Push or Wait? Analysis of starting hands vs. # hands left ***Repost**

[Pokerscott]

Images failing in this post also. Rehosting images in this post. Original post and commentary here



Many times in the SnG tournament, you will find yourself in a situation where you have to decide if you should push all in with this hand or wait for a better spot.

Lots of factors go into this decision (blinds, position, etc). One factor that I haven't seen much information on is what type of hand can I expect if I wait? It clearly depends on the number of hands you can afford to wait, so I wanted to address this question.

Methodology:

In order to address this question you have to make two decisions up front. First, how are you going to measure hand strength? Second, how are you going to summarize the possible strength of the hands you may get in the future?

In terms of evaluating hand strength, I used the data from here to rate the strength of the various hands. I did the analysis using the 2-handed strength ratings and the 4-handed strength ratings. I'm not sure which is best to apply to the push or wait question. Likely there are 4+ hands left, which argues for the 4-way. However, you are only going to be generally facing one opponent who calls, argueing for the 2-way. I personally think the 2-way is more correct, but the information is there if you feel otherwise...

In terms of summarizing the future hands, I decided to report the median best hand you could expect given N hands remaining.

How can you calculate median best hand given N hands remaining?

Imagine the all the possible hands ordered by hand strength. For each hand you also know the probability of getting that type of hand (e.g. AJs is 0.3%). If you draw a random number from a uniform [0,1] distribution, you can then map it to your ordered list of hands to determine a particular hand associated with that random number. If you want to figure out the best hand given two remaining hands, choose two uniform [0,1] random numbers and take the minimum. For N hands, choose N random numbers and take the minimum. (I choose the minimum instead of the maximum simply because the hands are ordered starting with the best first. Low percentiles correspond to better and better hands)

At this point, you basically have one possibility in terms of best hand given N future hands. If you want to know the median best hand given N future hands, you simply repeat the process thousands of times and take the median result. I did it 100k times to generate the table below (and yes I know the answer for 1 hand should be 50% [img]/images/graemlins/smile.gif[/img] )

Here is the table that summarizes the results:



How to read this table:

# hands left:
-This is the number of hands you are going to get to look at if you fold your current hand (e.g. if the big blind crushes you in 3 hands, you might want to look at the 3 or maybe the 2 row...)

Median 'Best-Hand' Strength Percentile:
-This is the result of the analysis reported in percentile. For example, if you have seven hands to go, the median 'best-hand' you can expect over those seven hands will be a hand strength percentile of 9.4%. Half the time your best hand will be better than the 9.4 percentile and half the time it will be worse.

Implied Hand (2-way rank)
Now that you know the hand strength percentile you can expect with 7 hands left, all you have to do is figure out the right ordering of hand strengths. If you think 2-way rank is right, then the hand that corresponds to the 9.4 percentile is an ATo.

Implied Hand (4-way rank)
Same information as the 2-way ranking except hands are ranked assuming 4 hands start and go all the way to the river. For the 4-way rank, the 9.4 percentile hand is pocket 7s.

Let me know if you have questions or think a tweak to this analysis would be a lot more helpful.

Cheers,

Pokerscott

[Scuba Chuck]

Great analysis. I appreciate the work very much. Someone told me once that you can expect a "playable" hand, in terms of bubble scenario, about once every 10 hands. It looks like your work supports that thought.

[johnnybeef]

[ QUOTE ]
Great analysis. I appreciate the work very much. Someone told me once that you can expect a "playable" hand, in terms of bubble scenario, about once every 10 hands. It looks like your work supports that thought.

[/ QUOTE ]

as im in a bit of a downswing and rigourously reviewing my play, i was curious, scuba, what you thought was a playable bubble hand.

[stlip]

Thanks, and you prettied up the chart a bit, too.

Now I have a print out sitting nearby for whenever I play.

[TylerD]

Nice, thanks for that.

[psparkyuk]

Very interesting post - thank-you.

I think there is a minor typo in the table. For 3 hands/4 way I think it should be A3s not A3o.

Regarding the 2-way/4-way issue, I have always thought this sort of question depends on position. If you are UTG then 4-way should apply, because even though you expect to end up HU, you will be against the BEST of the other 3 (at least in principle). If you are SB after 2 folds then I think using 2-way analysis is OK. I would be interested in your thoughts on that.

Finally, when you have a marginal decision, such as K5o with one hand to come where the table would say play, I think it might be better to wait. This is because the probability of winning with the top 10-15% hands rises sharply on an overwise fairly even distribution. Thus your average probability of winning might go up even though your average hand ranking will go down. Hope that makes sense.

Cheers, Psparky

[Pokerscott]

[ QUOTE ]

Regarding the 2-way/4-way issue, I have always thought this sort of question depends on position. If you are UTG then 4-way should apply, because even though you expect to end up HU, you will be against the BEST of the other 3 (at least in principle). If you are SB after 2 folds then I think using 2-way analysis is OK. I would be interested in your thoughts on that.


[/ QUOTE ]

I agree with you that you are usually playing the best of four hands remaining, but that is not the same as the four-way hand ranks. Four-way hand rank assumes all four hands make it to the river. This is different from picking the best of the other hands and then playing yours and the best hand to the river.

The 4 way over weights the value of suits/straights vs high cards, but the 2 way doesn't capture the 'playing the best of 4' either. That is why I reported both [img]/images/graemlins/smile.gif[/img]

[ QUOTE ]



Finally, when you have a marginal decision, such as K5o with one hand to come where the table would say play, I think it might be better to wait. This is because the probability of winning with the top 10-15% hands rises sharply on an overwise fairly even distribution. Thus your average probability of winning might go up even though your average hand ranking will go down. Hope that makes sense.


[/ QUOTE ]

I think this table is only one piece of information on the push or wait decision. Position, blinds increasing, stack sizes, etc. all play a big role.

I'm not exactly sure I understand your point. However, if I had to push k5o or a random hand next, I would definitely push the K5o. The random hand is likely worse AND you will have another person acting behind you when you push the random hand next.

Pokerscott

[lastchance]

I find these more useful:
Karlson-Sklansky hand rankings eastbay against ranges of hands