Poker Tournament Formula Revisited

[Mason Malmuth]

Hi Bob:

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It would not surprise me if Mason said that despite some of the flaws he finds in this book that he still believes it can help many players' in their tourney play.

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That's exactly what I've said. But the problem is that it frequently has you making the right plays for the wrong reason (in my opinion) and occasionally has you making negative expectation plays such as purchasing an add-on when you have a huge amount of chips relative to the field.

best wishes,
Mason

[Mason Malmuth]

Hi Bob:

The reason I used the example I did was to mimic The Poker Tournament Formula as closely as possible. It just turns out that this is something which I addressed originally in a 1986 issue of Poker Player and you would probably feel more comfortable with the examples used. If you want to see exactly what was written, most of the original work appears in my book Gambling Theory and Other Topics.

Best wishes,
Mason

[Shandrax]

These examples are all interesting, but there are still a couple of things that make me wonder. First of all, where is the break-even point for player A (given he has a 10% advantage)? Second, what sort of advantage does player A need to make Snyder's example work? Last but not least, why doesn't anyone tell Negreanu to stop making these excessive rebuys? At least he should be forced to donate some of his winnings to the American Statistical Association.

[BigAlK]

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...occasionally has you making negative expectation plays such as purchasing an add-on when you have a huge amount of chips relative to the field.

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It's possible that some following this thread might miss this subtle distinction. In the original post Mason mentions 5 conclusions that Snyder comes to based on his coin flipping example. Although it appears that there are other parts of these conclusions he disagrees with to some degree the only item he's addressing here is #1 on the list ("Always rebuy and add on regardless of how many chips you may have") and the disagreement is with the advice to always do this.

I should preface this with the disclaimer that the discussion below is based on my interpretation of what Mason is saying in this thread. If I'm missing the point I'm sure he'll correct me. [img]/images/graemlins/smile.gif[/img]

David Sklansky has a short section in TPFAP on re-buy tournaments. In that he concludes taking the add-on is correct up to a point. The rule of thumb he gives there is to definitely take the add-on if your stack at that point is less than average. He also discusses some situations related to the structure of the add-on that might make taking the add-on correct in his opinion even if your stack is larger than average. (These special situations are when the number of chips in the add-on are significantly larger than the number of chips in the original buy-in or when the add-on is selling chips at a discount).

Mason's example taking into account % payout tournaments demonstrates why there is a point at which the extra equity gained by adding on does not increase your expected pay off enough to off set the cost of the add on. Although this does not refute Snyder's proof that more chips gives you a greater chance of winning the tournament (and isn't intended to) it does show that there is a point at which taking the add on doesn't make sense. Where this point is up for grabs although Mason has clearly shown in his simplified example that this point exists.

If we assume that Sklansky's "rule of thumb" is correct and the add-on is EV+ if you have an average stack then the point where taking the add-on ceases to be correct is no lower than that. There is a stack size large enough that the add-on is EV- although this might be so large in a typical tournament that the chances of anyone building a stack this large in the rebuy period is extremely unlikely. I assume the variables to compute where this point is would be your stack size, the number of chips in play, the field size, and the structure of the payouts. From a practical standpoint computing this at the time you're making the decision probably wouldn't be possible. However doing so away from the table for different situations might be practical to give you a feel for how the various variable interact.

My gut instinct (possibly not based in reality) is the point where taking the add on is not correct is most likely high enough that in almost every situation you're likely to actually encounter taking the add on is the right move. I'll let this idea toss around in my subconcious for a while and see if I can think of a way to substantiate my feeling.

Al

[Mason Malmuth]

Hi Shandrax:

The break even point in this example was first place paying 89 percent of the prize pool.

As for Negreanu, it's correct to rebuy in percentage payback tournaments when you are broke, but wrong when you have a lot of chips. See my book Gambling Theory and Other Topics for more information.

