Ultra Deep Stack Texas Hold’em

Probability

Introduction

I use a few free-to-play poker apps, but since playing poker for money is illegal in Japan, I often play Japanese mobile games. Among them, the game I play most often has rules that appear to be the same as regular Texas Hold’em at first glance, but the playing style of the players seems to differ significantly from that of regular Texas Hold’em. It seems like there are a lot of players who adopt the so-called limper/caller playstyle (although this decreases at higher ranks, this trend doesn’t seem to be changing).

 Poker books often claim that these players are beginners and therefore easy suckers, so I thought I would be able to win easily, but from my own experience playing, my honest impression is that although the lower-ranked players are certainly not strong, the higher-ranked limpers/callers do not seem like opponents that can be easily defeated. When I asked ChatGPT how to play when there is a player with this kind of playing style under these rules, I got an unexpected answer, which I would like to introduce in this article. I was wondering why this phenomenon occurs, but it seems that there is a specific rule in the game that causes this phenomenon. However, there are some parts that are not certain (especially the author’s opinion, which is still being tried and tested), so I think it would be best to think of it as just a reference.

500bb Matches

The basic rules of the mobile games I often play are as follows:

  1. The game is basically played by six people, but the game can start with two or more players.
  2. Texas Hold’em follows standard rules.
  3. The ante is 0.25bb and every player puts points (chips) into the pot each time.
  4. You can buy in to a maximum of 500bb (ultra deep stack), and by beating other players you can increase your stack to 2500bb.
  5. The rake is fixed at 5%, but since users compete for rankings based on the points they have earned, it is probably not something you need to consider too much (it is a relative comparison of earned points, so the absolute value has no meaning). Points are given out every day as login bonuses, so it is likely only intended as a measure against point inflation.

 At first glance, it may seem like a regular Texas Hold’em game, except that it is not a real money game. However, among the rules above, there are some rules that clearly have unusual features. That is 4. In general cash games, the maximum buy-in is usually around 100bb. In this game, the stack is 500bb, so the preflop 3-bet is only about the same as the minimum raise in a 100bb game. For example, if you raise to 9bb with a 3 bet, the difference is clear when you consider what percentage of your preflop bets are made with a 100bb stack versus a 500bb stack.

 As a result, many players tend to stay in the game until the flop, and the rate of games becoming multi-way is very high. In addition, because it is multi-way, the pot tends to grow larger after the flop. It is important to note that the bet amount increases by twice as much for the same pot bet by 2 players and 5 players. As the bets pile up on the flop, turn, and river, it is easy to see that the bet amount after the flop will be several times higher than in heads-up. This game seems to be completely different in nature from the 3-bet/heads-up games often described in poker books with stacks of around 100bb.

 The players who participate in this game have certain characteristics, and in poker books they play in ways that beginners are told to stop because they are not rational (limpers/callers). Specifically, they are as follows:

  1. They have a high participation rate in the game and often limp in preflop. In most cases, they only raise once. Reactions to a 3-bet raise vary depending on the player; there are those who don’t call the 3-bet from other players (and basically fold except for AA or KK) and those who will call even if it’s a 3-bet regardless of the hand. If the latter type is prevalent, it is often the case that all five other players will call the 3-bet. Of course, there are also quite a few players who only enter the textbook 3-bet range.
  2. If they are not the aggressor, they will usually call or fold quietly on the flop. If they get a hand of two pair or better on the flop, they will likely make a donk bet or reraise to the aggressor’s bet.
  3. They will fold if the flop doesn’t look like it will bring them any good hands, but if they think they might get a strong hand, they’ll call persistently on the flop and turn (they won’t raise much if they don’t have a good hand).
  4. Their strategy on the river is unique; if they don’t get a strong hand, they fold, but if they do get a strong hand, they make a strong bet (even if they bet big enough, they don’t care if their opponent will fold if they find out how strong their hand is). It’s not uncommon for the river to turn into an all-in battle.
  5. They have a strong preference for hands close to the nuts, and often compete with straights, flushes, and full houses.

