These two factors are then put into Kelly’s equation:
Kelly % = W – [(1 – W) / R]

Where:
W = Winning probability
R = Win/loss ratio

To avoid confusion with the formula, it may help if you just use the albionresearch.com/kelly link.

I don’t use edge of winning. If you use the Kelly Criterion you will basically determine how important it is that you bet. If there are 5 people in the pot and you have a 35% chance of winning, you would simply change your pay out. Your win/loss ratio would be risk 1 to get 5 times that amount. If making a bet goes over your kelly you have to seriously consider the impact it will have in the rest of the tournament. In a fast blind structure, you should be willing to take more risks and go beyond kelly (risk more than kelly criterion). In a slow blind structure you should not. In a standard blind structure, early on you should not, then as you accumulate more chips and the antes get involved forcin you to play more hands, you should be willing to go beyond kelly. This is because if you don’t make a move, you will be forced to make a worse one.

I actually have a spreadsheet where I determine how many expected hands I have left based on my skill. This is not the standard “M” as determined by Harrington. This is considering the blind structure and skill level. You have to sort of us excel to consider the blindstructure, speed of play, and number of hands in each blind structure and figure out how many blinds per rotation on average you expect to win and see at what point your number of blinds becomes unmanageble. For some people in some situations under 20 big blinds is “all in or fold” mode. Others it’s not until 9 big blinds, although the amount of blinds won per rotation on average may change. It has to be the right amount for you. This spreadsheet helps me sort of balance the difference beween my kelly criterion and number of hands left to help me make a more informed decision.

formula for calculating the kelly value is:

(2(.6-.4))/1=.4 or 40%

In this example the .6 the same as:

1. 60% chance of winning the pot
2. 60% edge

I have been assuming it is a 60% chance of winning the pot.

——- new question ————-

I calculate my edge by doing the following.

Suppose I determine that I have a 35% chance of winning the pot.

so, then there is a 65% chance I will loose the pot.

If I am playing against 5 players, each of them have a 1/5 of the 65% chance of winning the pot. I.e., each of my opponents has a 13% chance of winning.

This means I have a edge over my opponents of 35% – 13% or an edge of 22%.

Is this a valid way of determining my edge?

This is much more applicable in slow structured tournaments with several entrants as a strategy which makes it deep consistently will result in the player playing for pots at a much bigger size where steals are exponentially more valuable. Managing your chipstack appropriately iearly s the key towards surviving to the rounds in which there is much more implied value in your survival is certainly important.

I’m sure you’d agree with me though that following the kelly criterion in a tournament will allow you to make decisions that prevent you from losing your bankroll, at least in the early stages. Obviously if you put in 100% of your chips and violate the Kelly to the max, your chance of survival is reduced dramatically. But that brings up the question “how valuable is your survival”? And “when is it worth sacrificing value in order to obey the kelly? It depends on how good of player you are and the blind structure, and the stage of the tournament but how would you determine that?

You see tournaments should not be treated as cash games when figuring out individual hands that have positive EV if it risks your tournament life, and that’s not because of the fact that the more chips you earn the less they’re worth (according to ICM)….

Instead it’s because of what I call the “implied skill value”. This is the value that’s implied that you will earn should you not get eliminated from the tournament. By putting your tournament life at risk, you give up some equity in this when you lose. However, you may gain additional “implied skill value” when you win, that may or may not make up for your loss.

Imagine a person’s expected amount of chips throughout a poker tournament is summed up in the following equation

Total chips=S+E1+E2+e3+E4+E5+e6+e7+e8+e9+e10+etc

S=starting stack… Each “E” is the sum of all chips gained at that level on average. e1 is what’s expected to be gained during blind level 1, e2, level 2 etc

Now if you go all in, you not only risk losing what’s in front of you, but also your future edge in the tournament. When you go all in, you also not only gain what’s in the pot to win, but you also gain future expected value as you gain the psychological edge and the ability to outplay opponents and call in situations that had you not doubled up, you may not have had the implied odds to call.

