Matt Matros article in Cardplayer about coinflips

[A_PLUS]

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He says you only need a 59% chance or better of doubling your stack at some point if you fold here. I don't have the data to back it up, but I think this is definitely possible at a table full of crap players.

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Your missing a key point of his analysis.

It isnt that you just have to double up at some point in the tournament. For the situation to be equal you have to catch up to the 20K stack.

Here is a good way of thinking about it.

You clone yourself and enter into a tournament. Both versions of yourself have the QQ vs AK scenario for the first hand. Version A takes the flip, version B folds.

From there both versions go and accumulate chips. As soon as Version A (assuming he wins the flip) increases his stack, version B now has a new target. You not only need to make up for the 10,000 chips you missed out on by the coin flip, but also all of the chips that version A has won in the same amount of time.

Where the 59% came into play in the article was taking into account these 'newly accumulated chips'.

We take any time frame
-1 hand

If Version A of myself failed to accumulate any chips, I would only need a 53% chance to double up to be even with him (in terms of EV)

53% of the time A has 20,000 chips, so EV = 10600
We want to know how often we need to get to 20K
20,000 x X% = 10,600......X% = 53%

-100 hands
Version A is expected to win 700 chips. Now my target is 20, 700 chips. During the same time frame, how often would I need to double to be equal to A in terms of EV?

EV(A) = 20700 x .53 = 10,971
EV(B) = 20000 x X% = 10,971
X% = 54.8%

The longer it will take you to double up, the higher frequency you will have to do it with to be even with the Version A (takes flip) of yourself.

It is easy to pass on a flip, then look back at the 1st break and say "hey, I doubled up anyway, I must have been correct to pass". We forget to think about the fact that if we had taken the flip, we would be at 3x our original stack now, not just double.

hope this helps

[twang]

Ok, I'll probably make a fool of myself, but I thought about how significant doubling your % of chip total from 0.1% to 0.2% really is. At first glance it seems pretty insignificant in a large field; increasing your % of the chips total from 0.1% to 0.2% seems like nothing. But let's look at an example:

1000 players of the same skill level plays an MTT. Buyin is $30. Prize pool is $30K. (First price is $6500.) Each player start with $1000 in chips.

In other words, you start the tourney with 0.1% of the chip total. This makes your share of the prize pool 0.1% * $30,000 = $30.

Now, assume you play a 50-50 hand all-in the first hand in the MTT. If you lose the flip your share of the total prize pool is 0. If you win the flip, your share of the flop is all of a sudden $60, $30 more than your buyin. I think that this is a likeable bet.

Given that the bet above is good, what about making the same bet further into the tourney? Say you are in 2nd hour and your stacksize is $5000. $5000 is 0.5% of the chip total, which makes your share of the prize pool 0.5% * $30,000 = $150.

Now the same situation comes up again and you're facing another 50-50 bet. If you win the flip, your share of the prize pool is 0. But if you win the flip your share is $300.

If the examples above are valid, the first thing one realizes is that the bigger stack you have when making a flip vs an equally sized stack, the better the payoff (doh!). At these early levels the bets are good, but not overwhelmingly great. But when ITM they are a sweet deal, because losing doesn't mean 0 - it means the bustout prize, whatever that is. And if you win, the payoff is huge, the extreme example being flipping between 1st and 2nd prize. It's a win-win situation, basically.

The other lesson is that the value of an early coin-flip depends of the size of the prize pool. If we would change the prize pool in the example above from $30,000 to $15,000 (everything else stays the same), taking a coinflip in the first hand would not be good.

For some reason, all this reminds me about Ed Miller's "You guys fold too much"-post where the billionaire walked by and dropped an "extra" $1000,000 in the pot. In MTTs the prize pool is the pot and the bigger the potential win, the better the bet. Coinflipping at the FT are the best bet there is.

Simple 50/50 coin-flipping is always a bad idea unless you're head-to-head. Because when you coin-flip, it's win-win for the rest of the people in the tournament.

Let's say that there are three people left in the tournament. Prizes are $500, $300 and $200. You and player B have $4999 in chips and player C has $2 in chips. If you flip a coin with player B, one of you will bust out and take the $200 prize. The other will be in great shape to take the $500 first prize. On average you win $350. If you don't take the flip, player C will almost certainly take 3rd prize and you and B will win $400 on average. So by flipping, you're donating $100 to player C.

Bad move...

[A_PLUS]

You started off so good....

1.) changing the prize pool, doesn't change anything. We are thinking of things in terms of % of total prizes, so it doesnt change anything if it 1$, or a million

2.) Once we are in the money, the prize you get when you bust out now is completely irrelevant. Everyone gets at least that much, so it doesn't effect decision making if it is 0 or a million, doesnt matter. What matters is the distribution of the rest of the payouts.

3.)Flips make less sense at the final table. Here, your % of total chips does not equal the % of the total prize pool, b/c some of the prizes have already been given out. Also, just surviving has real $ value. Each time someone busts out you make money.

[A_PLUS]

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Simple 50/50 coin-flipping is always a bad idea unless you're head-to-head. Because when you coin-flip, it's win-win for the rest of the people in the tournament.

Let's say that there are three people left in the tournament. Prizes are $500, $300 and $200. You and player B have $4999 in chips and player C has $2 in chips. If you flip a coin with player B, one of you will bust out and take the $200 prize. The other will be in great shape to take the $500 first prize. On average you win $350. If you don't take the flip, player C will almost certainly take 3rd prize and you and B will win $400 on average. So by flipping, you're donating $100 to player C.