 On the Internet, it is often explained that because there are so many such players, the players of this game are low-level, or that there are many beginner-level players. In order to encourage such players to play correctly, a countermeasure that is sometimes suggested is to forcibly create an advantage for tight-aggressive play, such as increasing the open raise bet amount (e.g., 6bb entry). However, as I wrote at the beginning, I don’t think that players who adopt this type of playing style are weak players, and the orthodox playing style written about in poker books doesn’t seem very effective to me.

 I was thinking about how I could play the game to become the most powerful I could be, but I couldn’t come up with a good idea, so I did something strange and decided to ask ChatGPT. The answer I got was so unexpected that I was like, “Come on, can this really be true?” It was as follows.

How To Handle 500bb Match

According to ChatGPT’s response, the strategy when the stack is 500bb is completely different from the strategy when the stack is 100bb, and the optimal strategy is closer to the beginner-like play style (limper/caller) described in the previous section, and the strategy when the stack is 100bb as explained in poker books is rather a play that throws away EV (expected value minus play) and is not recommended.

 According to ChatGPT, the characteristics of 500bb matches can be summarized as follows:

  1. Postflop play becomes extremely deep. Because the implied odds become so large, even hands that look weak preflop become more widely available. In particular, low-ranking pocket pairs (22-66), Suited-Connectors (54s, 43s, etc.), and Suited-One-Gappers (75s, 64s, etc.) will become available hands (their value will increase significantly).
  2. Pre-flop, there are more situations where limping in or a small 3-bet is effective. Because the stacks are so deep, you need to be extremely careful when 4-bet or 5-bet preflop with anything other than AA or KK (if your opponent has AA or KK, you will be all-in and suffer a huge loss). As a result, 3-bet is often the upper limit, and the range of hands that can call a 3-bet based on implied odds is significantly wider. Limping in with a weak hand and waiting to see what happens until the flop is an option.
  3. This requires different play from general stack battles, such as building a range that focuses on the nuts hand (the strongest hand that can be constructed from common cards) and placing huge bets on the river.

As a result of the large implied odds in 500bb matches, the following characteristics arise in the game:

Characteristics Description
High VPIPMany hands are potentially strong, so it’s worth participating.
Easy to become multi-wayMany players participate with hands that are “weak now, but could be strong if they hit.”
Poker becomes more complicated after the flopIt’s hard to tell who has what hand, so you need to play nuts-oriented.
Bluffing becomes harderThe chances that the opponent will hit something are high, so stealing without careful thought is dangerous.
The strategic value of slow playIt is necessary to make your opponent make a hand and draw out the bet without being overturned.

The strategy comparison between 100bb and 500bb matches seems to be as follows:

100bb matches500bb matches
(Low Rank) Pocket PairSet mines are not in line with the oddsSet mines are very effective
Suited-ConnectorFolds if low rank Widely playable
Top Pair (One Pair)Aggressive value bettingPlay cautiously (two pairs are more likely)
Draw HandUse semi-bluffsBig bet if hit after the turn
Strong hands on the riverMaximum per pot betYou can bet 3 times the pot or more
VPIP20~25%25~30%
The importance of pre-flopVery high (miss-play is fatal)Still important, but flexible
The importance of post-flopLimited (often ends after 1-2 streets)Very high (assuming all streets are used)
Player typeGTO, tools-oriented, math-heavy, preflop optimization geekPsychological warfare (profiling opponents) and manipulation (drawing out the other player’s actions)

In the game I play, the ante is 0.25bb, so I would need to raise my VPIP by another 10% or so, so I think a VPIP of around 35-40% would be an appropriate level. Regarding the strategy I use of participating with all suited cards, I was told that if your position is BN or BB, you can participate with almost any suited card in your hand.