If you’re faced with a decision for all of your chips and you have a 60% edge the CORRECT decision is not JUST a question of “does this decision right now have a positive expected value” The CORRECT decision is “does this decision have a greater positve expected value than not WHEN CONSIDERING all future expected outcomes that result”

IF .6*(r1+r2+r3+r4+r5+r6+r7+r8+r9+r10) – (e1+e2+e3+e4+e5+e6+e7+e8+e9+e10) > .4*( e1+E2+e3+E4+E5+e6+e7+e8+e9+e10) Then call

IF .6*(r1+r2+r3+r4+r5+r6+r7+r8+r9+r10) – (e1+e2+e3+e4+e5+e6+e7+e8+e9+e10) < .4*( e1+E2+e3+E4+E5+e6+e7+e8+e9+e10) Then fold

r1,r2,etc= what you gain or lose in blind level 1,2,etc if you successfully double up)

e1,e2,etc= what you gain or lose in blind level 1,2, etc if you fold

Most math players, even the higher level ones, omit this, simply because it has too many unknown variables. How good of a player are you? How bad are the players around you? Is there anyway you can actually have enough data to come up with a valid conclusion even after playing in hundreds of tournaments against the same players in the same blind structure? Probably not, and plus more total chips isn’t even neccesarily worth additional risk. Consider you’re on the bubble in a flat payout supersattelite where 200 players pay and there’s 199 players left. If you do anything other than the strategy that gives you the highest chance of not being eliminated, you probably are making a huge mistake.

In most cases, If somehow this information was available, I believe good players, particularly good loose aggressive players would find that there survival is often worth more than a 60% edge the very first hand by following the equation mentioned. Therefore I think in the early stages of a tournament with a large field that it is paramount that you value survival, and whenever possible try to obey the kelly criterion. Although this equation above is a better model, the Kelly Criterion even if not ideal is in my opinion a much more applicable strategy to use early on.
That’s not to say that you should fold a hand with positive EV just because you have to violate your Kelly % to call, however, if you call you’ll have to expect more varience, a higher chance of elimination, and ultimately you will have to often a significant amount of implied skill value that you would normally expect to gain in the later stages. By disobeying the Kelly, you decrease your chances of doing so dramtically. So you can justify violating it only if you can make up for that lost edge by using your larger chipstack to increase your implied skill value.

