maths sorry) shifts the optimal strategy to a pure bet/raise, call or a check/fold.

I agree with you that if you do it very often it's a pretty big tell. In practice, we're randomising so infrequently that it shouldn't be a huge tell, the same situation probably won't repeat itself + we're (trying) to play an unexploitable strategy anyway. Then again you don't really lose much by randomising using suits so I still like your method better :).
 
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sxm59

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Thank you. You said "Well, presumably we're playing a mixed strategy to approach the GTO equilibrium which in theory is unexploitable so we don't care if they know we have a mixed strategy hand." To be more precise, we don't care if Villain knows our 4-betting range (AA 100%, KK 100%, AK 50%, in my example) in the following sense: if we knew that Villain will respond optimally to our range, we would not want to change our range. However, that does not mean that we do not care if Villain can eliminate AK from our range because he noticed that we did not randomize when we re-raised him. The fact that a range is unexploitable does not mean that we can play it with our cards faced up. I am sure you did not mean to imply that, and that we are in agreement, but wanted to clarify things a bit.
 
StealTheButton

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Yes, but it is amazing how little others are really paying attention to the hands I am playing. They may be stubborn players who are two focused on their own hands, better players who are playing too many tables, or just poor players in general. With that said, if I am going to raise with a hand it needs to have some possiblity of turning into a real hand. About the worst hands that I would raise with are something 6 8 or 7 9 offsuit, or perhaps something like K5s. I don't need to be THAT unpredictable. And there are too many player that are calling too loose, so if I am going to raise it won't be with something like 9 3 off suit which I will auto muck.
 
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Hey, mixing strategies in poker can be a real game-changer, right?
 
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