Best wishes,
Mason

[Mason Malmuth]

Hi Al:

I think you have this right. If the tournament was winner take all and you were a superior player then you should always take the add-on and rebuy as soon as you can as Snyder recommends. If the tournament is a typical percentage payback then you should take the add-on unless you are doing very well in the tournament and wait until you go broke to rebuy.

This has significant strategy implications. For instance, automatically playing the first hand in an attempt to lose one chip so that you can rebuy seems like silly advice to me in a percentage payback tournament.

Best wishes,
mason

[trojanrabbit]

I decided to take a closer look at this. Tournament players know that in percentage payback tournaments, every chip is worth less than the chip before it. The question is at what point do you have so many chips that taking an add-on is not worth it?

I started by looking at the coin flipping problem. Imagine a 10-player tournament that pays 50/30/20 to the top 3 spots and where everyone starts with 1 chip. 2 players are selected at random and they flip for 1 chip. I did some simulations and it turns out that a 10% skill advantage is way too high an assumption for this problem. If our skilled player wins coin flips 55% of the time, he wins the tournament 20% of the time. This is much higher than good SNG players can do; a more reasonable number is 14% wins.

So let’s take a skilled player that has a finish distribution in the top 3 spots of 14.0/13.4/12.7%. For a $100 tournament, this equates to an EV of +$35.60 (minus the entry fee). What if he bought twice as many chips and no one else bought any? His finish distribution will be about 24.6/20.3/16.4% for an EV of +$38.37 (minus entry fee) for a gain of $2.77. [img]/images/graemlins/blush.gif[/img] That percentage payback effect is pretty big. Even when everyone has average chips, superior skill barely covers the strong diminishing returns you experience with tournament chips.

What if at the end of the rebuy period he was able to build a stack equal to twice the amount of the other players? Should he now take the additional add-on? By not taking the add on, his finish distribution is still 24.6/20.3/16.4% and his EV is +$138.37. If he takes the add-on, his distribution only improves to 32.8/23.9/16.8% and his EV drops to +$96.23. That add-on costs $42.14 in profit!

Tysen

[excession]

'Let's go back to Snyder's coin flipping model where Player A has a 10 percent playing advantage over Player B, but this time the winner of the tournament gets 60 percent of the prize pool and the loser gets the remaining 40 percent. (I think everyone will agree that this more accurately represents what happens in a poker tournament than the winner take all model.)'

I'm not sure I do agree when we are talkig about rebuy MTT's.

The prize distributon is so heavily weighted in favor of the final table that the 'winner takes all' model (if by 'winning' you mean making the top 1% of the field) may well be better than assuming a HU SNG with a 60/40 split.

Of course neither is perfect - I wouldn't know where to start running EV simulations for a 1000 person MTT with rebuys, but I suspect when working out whether or not to rebuy the winner takes all approach is going to get closer to how a large MTT operates in the first hour with a big field...

Also I think that whoever is taking the maintinable 'edge' from the results of folks who are playing say 10 SnG's at once may be undestimating how much dead money there is in big online MTT's. An edge of 5% doesn't seem that outrageous to me - but that's an argument for another day..

[Crix]

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Hi BigAlK:

Yes. If Player A at some point in a tournament has more chips than Player B then he is a favorite at that instant over Player B. And in your example, Player A does have a 2/3's chance to win the tournament.

best wishes,
Mason

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Surely this is only if A & B are the now the only players remaining at the point A doubles up. If there's 200 people in a tournament, player A doubles up on player C on the first hand you can't tell me he now has a 67% chance to win outright.

[George Rice]

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Hi BigAlK:

Yes. If Player A at some point in a tournament has more chips than Player B then he is a favorite at that instant over Player B. And in your example, Player A does have a 2/3's chance to win the tournament.

best wishes,
Mason

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Surely this is only if A & B are the now the only players remaining at the point A doubles up. If there's 200 people in a tournament, player A doubles up on player C on the first hand you can't tell me he now has a 67% chance to win outright.

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Of course not. The example was for a heads-up situation.