 In general, it seems that a strong strategy is to open the flop with a small investment, accelerate with an aggressive bet if you have a strong hand close to the nuts, and aim to win a big pot at the showdown. You might think that a strong bet would get folded, but in multi-way poker, there is a high probability that there will be a player who has some kind of strong hand or a drawing hand, so even with this strategy you can increase the pot. Players who are used to 100bb games might be tempted to tell them not to play like that, but it seems that this type of strategy wins out in 500bb games.

Play Loose Passively and Aggressively with Strong Hands

In summary, while a beginner-like loose passive strategy can be effective in 500bb matches, when you have a strong hand like the nuts, it is important to be aggressive and not hesitate to bet aggressively over the pot. Based on ChatGPT’s response, let me briefly summarize my opinion on what we should do.

  1. In multi-way you can call/raise with a wide range of cards preflop since narrowing your hand does not increase your expected value, and preflop bets tend to be very small (even 3-bet) due to the rules of the game. It may be best to enter with a range slightly narrower than your opponent. For example, if your opponent has a VPIP of around 60%, it would be best to enter with a VPIP of around 40-50%. You might be tempted to fold to a 3-bet with a weak hand, but because the implied odds are so high, it’s okay to call with most hands.
  2. The hand range includes many Suited and Connected hands, such as low rank pocket pairs(66-22), Axs, Kxs, low-ranked Suited-Connectors (54s, 43s, etc.), and Suited-One-Gappers (75s, 64s, etc.). On the other hand, since off-suits tend to be weak in multi-way poker, it may be better to fold questionable hands like K3o, Q5o, and J6o. However, at tables where 3-bets are rarely made, it may be better to limp in for the time being.
  3. It is better to think of premium hands as only AA and KK. AK is not a very strong hand in a 500bb match. It is better to go all-in with AA and KK preflop if possible. If you let the flop show after about 3 bets, your hand may not be that strong (If your opponent has two pair, your chances of coming back are low. In the games I play, it is common for AA or KK to lose to a hand like 64 or 53 that has two pair.). If you open the flop with 3 bets or less, it is better to play normally with AA or KK (don’t get bullish for no reason; until you hit anything, just think of it as an over-pair).
  4. If you don’t hit on the flop, you should basically fold. There is little need to hold out with a bluff, and the preflop bet amount will be small even if you cut your losses. On the other hand, if you have a monster hand (two pair or better), you should aggressively inflate the pot. If the aggressor is aggressive, you should call until the river and then reraise on the river (if you reraise along the way, they will tend to become wary and fold). However, if there is a possibility that the opponent can get a stronger hand (for example, if you have the nut straight but are afraid of a flush), it is better to reraise quickly. On the other hand, if the aggressor is passive, try to provoke him by making a donk bet or a small reraise (to make it look like you’re trying to bluff him into folding).
  5. If the flop shows a one pair, such as top pair top kicker (TPTK), it is better to bet moderately and fold if your opponent comes out aggressively. It may be a strong hand in heads-up, but in multi-way, it seems that players often play aggressively based on whether they can beat the top one pair. If there are many opponents remaining, try to call draw hands such as straight draws and flush draws as persistently as possible. Even if you don’t have the required win percentage in a heads-up match, if there are 4 or 5 players left, your required win percentage will be about half. Also, because the implied odds are large, it is often worth betting on the small chance of winning.
  6. Against players who open raise frequently to 6bb or 9bb (isolation raises), a back raise strategy is effective. You can discourage easy raises by deliberately limping in with strong hands such as AA, KK, or AK, and then following up an open-raise with a 4x reraise (AK) or going all-in (AA or KK). If you use AA or KK and your all-in is called, you can often get lucky and take the whole stack (although sometimes you can get into a bad situation). It is a good idea to include a certain number of strong hands in your limp-in range to give the impression that limping in is not necessarily a weak hand. By using such a strategy, you can make it easier to see the flop even with weak hands.
  7. Furthermore, even 6bb or 9bb are small bets, so it is okay to call with many hands. A player who isolates raises is likely to have a tight range, so you can estimate your opponent’s hand range within a narrow range. On the other hand, your opponent will have no way of guessing the limper/caller’s range, so you’ll likely have an advantage after the flop. If your hand range is wide, your win rate will decrease, but if the implied odds are large, the low win rate will not be a big problem. Narrowing your hand range will allow your opponent to follow your plan, so it is a good idea to use a method to take advantage of this.
  8. You can bluff on the river or use polarized bets, but do so less frequently. Most people who fold when bluffing are with weak hands (high cards, bottom pair), and limpers/callers will usually call if they have a hand of top pair or better. There is no need to use polarized bets, as your opponent will usually call you if they have top pair or better. Also, players at the table change frequently, and most players will not remember who is playing what. Since you don’t know your opponent’s strategy, you have no choice but to call with a strong hand even if there is a possibility that you will lose (it will also be difficult for you to fold to your opponent’s aggressive bet, and you will be forced to call with top pair or better).
  9. In multiway, the strategic value of bluffing is reduced, while slow play must be effectively implemented. You need to find the balance between the risk of a reversal and the return you can get from other players’ calls/bets, and choose whether to make a strong bet or to draw out a bet from your opponent. For example, if you get a full house on the flop but two cards of the same suit are dealt or the board looks like it could make a straight, a possible strategy would be to wait until the river (for another player to make a straight or a flush), because you won’t get much chips by folding on the flop. In this case, you may be able to draw a bet on the turn, or you may be called even if you go all-in on the river.

