user20657: Choker (chess + poker) was released recently as a mobile app. It is a game where players have a round of poker to bet on cards they draw. They then use these cards to play chess and win the bets. It's 1 on 1, like regular chess.

My concern is that choker is not quite balanced in that I think it happens too frequently that one of the players has a really strong hand in that the other ends up being down a piece.

Another reason I think this is especially due to the fact that you cannot see your opponent's pieces until they place all of them. (However, this does not seem to be the case in the most recent version of the app.)

Also, there's that you can't quite have 2 pieces of the same "suit" (there are pre-chess-promotion and demotion rules) or even place the pieces except pawns anywhere on our side besides the 1st 2 rows.


Question: Is this a balanced game?
Sub-questions: What are the probabilities of the hands in choker? How far apart are the 2 player's hands on average? Do the promotion/demotion rules make choker less balanced?

user4399: 2021 Update: i think they've done more edits to the app and the game.
The app: The app was unfortunately not so good but I believe at least a little better now.
The game: I think the game is pretty balanced and fun and indeed requires skill in both chess and poker (well, maybe depends if the game has proper blinds and stuff). Thus, 'worth playing'. I think the best evidence for this is that there's already a choker cup, livestreamed by chess24.
Note that by giving the choker cup as an argument, this argument is more a posteriori than a priori or something. I'm not really arguing in terms of the rules of the game. I'm arguing like if there's a choker cup and Hikaru Nakamura, Alex Botez and Eric Rosen are playing this, then the game must be pretty balanced or whatever and thus 'worth playing'.

user-1: I am referring to the following rules. 

My concern is that this is very unfair to one of the players as often
  even strong hands are not strong enough and end up being down a piece.

Let's calculate the material imbalance of one million random hands (sorry, it would have been too much hard for me to program the promotion and demotion rules).
import itertools
import random
import matplotlib.pyplot as plt
import numpy as np

deck = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,9,9,9,9]

cardCombinations = list(itertools.combinations(deck, 5))

arrayUnbalance = []

for i in range (1000000):
    randomHandWhite = random.randint(0, len(cardCombinations)-1)
    randomHandBlack = random.randint(0, len(cardCombinations)-1)
    unbalance = abs(sum(cardCombinations[randomHandWhite])-sum(cardCombinations[randomHandBlack]))
    arrayUnbalance.append(unbalance)

plt.hist(arrayUnbalance, bins=range(0,30,1))
plt.show()


The imbalance is always an even number. I think this is because all values are odd and all subtractions results in an even number.

~12% ~14% of hands are equal and perfectly playable, but titled players could find them drawish.
~22% ~27% of hands are unbalanced +2, and at a medium level the weak side can play for a draw to recover half of the pot, especially if you play the white pieces.
~66% ~59% of hands are resigning positions at my level.

After D M calcs with the full rules

Another reason I think this is especially due to the fact that you
  cannot see your opponent's pieces until they place all of them.

Where I play this is not the case. Players place the pieces in turns and you can see where your opponent is placing the pieces. 
A minor consideration is that black has a slight disadvantage in this step of the game, as white's last piece can create forks and gain material (it is white's turn).

Also, why can't we pre-move or have more than 2 pieces of the same
  "suit" or even place the pieces anywhere on our side rather than first
  2 rows?

I agree pre-moves are important when you play a 3 minutes (end)game on a smartphone. I would like the site I play allow them.
A player with three bishops or knights would be a bit weird in my opinion. To place two bishops in the same color square is not allowed. I find it logical as promotions to bishops or knights are rare in chess.
To allow pawns to be placed on the 7th rank would alter the poker part. I like your idea of allowing the rest of pieces to be placed on all rows, the chess game would become more aggressive, but maybe this would give white a big advantage.

After that, I think a titled player could not profit his chess skill to beat a top poker player (maybe Nakamura would do). With a medium chess knowledge the poker player would beat the chess player as they do at Texas holdem. 
Another problem I see is there are no online cash games at the moment. And what happens when you play poker with no cash? Everybody goes all-in with trash. You don't learn anything. 
If you wish to play a serious game against a casual poker player and a 1800 rated chess player, you can add me as a friend on the app, my nickname is briest-man.
Ay, my level the game is funny. You can create threats when you place the (white) pieces and you have not a lot of time to finish the endgame. I profit my chess skill to beat players with my poker level, but weaker than me. I can stay on the site not paying any penny for the virtual chips. I wish there were cash games to play at low tables. 

user12629: 
My concern is that this is very unfair to one of the players as often even strong hands are not strong enough and end up being down a piece. 

