I play in an underground room which runs 1-2, and occasionally the game will feature a "straddle chip" worth $5. The rules governing this chip are as follows:

--the player who has the chip must use it straddle when UTG, although it also can be used with an extra $5 to double-straddle from UTG+1.
--if the player forgets to straddle UTG while in possession of the chip, the chip is forfeited and tossed into the next hand's pot.
--the chip cannot be used to bet or call, unless the player is betting or calling all-in.
--the chip can only be cashed out if the table breaks; otherwise, if one leaves while holding the chip it gets tossed into the next pot.

Although the chip clearly has monetary value, since it pays for our blind when others who want to play the hand have to match it with real redbirds, it feels like the restrictions on its use makes it worth less than $5, which is messing with me with respect to bet sizing, pot odds, etc.

Can anyone offer an opinion as to the value of this chip?

I'm going to ignore the double straddle and assume you never forget to straddle when you hold it UTG.

The chip is like a $5 chip, with two disadvantages. First, holding it obligates you to straddle when UTG. Blind straddling has a negative EV. Second, if you leave before the table breaks, you forfeit its value.

If you're planning to play a while and the table is not near breaking, the second factor is negligible. Holding the chip now has small effect on who will hold it when you leave or the table breaks. This factor only comes in to play late in the game.

If you hold the chip early in play, I'd say it's worth something like $4.50. You'll likely hold the chip the next time you're UTG (the only other scenario is you go all-in and lose, which isn't common), so you'll lose the EV of a $5 blind straddle, which is maybe $0.50 depending on the game. That $0.50 is a benefit to the other players at the table.

I think I disagree. If you consider a single UTG hand where you have the chip, then I think it's value in that hand is potentially MORE than $5. You can almost consider the chip as having $0 in cash out value. So posting it as UTG means you're paying a $5 with money that's worth nearly zero. It's like someone posted for you. Playing the hand might only be worth $4 but that's more like +$4, not -$1

If it has a negative value overall I think it might come from places where you're the SB or BB and UTG has the special chip, because now your BB will lose even more than normal.

If you were in a hand where the straddle chip was in play, would you would treat the chip as being equal to $5 in your equity calculations? If not, what value would you assign it?

I was answering the question of the value of having the chip. Since the chip will be worth $5 to someone when the table breaks up, any difference of chip value from $5 must be offset by equal and opposite value shared among the other players, the ones who do not hold the chip. Since I think it's worth $4.50 to the person who holds it, it's worth a few cents to the people who don't hold it.

I don't understand your logic about the value. You say the chip is like posting $5 with something worth nearly zero. You then say (I think) that posting the $5 might be worth $4 to you. In that case, the value of holding the chip is $4, since that's what it buys you, and you're compelled to spend it.

Say you're playing poker UTG and before you look at your cards, the poker room manager comes over and puts in a $5 blind straddle for you as a good customer promotion (assume the other players don't object). Do you agree that makes you $4 or $4.50 richer than you were before? And that the other players at the table share a value that adds up to $1 or $0.50 or whatever makes the total value $5? In that case, I think you agree with me about the chip value.

Yeah I think I do agree with you although I kind of get myself confused thinking about it too much.

It's a bit like the rule of thumb in basketball that says possession of the ball is worth one point. In that case, shooting a two-point basket is a break even event. You get two points, but you give up a net two because possession shifts from your team (+1) to the other team (-1). In order to pull ahead in the game you have to make a shot AND get the ball back without allowing the other team to score.

If the straddle chip is worth $5, then it's not worth much, because you have to bet it blind, in which case it belongs the the player with the best hand, which has only chance one over the number of players of being you. It's worth the same to every player, holding it doesn't matter. But then if the straddle chip isn't worth much, it's worth nearly $5, because you can post a $5 bet with something worth very little.

I can see why it's confusing.

I think you guys are way overestimating its value.

In full ring play, a decent win/loss rate from the big blind is roughly -40bb/100. That means that you on average lose 40% of your bb. Since the straddle is going to behave similarly to an additional blind, I'd say the value of the $5 chip is probably something like $3.

Edit: Actually, since it has less value for other players to attack than a full $5 blind (just $3), you'll keep it more and the value is a bit higher. However, it seems like this would only move the value to about $3.50.

The chip is worth $5 less the average rake percentage.

How much of that amount translates to the holder of that chip is dependent on many factors such as the number of players, relative skill of each player for their respective positions, style of players in late position, absentmindedness etc.

Not necessarily in that order. If I'm holding the chip, it's worth about $0.50.

As AB said the balance of that $5 - $5 * R% goes to the other players at the table.

If you take out skill, on average, the button gets the largest share of the balance and other players shares would decrease with position.

As NYC_Jon hints, how that $5 is divided up, a first order estimate could be based on average win-rates in each position although just introducing that chip would change these numbers by some significant amount making the problem a bit more complex than that.

Since it seems to be implied that the house is supplying the chip, it also makes me wonder what the conditions for introducing it would be and if it impacts the rake when it's introduced?