Bad move...

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You gave an example of one very specific case when you shouldn't take a coin flip. A little different than proving that you shouldnt take 50/50 flips period.

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53% of the time A has 20,000 chips, so EV = 10600
We want to know how often we need to get to 20K
20,000 x X% = 10,600......X% = 53%

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Respectfully, IMHO there is a problem with this analysis. This is no limit, not limit or pot limit.

53% of the time you double and still have a chance to cash. 47% of the time you are out and have no chance to cash.

In neither case has any financial expectation been reached. And isn't that the whole point, financial expectation rather than tournament chip expectation?

The real questions to be asked and answered for the analysis are:
- On average for 1000 runners all starting at 10K, how many chips are required to cash and to make the final table?
- Does the 1st hand double increase the chances of getting to that point?

Without going back to BurningYen's post for reference, I would speculate for purposes of discussion, that it takes roughly 2% or better of the tournament chips to get to the money and roughly 8% or better to get to the FT.

In the OP example, there are roughly 10M tournament chips in play. You need roughly 2% or 200K to get to the money and roughly 800K for the FT.

Does that first hand double significantly increase your chances of getting to 200K or 800K minimum thresholds? This is the real question IMHO.

I think part of the answer lies in the skill of the player, as another poster hinted at. If I'm the worst player in the tournament, then yeah, maybe I take that shot because I'm going to have to hit the lottery just to cash anyway. Might as well try to get lucky right off the bat.

On the other hand, if I'm one of the top players in the tourney and figure that I'm even money to get to minimum cash and maybe 9-1 to make the FT, then there's no way I take that risk when I know that I have more than a reasonable chance of grinding this player and other players out of their chips.

[A_PLUS]

No matter which way you slice it, you need to get to the 20K point in chips.

You can start at 20K 53% of the time
or
You can start at 10K 100% of the time

No matter what way you have of measuring $EV, 20K is better than 10K.

It will take you a certain number of hands to reasonably expect to get to 20K from 10K. This will be different for every player.

During the time it will take you to get from 10K to 20K, you also could have been playing with a 20K stack (53% of the time if you took the coin flip).

So, at the end of this time period you have two stacks to analyze, the 20K that you earned from the 10K, and how many total chips you would have if you won the QQ coin flip and played the same way. Lets say it is 30K.

Since 30K is greater than 20K, it must be more valuable. However you want to calculate $EV doesnt matter, more is always better. Since 30K is better, we need to answer the question,

What would I rather have?

A 53% chance of having 30,000 chips
or
a X% chance of having 20,000 chips

No matter how you think chips turn into $ profit, if X% is not greater than 53%, you will never pick the 20,000 chip option. So, you need a greater than 53% chance, that is a mathematical certainty.

The rest is just how much $value you think the extra 10K in chips has. But it is 50% more chips, so it has to have some pretty significant value, or else you are arguing for passing up some seriously large edges.

[jacksup]

The idea is to compare rewards. So if I pass on the ak/qq spot, the reward is that I'll have a better chance to get to 20k later. I won't necessarily have a better chance to get all my chips in at once. In fact, a lot of players think the main reason to pass on the edge is that they'd rather try to double up by hammering away at small pots.

If I take the ak/qq spot, the reward is that I have a 53.8% chance (or whatever I said the number was) to have 20k right now. 20k right now is worth more than 20k at some point down the road. So Bill Chen had the idea to use something like 21k or 22k as the future stack size in order to account for this difference. There's no way to know what the number should be exactly, but I think anything in the 21k-23k is reasonable. The point is just that if you had, say, a 53.9% to get to 20k at some later time, then you should definitely take the 53.8% shot now, because the chips are worth more if you get them earlier.

Best,
Matt

[A_PLUS]

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The idea is to compare rewards. So if I pass on the ak/qq spot, the reward is that I'll have a better chance to get to 20k later. I won't necessarily have a better chance to get all my chips in at once. In fact, a lot of players think the main reason to pass on the edge is that they'd rather try to double up by hammering away at small pots.

If I take the ak/qq spot, the reward is that I have a 53.8% chance (or whatever I said the number was) to have 20k right now. 20k right now is worth more than 20k at some point down the road. So Bill Chen had the idea to use something like 21k or 22k as the future stack size in order to account for this difference. There's no way to know what the number should be exactly, but I think anything in the 21k-23k is reasonable. The point is just that if you had, say, a 53.9% to get to 20k at some later time, then you should definitely take the 53.8% shot now, because the chips are worth more if you get them earlier.

Best,
Matt

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I think we are saying the same thing, but from different angles. Basically the 2-3K is just a proxy for the value of the number of hands you will have to play to get to 20K, given your skill level.

I am thinking about this graphically, so I may be doing a bad job of putting it into words.

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I've seen players in tournaments of various sizes who rather than avoid the 50/50s (and sometimes even some less favorable odds) actively seek out such situations early in a tournament in an effort to either quickly accumulate chips or bust out and do something else with their time (as opposed to spending several hours to just barely make the money or end up busting out on the bubble b/c of a low chip stack).
Tiffany



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You can't be serious. If that "logic" is true, then the player should take his buy-in to do the whatever is better option , skipping the tournament completely