But in regular poker, the hand would simply be over at this point. If you're looking for a fair chess game, just play chess!
I included the promotion/demotion/palace/empress rules and simulated a million hands, and came up with the following material imbalances:
0   : 141731
2   : 268811
4   : 223876
6   : 154819
8   : 94144
10  : 54601
More: 62018

This is slightly more equal than without those rules, but it's still rather imbalanced. The median hand will give one side a +4 advantage. I think the idea is that someone is supposed to fold during the betting if there is a large difference between the hands; this may reduce the number of uncompetitive chess games.
I think this variation may be somewhat useful for those who are not able to consistently win an early endgame position with a +2 or +4 advantage. Given that you probably don't get a lot of time to play the game, it may also be useful for practicing being in time trouble at the end of the game. 
But there are probably better ways you could practice your endgame.  In the end, it's worth playing if, and only if, you have fun.

20657: <p><a href="https://chokergame.com/" rel="nofollow noreferrer">Choker (chess + poker)</a> was released recently as a mobile app. It is a game where players have a round of poker to bet on cards they draw. They then use these cards to play chess and win the bets. It's 1 on 1, like regular chess.</p>
<ol>
<li><p>My concern is that choker is not quite balanced in that I think it happens too frequently that one of the players has a really strong hand in that the other ends up being down a piece.</p>
</li>
<li><p>Another reason I think this is especially due to the fact that you cannot see your opponent's pieces until they place all of them. (However, this does not seem to be the case in the most recent version of the app.)</p>
</li>
<li><p>Also, there's that you can't quite have 2 pieces of the same &quot;suit&quot; (there are pre-chess-promotion and demotion rules) or even place the pieces except pawns anywhere on our side besides the 1st 2 rows.</p>
</li>
</ol>
<p>Question: Is this a balanced game?</p>
<p>Sub-questions: What are the probabilities of the hands in choker? How far apart are the 2 player's hands on average? Do the promotion/demotion rules make choker less balanced?</p>
 4399: <p><strong>2021 Update</strong>: i think they've done more edits to the app and the game.</p>
<p>The app: The app was unfortunately not so good but I believe at least a little better now.</p>
<p>The game: I think the game is pretty balanced and fun and indeed requires skill in both chess and poker (well, maybe depends if the game has proper blinds and stuff). Thus, 'worth playing'. I think the best evidence for this is that there's already a <a href="https://www.youtube.com/watch?v=dsHpVDuWRyI" rel="nofollow noreferrer">choker cup</a>, livestreamed by chess24.</p>
<p>Note that by giving the choker cup as an argument, this argument is more a posteriori than a priori or something. I'm not really arguing in terms of the rules of the game. I'm arguing like if there's a choker cup and Hikaru Nakamura, Alex Botez and Eric Rosen are playing this, then the game must be pretty balanced or whatever and thus 'worth playing'.</p>
 -1: <p>I am referring to the following <a href="https://chokergame.com/rules/" rel="nofollow noreferrer">rules</a>. </p>

<blockquote>
  <p>My concern is that this is very unfair to one of the players as often
  even strong hands are not strong enough and end up being down a piece.</p>
</blockquote>

<p>Let's calculate the material imbalance of one million random hands (sorry, it would have been too much hard for me to program the promotion and demotion rules).</p>

<pre><code>import itertools
import random
import matplotlib.pyplot as plt
import numpy as np

deck = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,9,9,9,9]

cardCombinations = list(itertools.combinations(deck, 5))

arrayUnbalance = []

for i in range (1000000):
    randomHandWhite = random.randint(0, len(cardCombinations)-1)
    randomHandBlack = random.randint(0, len(cardCombinations)-1)
    unbalance = abs(sum(cardCombinations[randomHandWhite])-sum(cardCombinations[randomHandBlack]))
    arrayUnbalance.append(unbalance)

plt.hist(arrayUnbalance, bins=range(0,30,1))
plt.show()
</code></pre>

<p><a href="https://i.stack.imgur.com/ExW4P.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ExW4P.png" alt="enter image description here"></a></p>