 Overall, at first glance, this playing style may seem like a companion to the Limper/Caller style, but in terms of maximizing expected value, it is likely to be close to the optimal solution. In the game I play, there are two types of limpers/callers: beginners who become limpers/callers, and advanced players who play like limpers/callers in order to make full use of their 500bb stacks. In the former case, it is easy to win, but in the latter case, it is possible that the player is using a strategy close to the optimal strategy, making it difficult to win. In 500bb matches, a limper/caller-like strategy may be close to a Nash equilibrium strategy, and unfortunately it is unlikely that there is an easy exploit strategy (In the end, it doesn’t look like I’ll be able to be the most powerful…).

 The reason why players who use 100bb strategies can still compete reasonably well is probably because there is a high proportion of beginner limpers/callers, and there are not many players who consciously employ a style of play that makes full use of 500bb stacks. There are also many players who use strategies for 100bb matches, and there are probably many cases where players simply have 500bb stacks (effectively a 100bb match). Players who use 100bb strategies often find themselves frustrated when facing advanced limpers/callers. Some people may be tempted to criticize others by saying, “Don’t come in with such a weak hand, that’s what amateurs do (angry)” when their strong hand is stabbed by the slow play of a weak hand, but in this game, the player who uses such a strategy may be one step ahead.

 If you apply a strategy that is effective in 500bb matches to a regular game, it may end up being a strategy that only works for amateurs, so it should only be used in 500bb matches. The exception to this is that at high stakes tables the buy-ins for stacks are sometimes “uncapped”, meaning that wealthy players are playing with over 500bb of chips at the table. In this case, you should be careful because textbook play may not be very effective. Well, this is probably not relevant to most people, including me…

Appendix: If You Still Can’t Tolerate the Limpers/Callers

For those who still cannot tolerate the Limper/Caller, let’s consider some countermeasures against them. The weaknesses of the Limper/Caller are as follows:

  1. The hand range is too wide, so it includes many relatively weak hands.
  2. It is not uncommon to limp-in even with strong hands preflop.
  3. Less tolerant of bluffs (especially on the flop).
  4. Since the actions are different when they have a strong hand (donk bet or check-raise) and when they have nothing (check-call), it tends to be easy to guess the strength of their hand.
  5. Even if they have a weak hand, if they have a draw (straight draw, flush draw), you will tend to call until the river. If they have a strong hand, they will take obvious action such as making a huge bet on the river.
  6. They rarely bluff or catch. Since there is almost no need to suspect a bluff or bluff catch (because it is a value bet), it is easy to take appropriate evasive action.