You can do this move where you bet more like 15% of your opponents stacks after you’ve done it for awhile and think they are ready to start calling you with weird hands. Now they might plan to check raise all in, or lead out weak Well, it’s possible that you can move all in on the flop, knowing that you have a huge stack anyways, and really putting your opponents to the test. First you make this move with rags but a read that your opponent is weak, then you make it with high cards, then you make it with a big ace, then you make it with a big hand. And first you’re willing to move in with ANY draw, even a gutshot, then you’re willing to move in with a premium draw, then you need a premium draw with overcards, and then you need either a big hand, or maybe ace king with a backdoor flushdraw and backdoor straight draw. First you start out with any hand requirements, then you tighten them up gradually as you assume your opponents are adjusting. It’s best to do this when you have well over double the average stack , and double the biggest stack at the table. If they catch you, you’re back to even, if you can get away with this a few times (while mixing in small ball), then you can go back to small ball. It confuses them like crazy. Does a big bet mean a big hand? is this guy crazy? should I call hoping to hit with any two cards knowing that this guy has moved all in on the flop so often since I now have the implied odds? Your opponents don’t know if you will push after a small raise, they think you’re a maniac, and of course, in many ways you are, you just have shifted gears, and they have no idea what’s coming next. Of course, any straightflushdraw, or gutshot straightflushdraw, or ace high straight flushdraw you can make a HUGE over shove into a small pot (as well as with a set). This further perpetrates the idea that your opponents should call you with any two, and if they hit,they will win a big pot (or so they thik). While you can, you start betting small, now it especially works if you have a straight flushdraw, and someone checkraises you and you shove and he folds. This means that your opponents only weapon from now on is to play fit or fold (hit or miss_) poker. They will call way too many bets preflop even if you’re betting 3.5-5 timesw the big blind. You gradually want to increase your bets until you settle around 5 times the big blind. Now be mindful of limpers, start to limp behind and play small ball, they’re probably setting a trap. You just can’t let them win. So you play where you take a stab at the pot then shut down. I suggest that the moment you sense people will start calling you down with marginal hands that you shut down and forget the continuation bet. Actualy, even before that moment comes you want to mix things up and stop making the continuation bet on the flop and instead make it on the turn. Maybe overbet the turn though to intice them to slow play monsters. Keep them predictable and tight and passive.
Control how the table plays, give them the idea that they only have one way to beat you, and that’s by picking up a hand. The moment they reraise, fold. The moment they call you shut down. Of course once you fold a couple times the game is likely over, at least unless you can enter the hands a lot less and actually have a hand enough times so you can make another bet and get paid off. You have to play a different game and stay one step ahead. This is very tricky, but possible, and if you can acheive this point, you can often times take control of the table, appear to be absolutely insane, and then suddenly play rational with only overbets with big hands and good draws. Your opponents won’t be able to tell if you are still insane, if you were always insane, if you were only temporarily insane, or if it was all a plan. If they think they have a way to play you and suddenly it fails, they may be inclined to change. They may go from tight postflop to tight preflop. They generally won’t adapt to the raise sizes enough, and it may not matter. Now you migth come in for a minraise and win the blinds, or a 5x raise and get called. Or vise versa. You may get reraised when you raise big, and just called when you raise small. You should be able to control the action. You want to have a slight degree of randomnes. So if they call or raise big bets but fold or call small bets, generally maybe 75% of the time you will bet big with good hands, and small with weak hands. But 25% of the time you reverse it. You will mix up your bets on the flop. Half pot bets, overbets by 1.5potsizes, and underbets and small bets. Mix things up, but then go back to more standard play, and then small ball. If your opponents think you’er random, they’ll just wait and hope the situation comes there way, or they’ll overplay and try to make something happen. Either way this plays right into small ball, which is what you will progress towards using. They think you’re nutty, so now you’ll really get paid off with your big hands. That’s how you control a table. It’s not easy, but if you can pull it off, you can often just continue to dominate.

In that case, i’m going to get called more, but I’m willing to get called becasue I want to fire again on the flop. Now I’m representing JJ, QQ, KK, or AA, and because it’s later on in the tournament against better players, they’re more wiling to believe me. Or I may just check it down if I think I can still win.
Just beware of trappers, and people that may limp raise. You may wish to start this move before hand, but it is also a play where if you have to fold, you’re still in okay shape, but if you win you’re in much better shape.

Consider another bold play. I have 500 in chips 5 players limp in that spot putting 1550 in the pot, or 1200 if it’s before the antes. I’ll bet 2400, effectively committing me all in to any push. Now is 1550 chips worth my tournament life? Perhaps… If I can leverage that steal into more steals that require less risk, and if that move will get me more action later when I have a hand and make that same raise, then yes, that’s weird, but yes. Of course, there’s also nothing wrong with trying to limp a few times. Personally, I prefer aggression late in the tournament, and I feel like I need to climb fast uphill while I can, even if it might mean taking the worst of it. I simply can’t blind down to nothing here. I prefer to make that move sooner when I can continue on the flop, but hey, it’s about time to start being willing to take risk, so why not come up with a big steal and use my tight image wile I can?

Now this is the basic mathematical level.
The advanced level anticipates how opponents will react to you, based on how they have reacted and adapted to other players, and you have to get a feel for their hand range preflop based on you acting in a certain way. If you exploit an opponent too much, he/she will probably adapt, as will the players around you.