The value of the chip to the person holding it is going to depend on three factors - their position, their playing style, and how many hands are left to play before the end of the night. Let's model this with some slightly simplifying assumptions:

• A 6-handed table
• Every player has probability p of keeping the chip if they hold it UTG
• Every non-UTG player has equal probability of getting the chip when it is used
• Instead of "when the table breaks" as the end condition, let's use "in n hands"

What's the probability of straddle keeping the chip? I'm going to guess that a strong aggressive player would have a 40% chance six-handed, but by making it a variable, I can eliminate the guesswork and also let other people plug in the value they prefer.

With these assumptions, the only things that determine value to me are: Who has the chip; what position I am in for this hand; and how many hands are left to play. Rather than determining how much the chip is "worth" to each player, I'll compute the probability that any given player will have it at the end of the night.

When n = 0 - after the last hand has been played - the chip held by the person holding it. This gives that person 100% and everybody else 0%.

When n = 1 - at the start of the final hand - the chip is still 100% with the holder unless she is UTG. In that case, the chip is p with the holder, and (1 - p)/5 with everyone else. At p = 0.4, it's 40% to the holder and 12% to the other players.

When n = 2 and the holder is UTG, things get a bit more interesting. Using the 40% example, 40% of the time she keeps the chip; 48% of the time she loses it to a player who keeps it until the final hand; but 12% of the time she loses it to HJ, and it then goes into the pot again. So HJ only gets it 40% of 12% (4.8%), while everyone else gains an extra 12% of 12% (1.44%).

In general, this model is easy to compute by iterating 36 values: we need to keep track of each position's probability at the table on each hand, and there are 6 possible places for the chip to be relative to the button.

Interestingly, the chip does not end up being distributed evenly to everybody in the long run, which is what I would have expected. For 40%, the values converge as follows (for the seats that people are sitting in on the final hand):

UTG 10/105
HJ 13/105
CO 16/105
BT 19/105
SB 22/105
BB 25/105

By trial and error, I have determined that for probability p, the values converge as follows: UTG gets p/(3(p + 1)), and each move of one seat to the right from there gains (1 - p)/(15(p + 1)) over the previous seat. As far as just the straddle chip goes, you prefer to be sitting in the big blind at the end of the night.

Just to forestall the inevitable comments, I am aware that this is only a model. I am aware that different positions are stronger and weaker. But as a first approximation, I think this is a decent place to start.

Is the double straddle option available when UTG folds/doesn't straddle ..not sure how that would work?
If the double straddle does require additional funds we can indeed ignore it
...except as a tool for generating action -which is presumably why it's there in the first place. As such you probably want to encourage the double straddle and then 'forget' to do so.

I suspect that this will be a game where 40% retention UTG is optimistic in general with a lot of action and wide variety of skill.

Having it at the table could well be worth more than $5 (as an action generator) to the skilful player regardless of who holds it.

In hand.. it's going to be in the $3-$4.5 range but highly dependent on the table in question.
I'd be tempted to call it $3 for your pot odds calculations to be on the safe side: you want to err on the side of profitability. (assume the opponent treats it as $5 if you think they are doing PO Calcs)

I would expect the value of the chip [B]to the table to be negative[b] since it will get raked itself maybe twice every time round the table and probably generate extra (raked) action even outside the hands it is used.

This is all excellent for the winning player* but bear in mind that it's effectively increasing the size of the blinds which affects your effective stack size and bankroll management.

* be careful about how you let it affect your play. In particular don't straddle when you don't have it (unless you are trying to generate action).

It's worth about 25 cents at the start of a session and about $5 1 hand before the game breaks.

I think this ignores the important factor of how having the chip affects your chances of collecting regular chips.

Consider the hands that you straddle with the chip and win, and that you would have won without the chip. On average, we expect these winning pots to be larger by more than the straddle chip amount. That doesn't have to be true, for example the straddle could induce everyone to fold, when you would have otherwise would have won a large pot on the river. But just as larger blinds make for larger pots, increasing the initial bet without giving information to suggest your hand is strong, likely increases the average pot.

Next there are the hands that you would have folded without the straddle chip, and fold at your first opportunity with the straddle chip. On these you lose the straddle chip, but nothing else. So you're no poorer in regular chips for having held the straddle chip.

Next there are some hands that you would have folded without the straddle chip, but see the flop because you had the chip. On average, we expect you to make money on these hands, or at least more money than you make on other hands. You got to see the flop more cheaply than you should have, and you got information on all the other players at the table before you had to make your first voluntary contribution.

Thus I think most of the value of holding the straddle chip comes from the possibility of turning it into regular chips before the end of the session. I agree that holding the chip any time other than late in the session has little influence on who is likely to cash it in. But I think that approach undervalues holding the chip.

Just to clarify/correct my earlier thoughts.

The chip is valuable to the table as a whole if they don't respond by playing more loosely and if it frequently passes through the pot without being raked (assuming uncalled pots are not raked).
You should play tighter with this chip on the table (though still adjust that for the behaviour of other players).