 A strategy to attack these features might be as follows:

  1. Use a range slightly narrower than the limper/caller and enter relatively strong. Use light 3-bets (reraise by 2x) and isolation raises, but fold weak hands to keep the strength of your range appropriate. Don’t call back-raise all-ins or re-raise all-ins, except with AA or KK. Don’t ruin your strategy by repeatedly making isolation raises without maintaining the strength of your range, or by calling a re-raise all-in in anger.
  2. Make it a point to make the final raise preflop, as you are more likely to be the aggressor and take control of the pot. After the flop, you should manage the pot only when the board is favorable for you, and check on tricky boards to avoid giving unnecessary chips to passive players.
  3. If you are an aggressor, unless the board is extremely unfavorable, you will CB 33% of the time on the flop. If you are lucky, everyone will fold. Other than this, you will not make any unnecessary bluffs.
  4. If you receive a donk bet or check-raise, your opponent has two pairs or better, so fold if you have no chance of winning. On the other hand, if you have a nut level hand (nut straight/nut flush or full house), you have a chance, so inflate the pot to all-in. Even if you go all-in, there is a high chance that your opponent will call.
  5. If your opponent is shy but keeps calling, they probably have a straight draw or a flush draw, so if you can guess what hand they are aiming for, you should raise your bet and hope that their hand does not get made. If the hand is not made, there is a high possibility that you can bluff even if your hand is a garbage hand. If you want to use bluffing, do it on the river. If you bluff on the river, do not hesitate to hit a huge bet size bluff (such as a 3x pot bet). Don’t let your opponent call with a half-decent one pair. If your opponent re-raises, give up because your opponent’s hand is valid (not a bluff catch).
  6. If there are four or more players on the flop (which frequently occurs even if you 3-bet or isolate raise), the above strategy is less likely to work, so you should just wait patiently for a strong hand. Don’t try to force your opponent to take countermeasures against limpers/callers. If you try to force your opponent into a heads-up match, you will likely end up facing a player with a strong hand, so if you can’t narrow down the number of players in a certain way, it’s better to give up.
  7. The strategy to deal with Limper/Caller is generally to pick up pennies in front of the bulldozer, and one mistake can take away your entire stack, so you need to be extremely careful when using it. If you see any suspicious moves, it is better to choose to fold. You can’t assume that they don’t have this hand, so you need to always assume the worst case scenario when deciding what to do.

You may be thinking, I know that, but it still doesn’t work, but the reason Limper/Caller hunting fails is because these strategies are difficult to implement properly. Limpers/callers are also aware of these strategies, and if there is a player making an isolation raise, they may target you and attack you, so if you feel like you are being targeted, it may be best to leave the table.

 As another option, I asked ChatGPT if I could set my own buy-in to 100bb and fight like it was a 100bb match, but the answer was “no.” It could be said that players who are good at 100bb matches are those who are confident in using bluffs effectively. However, if your opponent has a 500bb stack and you only have 100bb, will your bluff all-in scare the player with the 500bb stack? If they only lose 20% of their stack if they lose, they seem less likely to fold out of fear of their opponent’s strong hand in a game they have a reasonable chance of winning. On the other hand, if a player with 500bb judges that they have an advantage on the flop, and there is a player with only 100bb, they will tend to play “I’ll just require for an all-in for now,” and the player with only 100bb will be at a disadvantage in that they will be limited in the number of decisions they can make.

 In the end, in order to bluff effectively in Texas Hold’em, you need a relatively large stack, and without one you are at a disadvantage. It is often said that in poker, the chips on the table are like ammunition used to intimidate your opponent, and fighting with so few of them is like a small country going to war with a large one. When playing Texas Hold’em, it is easy to understand that it is generally more advantageous to buy in to the maximum amount.

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