<p>The imbalance is always an even number. I think this is because all values are odd and all subtractions results in an even number.</p>

<ul>
<li><s>~12%</s> ~14% of hands are equal and perfectly playable, but titled players could find them drawish.</li>
<li><s>~22%</s> ~27% of hands are unbalanced +2, and at a medium level the weak side can play for a draw to recover half of the pot, especially if you play the white pieces.</li>
<li><s>~66%</s> ~59% of hands are resigning positions at my level.</li>
</ul>

<p><em><a href="https://chess.stackexchange.com/a/27682/18196">After D M calcs</a> with the full rules</em></p>

<blockquote>
  <p>Another reason I think this is especially due to the fact that you
  cannot see your opponent's pieces until they place all of them.</p>
</blockquote>

<p><a href="https://play.google.com/store/apps/details?id=com.queenloop.choker&amp;hl=es_419" rel="nofollow noreferrer">Where I play</a> this is not the case. Players place the pieces in turns and you can see where your opponent is placing the pieces. </p>

<p>A minor consideration is that black has a slight disadvantage in this step of the game, as white's last piece can create forks and gain material (it is white's turn).</p>

<blockquote>
  <p>Also, why can't we pre-move or have more than 2 pieces of the same
  "suit" or even place the pieces anywhere on our side rather than first
  2 rows?</p>
</blockquote>

<p>I agree pre-moves are important when you play a 3 minutes (end)game on a smartphone. I would like the site I play allow them.</p>

<p>A player with three bishops or knights would be a bit weird in my opinion. To place two bishops in the same color square is not allowed. I find it logical as promotions to bishops or knights are rare in chess.</p>

<p>To allow pawns to be placed on the 7th rank would alter the poker part. I like your idea of allowing the rest of pieces to be placed on all rows, the chess game would become more aggressive, but maybe this would give white a big advantage.</p>

<hr>

<p>After that, I think a titled player could not profit his chess skill to beat a top poker player (maybe Nakamura would do). With a medium chess knowledge the poker player would beat the chess player <a href="https://www.pokernews.com/news/2018/03/chess-francisco-vallejo-pons-poker-tax-dispute-30327.htm" rel="nofollow noreferrer">as they do at Texas holdem</a>. </p>

<p>Another problem I see is there are no online cash games at the moment. And what happens when you play poker with no cash? Everybody goes all-in with trash. You don't learn anything. </p>

<p>If you wish to play a serious game against a casual poker player and a 1800 rated chess player, you can add me as a friend on the app, my nickname is briest-man.</p>

<p>Ay, my level the game is funny. You can create threats when you place the (white) pieces and you have not a lot of time to finish the endgame. I profit my chess skill to beat players with my poker level, but weaker than me. I can stay on the site not paying any penny for the virtual chips. I wish there were cash games to play at low tables. </p>
 12629: <blockquote>
  <p>My concern is that this is very unfair to one of the players as often even strong hands are not strong enough and end up being down a piece. </p>
</blockquote>

<p>But in regular poker, the hand would simply be over at this point. If you're looking for a fair chess game, just play chess!</p>

<p>I included the promotion/demotion/palace/empress rules and simulated a million hands, and came up with the following material imbalances:</p>

<pre><code>0   : 141731
2   : 268811
4   : 223876
6   : 154819
8   : 94144
10  : 54601
More: 62018
</code></pre>

<p>This is slightly more equal than without those rules, but it's still rather imbalanced. The median hand will give one side a +4 advantage. I think the idea is that someone is supposed to fold during the betting if there is a large difference between the hands; this may reduce the number of uncompetitive chess games.</p>

<p>I think this variation may be somewhat useful for those who are <em>not</em> able to consistently win an early endgame position with a +2 or +4 advantage. Given that you probably don't get a lot of time to play the game, it may also be useful for practicing being in time trouble at the end of the game. </p>

<p>But there are probably better ways you could practice your endgame.  In the end, it's worth playing if, and only if, you have fun.</p>
