Horse bankroll?

[Peacedout]

Hi i know how most people suggest 300-500 BB for limit holdem. And 20-30 buyins for NL Holdem. So i was looking around and skimming google for about 20 mins on the proper bankroll for a horse game. So basically my question is what is the proper bank roll for it or is it the same as limit holdem generally?

[Nsight7]

I don't really play HORSE often, so my naive guess would be to take average bankroll requirements across all the disciplines, though safer would be to simply use the game with the largest bankroll requirement and keep that when playing HORSE.

[SellingtheDrama]

its limit, I'd suggest the same buyin as holdem, but be a bit on the conservative side because the stud games have 3 big-bet streets instead of just two in flop games.

Your actual need depends largely on your relative skill level across all five games, and I obviously can't measure that from here.

[pzhon]

[ QUOTE ]
Hi i know how most people suggest 300-500 BB for limit holdem. And 20-30 buyins for NL Holdem.

[/ QUOTE ]
Yes, people recommend those figures. They do so when it is totally inappropriate. They don't notice that those guidelines are inconsistent, usually much more conservative for NL than for limit for typical solid small stakes winners in both games. It's a lot like answering 4:00 whenever anyone asks you for the time in English, and 8:00 whenever anyone asks you for the time in French. Either answer might be close occasionally, but only accidentally, and the answers are inconsistent.

See this post for better guidelines, and some details behind the formula

Bankroll = Comfort * Win Rate / (Standard Deviation^2).

One crucial point which is usually overlooked is that your bankroll requirements depend on your win rate. If you win at twice the rate (say, in a soft game), this cuts your mathematical bankroll requirements in half. That helps to show why it is wrong to say that you need 20 buy-ins in all NL games, as that is close to asserting that your win rate should be the same in a NL $5 game where people are giving money away and cold-calling all-in with ATo, and in tough NL $400 games where half of your opponents are professionals. As you improve at a fixed level, the number of buy-ins you need typically decreases. As you move up in stakes, the number of buy-ins you need for the same level of safety increases rapidly.

How does this apply to a HORSE game? If you know how to play each of the pieces, your can expect a greater win rate than normal when you play stud against Hold'em players and Hold'em against stud players than when you play people in their strengths. That's part of why many good players like mixed games. The mixed formats are entertaining, and make it harder for the losing players to see how much they are outclassed.

In general, when you mix games, your win rate is the average of your win rates for each piece (against those opponents), and your variance per hand (standard deviation^2 per hand, not standard deviation per hand) is the average of your variances per hand for each piece. If you have estimates for each of the pieces, you can estimate your win rate/(standard deviation^2) for the mixed game. For example, suppose you play an equal mixture of game A and game B. If you win $10/100 hands with a standard deviation of $100/100 in game A, and $5/100 hands with a standard deviation of $50/100 in game B, then in the mixed game, your win rate is $7.50/100 ((5+10)/2) and your standard deviation is $79.06/100 (Sqrt((50^2+100^2)/2)). That's more complicated than taking the linear average, but it's much more accurate when you combine games with quite different average pot sizes.

[pzhon]

[ QUOTE ]

Bankroll = Comfort * Win Rate / (Standard Deviation^2).


[/ QUOTE ]
That was supposed to be either

Bankroll = Comfort * (Standard Deviation^2)/Win Rate
or
Comfort = Bankroll * Win Rate / (Standard Deviation^2).

Sorry to anyone who tried to play NL $1000 on a $0.03 bankroll after using the incorrect formula.